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CPLEX 12

# Introduction

GAMS/Cplex is a GAMS solver that allows users to combine the high level modeling capabilities of GAMS with the power of Cplex optimizers. Cplex optimizers are designed to solve large, difficult problems quickly and with minimal user intervention. Access is provided (subject to proper licensing) to Cplex solution algorithms for linear, quadratically constrained and mixed integer programming problems. While numerous solving options are available, GAMS/Cplex automatically calculates and sets most options at the best values for specific problems.

All Cplex options available through GAMS/Cplex are summarized at the end of this document.

# How to Run a Model with Cplex

The following statement can be used inside your GAMS program to specify using Cplex

   Option LP = Cplex;     { or QCP, MIP, MIQCP, RMIP or RMIQCP }


The above statement should appear before the Solve statement. If Cplex was specified as the default solver during GAMS installation, the above statement is not necessary.

There are two Cplex links in the GAMS system: GAMS/Cplex and GAMS/CplexD. The CplexD solver link lack some functionality available in the Cplex link (e.g. sensitivity analysis for linear programs, support for SOS variables), but CplexD offers a few facility of interest to a small community:

• handles quadratically constraint models better than the production link. Some SOCP models are reformulated in the production link so that Cplex rejects these models while CplexD solves them nicely. Moreover, CplexD provides duals for this problem type.
• provides hot start capability in GUSS
• allows solving multiple instances of GAMSModelInstance in parallel using the high-level GAMS API
• supports remote solves via the Cplex Remote Object
• supports Cplex' distributed MIP algorithm
• allows to free some additional memory via the option FreeGamsModel which is benefitial if memory is tight Unless you have need for these features it is recommended to use Cplex not CplexD. In the near future the two links will be merged.

Finally, a bare-bone interface to the LP and MIP solver of Cplex is available under the name OSICPLEX. It comes free of charge with any GAMS system.

# Overview of Cplex

## Linear Programming

Cplex solves LP problems using several alternative algorithms. The majority of LP problems solve best using Cplex's state of the art dual simplex algorithm. Certain types of problems benefit from using the primal simplex algorithm, the network optimizer, the barrier algorithm, or the sifting algorithm. The concurrent option will allow solving with different algorithms in parallel. The solution is returned by the first to finish.

Solving linear programming problems is memory intensive. Even though Cplex manages memory very efficiently, insufficient physical memory is one of the most common problems when running large LPs. When memory is limited, Cplex will automatically make adjustments which may negatively impact performance. If you are working with large models, study the section entitled Physical Memory Limitations carefully.

Cplex is designed to solve the majority of LP problems using default option settings. These settings usually provide the best overall problem optimization speed and reliability. However, there are occasionally reasons for changing option settings to improve performance, avoid numerical difficulties, control optimization run duration, or control output options.

Some problems solve faster with the primal simplex algorithm rather than the default dual simplex algorithm. Very few problems exhibit poor numerical performance in both the primal and the dual. Therefore, consider trying primal simplex if numerical problems occur while using dual simplex.

Cplex has a very efficient algorithm for network models. Network constraints have the following property:

• each non-zero coefficient is either a +1 or a -1
• each column appearing in these constraints has > exactly 2 nonzero entries, one with a +1 > coefficient and one with a -1 coefficient

Cplex can also automatically extract networks that do not adhere to the above conventions as long as they can be transformed to have those properties.

The barrier algorithm is an alternative to the simplex method for solving linear programs. It employs a primal-dual logarithmic barrier algorithm which generates a sequence of strictly positive primal and dual solutions. Specifying the barrier algorithm may be advantageous for large, sparse problems.

Cplex provides a sifting algorithm which can be effective on problems with many more variables than equations. Sifting solves a sequence of LP subproblems where the results from one subproblem are used to select columns from the original model for inclusion in the next subproblem.

GAMS/Cplex also provides access to the Cplex Infeasibility Finder. The Infeasibility finder takes an infeasible linear program and produces an irreducibly inconsistent set of constraints (IIS). An IIS is a set of constraints and variable bounds which is infeasible but becomes feasible if any one member of the set is dropped. GAMS/Cplex reports the IIS in terms of GAMS equation and variable names and includes the IIS report as part of the normal solution listing. IIS is available for LP problems only.

Cplex can solve models with quadratic constraints. These are formulated in GAMS as models of type QCP. QCP models are solved with the Cplex Barrier method.

QP models are a special case that can be reformulated to have a quadratic objective function and only linear constraints. Those are automatically reformulated from GAMS QCP models. When such problems are convex, Cplex normally solves them efficiently in polynomial time. Nonconvex QPs, however, are known to be quite hard. Cplex applies various approaches to those problems, such approaches as barrier algorithms or branch and bound algorithms. Notably, in the branch and bound approach, there is no theoretical guarantee about the complexity of such a problem. Consequently, solution of such a problem (that is, a nonconvex QP) can take many orders of magnitude longer than the solution of a convex QP of comparable dimensions. Therefore, the default is to reject such model. The parameter OptimalityTarget allows to change this behavior.

For QCP models Cplex returns a primal only solution to GAMS. CplexD provides in most cases also dual values.

## Mixed-Integer Programming

The methods used to solve pure integer and mixed integer programming problems require dramatically more mathematical computation than those for similarly sized pure linear programs. Many relatively small integer programming models take enormous amounts of time to solve.

For problems with integer variables, Cplex uses a branch and cut algorithm which solves a series of LP, subproblems. Because a single mixed integer problem generates many subproblems,even small mixed integer problems can be very compute intensive and require significant amounts of physical memory.

GAMS and GAMS/Cplex support Special Order Sets of type 1 and type 2 as well as semi-continuous and semi-integer variables.

Cplex can also solve problems of GAMS model type MIQCP. As in the continuous case, if the base model is a QP the Simplex methods can be used and duals will be available at the solution. If the base model is a QCP, only the Barrier method can be used for the nodes and only primal values will be available at the solution.

## Feasible Relaxation

The Infeasibility Finder identifies the causes of infeasibility by means of inconsistent set of constraints (IIS). However, you may want to go beyond diagnosis to perform automatic correction of your model and then proceed with delivering a solution. One approach for doing so is to build your model with explicit slack variables and other modeling constructs, so that an infeasible outcome is never a possibility. An automated approach offered in GAMS/Cplex is known as FeasOpt (for Feasible Optimization) and turned on by parameter FeasOpt in a CPLEX option file. More details can be found in the section entitled Using the Feasibility Relaxation.

## Solution Pool: Generating and Keeping Multiple Solutions

This section introduces thesolution pool for storing multiple solutions to a mixed integer programming problem (MIP and MIQCP). The chapter also explains techniques for generating and managing those solutions.

The solution pool stores multiple solutions to a mixed integer programming (MIP and MIQCP) model. With this feature, you can direct the algorithm to generate multiple solutions in addition to the optimal solution. For example, some constraints may be difficult to formulate efficiently as linear expressions, or the objective may be difficult to quantify exactly. In such cases, obtaining multiple solutions will help you choose one which best fits all your criteria,including the criteria that could not be expressed easily in a conventional MIP or MIQCP model. For example,

• You can collect solutions within a given percentage of the optimal solution. To do so, apply the solution pool gap parameters SolnPoolAGap and SolnPoolGap.
• You can collect a set of diverse solutions. To do so, use the solution pool replacement parameter SolnPoolReplace to set the solution pool replacement strategy to 2. In order to control the diversity of solutions even more finely, apply a diversity filter.
• In an advanced application of this feature, you can collect solutions with specific properties. To do so, see the use of the incumbent filter.
• You can collect all solutions or all optimal solutions to model. To do so, set the solution pool intensity parameter SolnPoolIntensity to its highest value.

Please note, that the value for best possible can exceed the optimal solution value if CPLEX has already solved the model to optimality but continues to search for additional solutions.

### Filling the Solution Pool

There are two ways to fill the solution pool associated with a model: You can accumulate successive incumbents or generate alternative solutions by populating the solution pool. The method is selected with the parameter SolnPoolPop:

• The regular optimization procedure automatically adds incumbents to the solution pool as they are discovered (SolnPoolPop = 1).
• Cplex also provides a procedure specifically to generate multiple solutions. You can invoke this procedure by setting option SolnPoolPop = 2. You can also invoke this procedure many times in a row in order to explore the solution space differently. In particular, you may invoke this procedure multiple times to find additional solutions, especially if the first solutions found are not satisfactory. This is done by specifying a GAMS program (option SolnPoolPopRepeat) that inspects the solutions. In case this GAMS program terminates normally, i.e. no execution or compilation error, the exploration for alternative solutions proceeds.

The option SolnPoolReplace designates the strategy for replacing a solution in the solution pool when the solution pool has reached its capacity. The value 0 replaces solutions according to a first-in, first-out policy. The value 1 keeps the solutions with the best objective values. The value 2 replaces solutions in order to build a set of diverse solutions.

If the solutions you obtain are too similar to each other, try setting SolnPoolReplace to 2.

The replacement strategy applies only to the subset of solutions created in the current call of populate. Solutions already in the pool are not affected by the replacement strategy. They will not be replaced, even if they satisfy the criterion of the replacement strategy. So with every repeated call of the populate procedure the solution pool will be extended by the newly found solution. After the GAMS program specified in SolnPoolPopRepeat determined to continue the search for alternative solutions, the file specified by option SolnPoolPopDel option is read in. The solution numbers present in this file will be delete from the solution pool before the populate routine is called again. The file is automatically deleted by the GAMS/Cplex link after processing.

### Enumerating All Solutions

With the solution pool, you can collect all solutions to a model. To do so, set the solution pool intensity parameter SolnPoolIntensity to its highest value, 4 and set SolnPoolPop = 2.

You can also enumerate all solutions that are valid for a specific criterion. For example, if you want to enumerate all alternative optimal solutions, do the following:

• Set the pool absolute gap parameter SolnPoolAGap = 0.0.
• Set the pool intensity parameter SolnPoolIntensity = 4.
• Set the populate limit parameter PopulateLim to a value sufficiently large for your model; for example, 2100000000.
• Set the pool population parameter SolnPoolPop = 2.

Beware, however, that, even for small models, the number of possible solutions is likely to be huge. Consequently, enumerating all of them will take time and consume a large quantity of memory.

There may be an infinite number of possible values for a continuous variable, and it is not practical to enumerate all of them on a finite-precision computer. Therefore, populate gives only one solution for each set of binary and integer variables, even though there may exist several solutions that have the same values for all binary and integer variables but different values for continuous variables.

Likewise, for the same reason, the populate procedure does not generate all possible solutions for unbounded models. As soon as the proof of unboundedness is obtained, the populate procedure stops.

Cplex uses numerical methods of finite-precision arithmetic. Consequently, the feasibility of a solution depends on the value given to tolerances. Two parameters define the tolerances that assess the feasibility of a solution:

• the integrality tolerance EpInt
• the feasibility tolerance EpRHS

A solution may be considered feasible for one pair of values for these two parameters, and infeasible for a different pair. This phenomenon is especially noticeable in models with numeric difficulties, for example, in models with BigM coefficients.

Since the definition of a feasible solution is subject to tolerances, the total number of solutions to a model may vary, depending on the approach used to enumerate solutions, and on precisely which tolerances are used. In most models, this tolerance issue is not problematic. But, in the presence of numeric difficulties, Cplex may create solutions that are slightly infeasible or integer infeasible, and therefore create more solutions than expected.

### Filtering the Solution Pool

Filtering allows you to control properties of the solutions generated and stored in the solution pool. Cplex provides two predefined ways to filter solutions.

If you want to filter solutions based on their difference as compared to a reference solution, use a diversity filter. This filter is practical for most purposes. However, if you require finer control of which solutions to keep and which to eliminate, use the incumbent filter.

### Diversity Filter

A diversity filter allows you to generate solutions that are similar to (or different from) a set of reference values that you specify for a set of binary variables using dot option DivFlt and lower and upper bounds DivFltLo and DivFltUp. In particular, you can use a diversity filter to generate more solutions that are similar to an existing solution or to an existing partial solution. If you need more than one diversity filter, for example, to generate solutions that share the characteristics of several different solutions, additional filters can be specified through a Cplex Filter File using parameter ReadFLT. Details can be found in the example model solnpool in the GAMS model library.

### Incumbent Filter

If you need to enforce more complex constraints on solutions (e.g. if you need to enforce nonlinear constraints), you can use the incumbent filtering. The incumbent checking routine is part of the GAMS BCH Facility. It will accept or reject incumbents independent of a solution pool. During the populate or regular optimize procedure, the incumbent checking routine specified by the parameter UserIncbCall is called each time a new solution is found, even if the new solution does not improve the objective value of the incumbent. The incumbent filter allows your application to accept or reject the new solution based on your own criteria. If the GAMS program specified by UserIncbCall terminates normally, the solution is rejected. If this program returns with a compilation or execution error, the incumbent is accepted.

### Accessing the Solution Pool

The solutions are stored in GAMS Data eXchange (GDX) file and can be loaded by your GAMS program. Details can be found in the model solnpool in the GAMS model library and in . If you instruct Cplex to generate thousands of solution this becomes inefficient. The option SolnPoolMerge triggers the creation of a single GDX file containing all solutions.

The GAMS/Cplex link produces, if properly instructed, a GAMS Data eXchange(GDX) file with name specified in SolnPool that contains a set Index with elements file1, file2, ... The associated text of these elements contain the file names of the individual GDX solution file. The name is constructed using the prefix soln (which can be specified differently by option SolnPoolPrefix), the name of the model and a sequence number. For example soln_loc_p1.gdx. GAMS/Cplex will overwrite existing GDX files without warning. The set Index allows us to conveniently walk through the different solutions in the solution pool. A complete model can be found in the model solnpool in the GAMS model library.

...
solve mymodel min z using mip;

set soln           possible solutions in the solution pool /file1*file1000/
solnpool(soln) actual solutions;
file fsol;

loop(solnpool(soln),
put_utility fsol 'gdxin' / solnpool.te(soln):0:0;
display z.l;
);


If you instruct Cplex to generate thousands of solution this method becomes inefficient. The option SolnPoolMerge triggers the creation of a single GDX file containing all solutions. Details on usage of this option can be found in the model solmpool in the GAMS model library.

## Cplex Remote Object Server and Distributed MIP

The Cplex Remote Object Server allows you to use a server to offload all of your Cplex computations.

Cplex Remote Object Server licenses and software are not included in GAMS/Cplex. Contact suppo.nosp@m.rt@g.nosp@m.ams.c.nosp@m.om to inquire about the software and license. You can specify the server with the ComputeServer option.

Cplex also supports solving a single MIP instance utilizing multiple machines in a distributed fashion. The feature is know as Distributed MIP and builds on top of the Cplex Remote Object Server. This section describes the setup steps necessary to enable this feature. First there is some background information about CPLEX Distributed MIP.

### Solving a distributed MIP in parallel

CPLEX offers more support for the solution in parallel of mixed integer programs (MIPs) in a distributed computing environment. This feature, known as distributed parallel MIP optimization, is a mode of running CPLEX that harnesses the power of multiple computers or of multiple nodes inside a single computer to achieve better performance on some MIP problems.

Distributed parallel MIP optimization operates in two phases: first, a ramp-up phase, in which each worker applies different parameter settings to the same problem as the other workers; then, in the remainder of the solve (the second phase), each worker works in one part of a common MIP tree. Each worker communicates what it finds to the (unique) master node, which acts as the conductor or coordinator for the whole process.

Distributed MIP is based on the CPLEX remote object for distributed parallel optimization.

Distributed parallel mixed integer programming uses a variation of the well known branch and bound algorithm to solve a MIP in parallel. In contrast to conventional branch and bound implemented on platforms with shared memory, distributed parallel MIP implements a branch and bound algorithm in an environment of distributed memory, possibly across multiple machines. The implementation can use more than a single machine to solve a given MIP, thus making it possible to solve more difficult problems than a shared memory on a single machine could solve.

### Distributed optimization of MIPs: The Algorithm

This topic outlines an algorithm that implements a variation of branch and bound suitable for application across multiple machines (or multiple nodes of a single machine) to solve a difficult mixed integer program (MIP) in parallel.

This distributed parallel MIP algorithm runs on a single master associated with multiple workers. The master and the workers can be physical or virtual machines. Indeed, in this context, a virtual machine may simply be a process in the operating system of a machine. Throughout the runtime of this algorithm, the master coordinates the workers, and the workers perform the heavy lifting (that is, the actual solving of the MIP).

The algorithm begins by presolving the MIP on the master. After presolving, the algorithm sends the reduced model to each of the workers.

Each of the workers then starts to solve the reduced model. Each worker has its own parameter settings, possibly different from the parameter settings of other workers. Each worker solves the reduced model with its own parameter settings for a limited period of time. This phase is known as ramp up. During ramp up, each worker conducts its own search, according to its own parameter settings. Ramp up stops when the master concludes that at least one of the workers has created a sufficiently large search tree.

At that point, when ramp up stops, the master decides which of the workers performed best. In other words, the master selects a winner. The parameter settings used by the winning worker during ramp up are the basis for the master to determine which parameter settings to use in the ensuing distributed branch and bound search.

The search tree on each of the non-winning workers is deleted. The search tree of the winning worker is distributed over all workers, so that authentic distributed parallel branch and bound starts from this point. In other words, all workers now work on the same search tree, with the master coordinating the search in the distributed tree.

### Search tree

Distributed parallel branch and bound is similar to conventional, shared-memory branch and bound. They differ greatly, however, in their management of the search tree. In a conventional, shared-memory branch and bound, the search tree resides on a single machine, on disk or in shared memory. In contrast, distributed parallel branch and bound literally distributes the search tree across a cluster of machines.

In the CPLEX implementation of distributed parallel branch and bound, the master keeps a number of nodes of the global search tree. If a worker becomes idle, the master sends some of those nodes to that worker. The worker then starts branch and bound on those nodes. However, the worker does not simply solve a node, create some new nodes in doing so, and send them all back to the master. Instead, the worker considers the search tree node received from the master as a new MIP. The worker presolves that MIP and finds an optimal solution for that node using branch and bound. In other words, a worker not only solves a single node; in fact, the worker solves an entire subtree rooted at that node.

While this distributed parallel branch and bound algorithm is running, the master can ask a worker to provide some open nodes (that is, unsolved nodes). The master can then use these nodes to assign work to idle workers. To satisfy such a request from the master, a worker picks a few open nodes from its current tree. Because the current tree in a worker is a subtree of the global tree (indeed, it is the subtree rooted at the node sent to the worker), every node in that subtree is also a node in the global tree.

### Stopping criterion

The distributed parallel branch and bound algorithm stops if all the nodes of the global search tree have been processed or if it reaches a limit set by the user. Such limits include a time limit, a limit on the number of nodes processed, a limit on the number of solutions found, or other similar criteria.

### Using TCP/IP as the transport protocol with distributed parallel MIP

While Cplex has multiple transport protocols (e.g. MPI) GAMS/CPLEXD uses exclusively the TCP/IP transport protocol. In order to use the distributed MIP facility you need the additional software package from GAMS (contact suppo.nosp@m.rt@g.nosp@m.ams.c.nosp@m.om). Moreover you need a set of machines that act as workers. Upload the software (provided as a ZIP archive) to these machines. On each work machine create a directory and unzip the ZIP file in this directory:

   mkdir c:\tmp\gamscplexdistmip
cd c:\tmp\gamscplexdistmip
unzip from\some\where\windows_x86_32_cpxdistmip.zip


Find out the worker IP address, e.g. via ipconfig (on Windows based systems) and start the Cplex worker process:

   cplex -worker=tcpip -libpath=c:\tmp\gamscplexdistmip -address=myip:myport


where myip is the name of the host or its IP address and myport is the number of the port where the worker will listen for incoming connections. (You are free to choose a different port number here.

This command starts a TCP/IP server to wait for connections from the master. The TCP/IP server also spawns worker processes as requested. The server does not terminate itself, however. You must explicitly terminate it; for example, by pressing CTRL-C when your optimization completes.

On the master machine with a regular GAMS installation create a cplexd.opt file with the following content specifying the IP addresses or names and ports of the workers:

   computeserver myip1:myport1 myip2:myport2 ...


The host names and the port numbers must be the same in the CplexD option file as those used to start the TCP/IP worker on the corresponding host. Please note, that when you specify a single machine, one gets the Cplex Remote Object solving sequentially on a remote machine instead of a distributed MIP run.

Run GAMS solving a mixed integer model with CplexD and the option reading enabled.

The log of such a run will look as follows (please observe the mentioning of Starting ramp-up

   --- Generating MIP model william
--- magic.gms(81) 4 Mb
---   56 rows  46 columns  181 non-zeroes
---   15 discrete-columns
--- Executing CPLEXD: elapsed 0:00:00.019

IBM ILOG CPLEX   24.2.0 ....

>>  computeserver 192.168.178.37:12345 192.168.178.24
--- GMO memory 0.51 Mb (peak 0.51 Mb)
--- Dictionary memory 0.00 Mb
--- Cplex 12.6.0.0 link memory 0.00 Mb (peak 0.01 Mb)
--- Starting Cplex...

Tried aggregator 1 time.
MIP Presolve eliminated 0 rows and 1 columns.
MIP Presolve modified 6 coefficients.
Reduced MIP has 55 rows, 45 columns, and 135 nonzeros.
Reduced MIP has 0 binaries, 15 generals, 0 SOSs, and 0 indicators.
Presolve time = 0.02 sec. (0.06 ticks)
Running distributed MIP on 2 solvers.
Setting up 2 distributed solvers.
Setup time = 0.00 sec. (0.00 ticks)
Starting ramp-up.

Found incumbent of value 2942400.000000 after 0.00 sec. (0.01 ticks)
MIP emphasis: balance optimality and feasibility.
MIP search method: dynamic search.
Parallel mode: none, using 1 thread.
Root relaxation solution time = 0.00 sec. (0.09 ticks)

Nodes                                         Cuts/
Node  Left     Objective  IInf  Best Integer    Best Bound    ItCnt     Gap

*     0+    0                      2942400.0000  -313500.0000       28  110.65%
Found incumbent of value 2942400.000000 after 0.00 sec. (0.26 ticks)
0     0   985514.2857     7  2942400.0000   985514.2857       28   66.51%
*     0+    0                       991970.0000   985514.2857       28    0.65%
Found incumbent of value 991970.000000 after 0.00 sec. (0.33 ticks)
*     0     0      integral     0   988540.0000       Cuts: 8       31    0.00%
Found incumbent of value 988540.000000 after 0.00 sec. (0.54 ticks)
0     0        cutoff         988540.0000   988540.0000       31    0.00%
Elapsed time = 0.00 sec. (0.54 ticks, tree = 0.01 MB, solutions = 3)

Mixed integer rounding cuts applied:  3
Gomory fractional cuts applied:  4

Root node processing (before b&c):
Real time             =    0.00 sec. (0.54 ticks)
Sequential b&c:
Real time             =    0.00 sec. (0.00 ticks)
------------
Total (root+branch&cut) =    0.00 sec. (0.54 ticks)
in callback

Ramp-up finished (winner: 1).
Ramp-up time = 0.50 sec. (0.54 ticks)
MIP status(101): integer optimal solution.
Cplex Time: 4.20sec (det. 0.61 ticks)

Fixing integer variables, and solving final LP...
Tried aggregator 1 time.
LP Presolve eliminated 54 rows and 44 columns.
Reduced LP has 1 rows, 2 columns, and 2 nonzeros.
Presolve time = 0.00 sec. (0.02 ticks)

Iteration log . . .
Iteration:     1   Dual objective     =        988540.000000
Fixed  MIP status(1): optimal.
Cplex Time: 0.00sec (det. 0.04 ticks)

Proven optimal solution.

MIP Solution:       988540.000000    (30 iterations, 0 nodes)
Final Solve:        988540.000000    (1 iterations)

Best possible:      988540.000000
Absolute gap:            0.000000
Relative gap:            0.000000


### Parameters for Distributed MIP

There are a few parameters that effect the distributed MIP. The following parameters (only applicable in CplexD) enable you to customize this ramp-up phase for your model.

• To set the duration of the ramp-up phase, use the ramp up duration parameter, RampupDuration.
• To set a deterministic time limit on the ramp-up phase, use the deterministic time spent in ramp up during distributed parallel optimization parameter, RampupDetTimeLimit
• To set a wall-clock time limit in seconds on the ramp-up phase, use the time spent in ramp up during distributed parallel optimization parameter, RampupTimeLimit.

## Benders Algorithm

CPLEX implements Benders algorithm.

Given a formulation of a problem, CPLEX can decompose the model into a single master and (possibly multiple) subproblems. To do so, CPLEX makes use of annotations that you supply for your model. This approach can be applied to mixed-integer linear programs (MILP). For certain types of problems, this approach can offer significant performance improvements.

The parameter, BendersStrategy, specifies to CPLEX how you want to apply Benders algorithm as a strategy to solve your model. By default, if you did not annotate your model to specify a decomposition, CPLEX executes conventional branch and bound. If you annotated your model, CPLEX attempts to refine your decomposition and applies Benders algorithm. With this parameter, you can direct CPLEX to decompose your model and to apply its implementation of Benders algorithm in one of these alternative ways:

• 1: CPLEX attempts to decompose your model strictly according to your annotations.
• 2: CPLEX decomposes your model by using your annotations as hints and refining the decomposition where it can. CPLEX initially decomposes your model according to your annotation and then attempts to refine that decomposition by further decomposing the specified subproblems. This approach can be useful if you annotate certain variables to go into master, and all others to go into a single subproblem, which CPLEX can then decompose further for you.
• 3: CPLEX automatically decomposes your model, ignoring any annotations you may have supplied. CPLEX puts all integer variables into the master, puts all continuous variables into a subproblem and ecomposes that subproblem, if possible.

If you want to specify a decomposition to CPLEX, you need to annotate your model and specify a Benders partition of your variable space. These Benders partition can be conveniently specified with the dot option BendersPartition.

These Benders partition values specify to CPLEX whether certain variables belong to the master or to one of the subproblems assigned to workers (where the subproblems are numbered from 1 (one) to N, the number of subproblems). If you annotate a given variable with the value 0 (zero), CPLEX assigns that variable to the master. If you annotate a given variable with the value i, where i is greater than or equal to 1 (one), CPLEX assigns that variable to subproblem i. If a variable is not specified, the default will be to go into the master problem. Note that with variable.BendersPartition 1 you can assign all variables to the subproblem and then selectively assign the master variables with varname.BenderPartition 1.

CPLEX also produces an error if the annotated decomposition does not yield disjoint subproblems. For example, if your annotations specify that two (or more) variables belong in different subproblems, yet your model specifies that these variables participate in the same constraint, then these variables are linked. Consequently, the subproblems where these variables appear according to your annotations are not disjoint with respect to the partition.

# GAMS Options

The following GAMS options are used by GAMS/Cplex:

• Option BRatio = x;

Determines whether or not to use an advanced basis. A value of 1.0 causes GAMS to instruct Cplex not to use an advanced basis. A value of 0.0 causes GAMS to construct a basis from whatever information is available. The default value of 0.25 will nearly always cause GAMS to pass along an advanced basis if a solve statement has previously been executed.

• Option IterLim = n;

Sets the simplex iteration limit. Simplex algorithms will terminate and pass on the current solution to GAMS.

Cplex handles the iteration limit for MIP problems differently than some other GAMS solvers. The iteration limit is applied per node instead of as a total over all nodes. For MIP problems, controlling the length of the solution run by limiting the execution time (ResLim) is preferable.

Simlarly, when using the sifting algorithm, the iteration limit is applied per sifting iteration (ie per LP). The number of sifting iterations (LPs) can be limited by setting Cplex parameter SiftItLim. It is the number of sifting iterations that is reported back to GAMS as iterations used.

• Option ResLim = x;

Sets the time limit in seconds. The algorithm will terminate and pass on the current solution to GAMS.

• Option SysOut = On;

Will echo Cplex messages to the GAMS listing file. This option may be useful in case of a solver failure.

• ModelName.Cheat = x;

Cheat value: each new integer solution must be at least x better than the previous one. Can speed up the search, but you may miss the optimal solution. The cheat parameter is specified in absolute terms (like the OptCA option). The Cplex option ObjDif overrides the GAMS cheat parameter.

• ModelName.Cutoff = x;

Cutoff value. When the branch and bound search starts, the parts of the tree with an objective worse than x are deleted. This can sometimes speed up the initial phase of the branch and bound algorithm.

• ModelName.NodLim = x;

Maximum number of nodes to process for a MIP problem.

Option OptCA = x;

Absolute optimality criterion for a MIP problem. The OptCA option asks Cplex to stop when

\begin{equation*} |BP - BF| < \mbox{OptCA} \end{equation*}

where $$BF$$ is the objective function value of the current best integer solution while $$BP$$ is the best possible integer solution.

• ModelName.OptCR = x;

Relative optimality criterion for a MIP problem. Notice that Cplex uses a different definition than GAMS normally uses. The OptCR option asks Cplex to stop when

\begin{equation*} (|BP - BF|)/(1.0e-10 + |BF|) <\mbox{OptCR} \end{equation*}

where BF is the objective function value of the current best integer solution while BP is the best possible integer solution. The GAMS definition is:

\begin{equation*} (|BP - BF|)/(|BP|) <\mbox{OptCR} \end{equation*}

• ModelName.OptFile= 1;

Instructs Cplex to read the option file. The name of the option file is cplex.opt.

• ModelName.PriorOpt= 1;

Instructs Cplex to use priority branching information passed by GAMS through the variable.prior parameters.

• ModelName.TryInt= x;

Causes GAMS/Cplex to make use of current variable values when solving a MIP problem. If a variable value is within x of a bound, it will be moved to the bound and the preferred branching direction for that variable will be set toward the bound. The preferred branching direction will only be effective when priorities are used. Priorities and tryint are sometimes not very effective and often outperformed by GAMS/CPLEX default settings. Supporting GAMS/CPLEX with knowledge about a known solution can be passed on by different means, please read more about this in section entitled Starting from a MIP Solution.

GAMS/Cplex also sets many model attributes that can by used in your GAMS program by accessing ModelName.suffix. A list of model attributes available after the solve can be found here Model Attributes mainly used after solve.

Cplex has the concept of deterministic time i.e. a measure of time that respects the same solution path to arrive at the same values in the solution while it yields the same level of performance for repeated solving of the same model with the same parameter settings, on the same computing platform. The length of a deterministic time tick may vary by platform. Nevertheless, ticks are normally consistent measures for a given platform (combination of hardware and software) carrying the same load. In other words, the correspondence of ticks to clock time depends on the hardware, software, and the current load of the machine. For the same platform and same load, the ratio of ticks per second stays roughly constant, independent of the model solved. However, for very short optimization runs, the variation of this ratio is typically high. GAMS/Cplex reports the deterministic time ticks spend inside Cplex in the model attribute ETAlg. Normally ETAlg is reporting the seconds.

# Summary of CPLEX Options

The various Cplex options are listed here by category, with a few words about each to indicate its function. The options are listed again, in alphabetical order and with detailed descriptions, in the last section of this document.

## Preprocessing and General Options

Option Description Default
advind advanced basis use determined by GAMS Bratio
aggfill aggregator fill parameter 10
aggind aggregator on/off -1
calcqcpduals calculate the dual values of a quadratically constrained problem 1
clocktype clock type for computation time 0
coeredind coefficient reduction on/off -1
computeserver address and port of Cplex remote object server
cpumask switch and mask to bind threads to processors auto
datacheck controls data consistency checking and modeling assistance 0
depind dependency checker on/off -1
dettilim deterministic time limit 1e+075
feasopt computes a minimum-cost relaxation to make an infeasible model feasible 0
feasoptmode mode of FeasOpt 0
.feaspref feasibility preference 1
freegamsmodel preserves memory by dumping the GAMS model instance representation temporarily to disk 0
interactive allow interactive option setting after a Control-C 0
lpmethod algorithm to be used for LP problems 0
memoryemphasis reduces use of memory 0
names load GAMS names into Cplex 1
numericalemphasis emphasizes precision in numerically unstable or difficult problems 0
objrng do objective ranging no objective ranging is done
optimalitytarget type of optimality that Cplex targets 0
parallelmode parallel optimization mode 1
predual give dual problem to the optimizer 0
preind turn presolver on/off 1
prelinear linear reduction indicator 1
prepass number of presolve applications to perform -1
printoptions list values of all options to GAMS listing file 0
qpmethod algorithm to be used for QP problems 0
qtolin linearization of the quadratic terms in the objective function of a QP or MIQP model -1
reduce primal and dual reduction type 3
relaxpreind presolve for initial relaxation on/off -1
rerun rerun problem if presolve infeasible or unbounded yes
rhsrng do right-hand-side ranging no right-hand-side ranging is done
rngrestart write GAMS readable ranging information file ranging information is printed to the listing file
scaind matrix scaling on/off 0
solutiontype type of solution (basic or non basic) for an LP or QP 0
threads global default thread count GAMS Threads
tilim overrides the GAMS ResLim option GAMS ResLim
tuning invokes parameter tuning tool
tuningdettilim tuning deterministic time limit per model or suite 1e+007
tuningdisplay level of information reported by the tuning tool 1
tuningmeasure measure for evaluating progress for a suite of models 1
tuningrepeat number of times tuning is to be repeated on perturbed versions 1
tuningtilim tuning time limit per model or suite 0.2*GAMS ResLim
workdir directory for working files current or project directory
workmem memory available for working storage 128

## Simplex Algorithmic Options

Option Description Default
craind crash strategy (used to obtain starting basis) 1
dpriind dual simplex pricing 0
epper perturbation constant 1e-006
iis run the IIS finder if the problem is infeasible 0
netfind attempt network extraction 2
netppriind network simplex pricing 0
perind force initial perturbation 0
perlim number of stalled iterations before perturbation 0
ppriind primal simplex pricing 0
pricelim pricing candidate list 0, in which case it is determined automatically
reinv refactorization frequency 0, in which case it is determined automatically

## Simplex Limit Options

Option Description Default
itlim iteration limit GAMS IterLim
netitlim iteration limit for network simplex large
objllim objective function lower limit -1e+075
objulim objective function upper limit 1e+075
singlim limit on singularity repairs 10

## Simplex Tolerance Options

Option Description Default
epmrk Markowitz pivot tolerance 0.01
epopt optimality tolerance 1e-006
eprhs feasibility tolerance 1e-006
netepopt optimality tolerance for the network simplex method 1e-006
neteprhs feasibility tolerance for the network simplex method 1e-006

## Barrier Specific Options

Option Description Default
baralg algorithm selection 0
barcolnz dense column handling 0
barcrossalg barrier crossover method 0
barepcomp convergence tolerance 1e-008
bargrowth unbounded face detection 1e+012
baritlim iteration limit large
barmaxcor maximum correction limit -1
barobjrng maximum objective function 1e+020
barorder row ordering algorithm selection 0
barqcpepcomp convergence tolerance for the barrier optimizer for QCPs 1e-007
barstartalg barrier starting point algorithm 1

## Sifting Specific Options

Option Description Default
siftalg sifting subproblem algorithm 0
siftitlim limit on sifting iterations large

## MIP Algorithmic Options

Option Description Default
bbinterval best bound interval 7
.benderspartition Benders partition 0
bendersstrategy Benders decomposition algorithm as a strategy 0
bndstrenind bound strengthening -1
bqpcuts boolean quadric polytope cuts for nonconvex QP or MIQP solved to global optimality 0
brdir set branching direction 0
bttol backtracking limit 0.9999
cliques clique cut generation 0
covers cover cut generation 0
cutlo lower cutoff for tree search -1e+075
cuts default cut generation 0
cutsfactor cut limit -1
cutup upper cutoff for tree search 1e+075
disjcuts disjunctive cuts generation 0
divetype MIP dive strategy 0
eachcutlim sets a limit for each type of cut 2100000000
flowcovers flow cover cut generation 0
flowpaths flow path cut generation 0
fpheur feasibility pump heuristic 0
fraccuts Gomory fractional cut generation 0
gubcovers GUB cover cut generation 0
heurfreq heuristic frequency 0
implbd implied bound cut generation 0
lbheur local branching heuristic 0
liftprojcuts lift-and-project cuts 0
localimplied generation of locally valid implied bound cuts 0
mcfcuts multi-commodity flow cut generation 0
mipemphasis MIP solution tactics 0
mipkappastats MIP kappa computation -1
mipordind priority list on/off GAMS PriorOpt
mipordtype priority order generation 0
mipsearch search strategy for mixed integer programs 0
mipstart use mip starting values 0
miqcpstrat MIQCP relaxation choice 0
mircuts mixed integer rounding cut generation 0
nodefileind node storage file indicator 1
nodesel node selection strategy 1
preslvnd node presolve selector 0
probe perform probing before solving a MIP 0
qpmakepsdind adjust MIQP formulation to make the quadratic matrix positive-semi-definite 1
relaxfixedinfeas accept small infeasibilties in the solve of the fixed problem 0
repeatpresolve reapply presolve at root after preprocessing -1
rinsheur relaxation induced neighborhood search frequency 0
rtlcuts Reformulation Linearization Technique (RLT) cuts 0
solvefinal switch to solve the problem with fixed discrete variables 1
startalg MIP starting algorithm 0
strongcandlim size of the candidates list for strong branching 10
strongitlim limit on iterations per branch for strong branching 0
subalg algorithm for subproblems 0
submipnodelim limit on number of nodes in an RINS subMIP 500
symmetry symmetry breaking cuts -1
varsel variable selection strategy at each node 0
zerohalfcuts zero-half cuts 0

## MIP Limit Options

Option Description Default
aggcutlim aggrigation limit for cut generation 3
auxrootthreads number of threads for auxiliary tasks at the root node 0
cutpass maximum number of cutting plane passes 0
fraccand candidate limit for generating Gomory fractional cuts 200
fracpass maximum number of passes for generating Gomory fractional cuts 0
intsollim maximum number of integer solutions large
nodelim maximum number of nodes to solve GAMS NodLim
polishafterdettime deterministic time before starting to polish a feasible solution 1e+075
polishafterepagap absolute MIP gap before starting to polish a feasible solution 0
polishafterepgap relative MIP gap before starting to polish a solution 0
polishafterintsol MIP integer solutions to find before starting to polish a feasible solution 2100000000
polishafternode nodes to process before starting to polish a feasible solution 2100000000
polishaftertime time before starting to polish a feasible solution 1e+075
probedettime deterministic time spent probing 1e+075
probetime time spent probing 1e+075
rampupdettimelimit limits the amount of time in deterministic ticks spent during ramp up of distributed parallel optimization 1e+075
rampupduration customizes ramp up for distributed parallel optimization 0
rampuptimelimit limits the amount of time in seconds spent during ramp up of distributed parallel optimization 1e+075
repairtries try to repair infeasible MIP start 0
trelim maximum space in memory for tree 1e+075

## MIP Solution Pool Options

Option Description Default
.divflt solution pool range filter coefficients 0
divfltlo lower bound on diversity mindouble
divfltup upper bound on diversity maxdouble
populatelim limit of solutions generated for the solution pool by populate method 20
randomseed sets the random seed differently for diversity of solutions changes with each Cplex release
solnpool solution pool file name
solnpoolagap absolute tolerance for the solutions in the solution pool 1e+075
solnpoolcapacity limits of solutions kept in the solution pool 2100000000
solnpoolgap relative tolerance for the solutions in the solution pool 1e+075
solnpoolintensity solution pool intensity for ability to produce multiple solutions 0
solnpoolmerge solution pool file name for merged solutions
solnpoolnumsym maximum number of variable symbols when writing merged solutions 10
solnpoolpop methods to populate the solution pool 1
solnpoolpopdel file with solution numbers to delete from the solution pool
solnpoolpoprepeat method to decide if populating the solution should be repeated
solnpoolprefix file name prefix for GDX solution files soln
solnpoolreplace strategy for replacing a solution in the solution pool 0

## MIP Tolerance Options

Option Description Default
bendersfeascuttol Tolerance for whether a feasibility cut has been violated in Benders decomposition 1e-006
bendersoptcuttol Tolerance for optimality cuts in Benders decomposition 1e-006
epagap absolute stopping tolerance GAMS OptCA
epgap relative stopping tolerance GAMS OptCR
epint integrality tolerance 1e-005
objdif overrides GAMS Cheat parameter 0
relobjdif relative cheat parameter 0

## Output Options

Option Description Default
bardisplay progress display level 1
clonelog enable clone logs 0
mipdisplay progress display level 4
mipinterval progress display interval 0
miptrace filename of MIP trace file
miptracenode node interval when a trace record is written 100
miptracetime time interval when a trace record is written 1
mpslongnum MPS file format precision of numeric output 1
netdisplay network display level 2
quality write solution quality statistics 0
siftdisplay sifting display level 1
simdisplay simplex display level 1
writebas produce a Cplex basis file
writeflt produce a Cplex solution pool filter file
writelp produce a Cplex LP file
writemps produce a Cplex MPS file
writemst produce a Cplex mst file
writeord produce a Cplex ord file
writeparam produce a Cplex parameter file with all active options
writepre produce a Cplex LP/MPS/SAV file of the presolved problem
writesav produce a Cplex binary problem file

## BCH Facility Options

Option Description Default
usercutcall the GAMS command line to call the cut generator
usercutfirst calls the cut generator for the first n nodes 10
usercutfreq determines the frequency of the cut generator model calls 10
usercutinterval determines the interval when to apply the multiplier for the frequency of the cut generator model calls 100
usercutmult determines the multiplier for the frequency of the cut generator model calls 2
usercutnewint calls the cut generator if the solver found a new integer feasible solution 1
usergdxin the name of the GDX file read back into Cplex bchin.gdx
usergdxname the name of the GDX file exported from the solver with the solution at the node bchout.gdx
usergdxnameinc the name of the GDX file exported from the solver with the incumbent solution bchout_i.gdx
usergdxprefix prefixes usergdxin, usergdxname, and usergdxnameinc
usergdxsol the name of the GDX file exported by Cplex to store the solution of extra columns bchsol.gdx
userheurcall the GAMS command line to call the heuristic
userheurfirst calls the heuristic for the first n nodes 10
userheurfreq determines the frequency of the heuristic model calls 10
userheurinterval determines the interval when to apply the multiplier for the frequency of the heuristic model calls 100
userheurmult determines the multiplier for the frequency of the heuristic model calls 2
userheurnewint calls the heuristic if the solver found a new integer feasible solution 1
userheurobjfirst Similar to UserHeurFirst but only calls the heuristic if the relaxed objective promises an improvement 0
userincbcall the GAMS command line to call the incumbent checking program
userincbicall the GAMS command line to call the incumbent reporting program
userjobid postfixes lf, o on call adds –userjobid to the call. Postfixes gdxname, gdxnameinc and gdxin
userkeep calls gamskeep instead of gams 0

## The GAMS/Cplex Options File

The GAMS/Cplex options file consists of one option or comment per line. An asterisk (*) at the beginning of a line causes the entire line to be ignored. Otherwise, the line will be interpreted as an option name and value separated by any amount of white space (blanks or tabs).

Following is an example options file cplex.opt.

     scaind 1
simdisplay 2


It will cause Cplex to use a more aggressive scaling method than the default. The iteration log will have an entry for each iteration instead of an entry for each refactorization.

# Special Notes

## Physical Memory Limitations

For the sake of computational speed, Cplex should use only available physical memory rather than virtual or paged memory. When Cplex recognizes that a limited amount of memory is available it automatically makes algorithmic adjustments to compensate. These adjustments almost always reduce optimization speed. Learning to recognize when these automatic adjustments occur can help to determine when additional memory should be added to the computer.

On virtual memory systems, if memory paging to disk is observed, a considerable performance penalty is incurred. Increasing available memory will speed the solution process dramatically. Also consider option MemoryEmphasis to conserve memory where possible.

Cplex performs an operation called refactorization at a frequency determined by the ReInv option setting. The longer Cplex works between refactorizations, the greater the amount of memory required to complete each iteration. Therefore, one means for conserving memory is to increase the refactorization frequency. Since refactorization is an expensive operation, increasing the refactorization frequency by reducing the ReInv option setting generally will slow performance. Cplex will automatically increase the refactorization frequency if it encounters low memory availability. This can be seen by watching the iteration log. The default log reports problem status at every refactorization. If the number of iterations between iteration log entries is decreasing, Cplex is increasing the refactorization frequency. Since Cplex might increase the frequency to once per iteration, the impact on performance can be dramatic. Providing additional memory should be beneficial.

CplexD also provides the option FreeGAMSModel to free some memory allocated by the GAMS link and making it available to Cplex. This only works when the GAMS parameter SolveLink is set 0 which should be always done when memory is tight because GAMS completely vacates memory.

The Threads options also has a significant impact on memory consumption. The concurrent solvers keep multiple copies of the problem in memory which double or even triples the amount of memory consumed. If memory tight, set the Threads parameter to 1.

## Using Special Ordered Sets

For some models a special structure can be exploited. GAMS allows you to declare SOS1 and SOS2 variables (Special Ordered Sets of type 1 and 2).

In Cplex the definition for SOS1 variables is:

• A set of variables for which at most one variable may be non-zero.

The definition for SOS2 variables is:

• A set of variables for which at most two variables may be non-zero. If two variables are non-zero, they must be adjacent in the set.

## Using Semi-Continuous and Semi-Integer Variables

GAMS allows the declaration of semi-continuous and semi-integer variables. These variable types are directly supported by GAMS/Cplex. For example:

     SemiCont Variable x;
x.lo = 3.2;
x.up = 8.7;

SemiInt Variable y;
y.lo = 5;
y.up = 10;


Variable x will be allowed to take on a value of 0.0 or any value between 3.2 and 8.7. Variable y will be allowed to take on a value of 0 or any integral value between 5 and 10.

## Running Out of Memory for MIP Problems

The most common difficulty when solving MIP problems is running out of memory. This problem arises when the branch and bound tree becomes so large that insufficient memory is available to solve an LP subproblem. As memory gets tight, you may observe frequent warning messages while Cplex attempts to navigate through various operations within limited memory. If a solution is not found shortly the solution process will be terminated with an unrecoverable integer failure message.

The tree information saved in memory can be substantial. Cplex saves a basis for every unexplored node. When utilizing the best bound method of node selection, the list of such nodes can become very long for large or difficult problems. How large the unexplored node list can become is entirely dependent on the actual amount of physical memory available and the actual size of the problem. Certainly increasing the amount of memory available extends the problem solving capability. Unfortunately, once a problem has failed because of insufficient memory, you can neither project how much further the process needed to go nor how much memory would be required to ultimately solve it.

Memory requirements can be limited by using the WorkMem, option with the NodeFileInd option. Setting NodeFileInd to 2 or 3 will cause Cplex to store portions of the branch and bound tree on disk whenever it grows to larger than the size specified by option WorkMem. That size should be set to something less than the amount of physical memory available.

Another approach is to modify the solution process to utilize less memory.

• Set option NodeSel to use a best estimate strategy or, more drastically a depth-first-search. Depth first search rarely generates a large unexplored node list since Cplex will be diving deep into the branch and bound tree rather than jumping around within it.
• Set option VarSel to use strong branching. Strong branching spends extra computation time at each node to choose a better branching variable. As a result it generates a smaller tree. It is often faster overall, as well.
• On some problems, a large number of cuts will be generated without a correspondingly large benefit in solution speed. Cut generation can be turned off using option Cuts.
• Set option MemoryEmphasis to instruct Cplex to conserve memory wherever possible.

## Failing to Prove Integer Optimality

One frustrating aspect of the branch and bound technique for solving MIP problems is that the solution process can continue long after the best solution has been found. Remember that the branch and bound tree may be as large as $$2^n$$ nodes, where n equals the number of binary variables. A problem containing only 30 binary variables could produce a tree having over one billion nodes! If no other stopping criteria have been set, the process might continue ad infinitum until the search is complete or your computer's memory is exhausted.

In general you should set at least one limit on the optimization process before beginning an optimization. Setting limits ensures that an exhaustive tree search will terminate in reasonable time. Once terminated, you can rerun the problem using some different option settings.

## Starting from a MIP Solution

You can provide a known solution (for example, from a MIP problem previously solved or from your knowledge of the problem) to serve as the first integer solution. When you provide such a starting solution, you may invoke relaxation induced neighborhood search (RINS heuristic) or solution polishing to improve the given solution. This first integer solution may include continuous and discrete variables of various types, such as semi-continuous variables or special ordered sets.

If you specify values for all discrete variables, GAMS/CPLEX will check the validity of the values as an integer-feasible solution; if you specify values for only a portion of the discrete variables, GAMS/CPLEX will attempt to fill in the missing values in a way that leads to an integer-feasible solution. If the specified values do not lead directly to an integer-feasible solution, GAMS/CPLEX will apply a quick heuristic to try to repair the MIP Start. The number of times that GAMS/CPLEX applies the heuristic is controlled by the repair tries parameter (RepairTries). If this process succeeds, the solution will be treated as an integer solution of the current problem.

A MIP start will only be used by GAMS/CPLEX if the MipStart parameter is set to 1. The starting values must be set via the .L variable attribute in the GAMS model before the solve statement.

## Using the Feasibility Relaxation

The feasibility relaxation is enabled by the FeasOpt parameter in a CPLEX solver option file.

With the FeasOpt option CPLEX accepts an infeasible model and selectively relaxes the bounds and constraints in a way that minimizes a weighted penalty function. In essence, the feasible relaxation tries to suggest the least change that would achieve feasibility. It returns an infeasible solution to GAMS and marks the relaxations of bounds and constraints with the INFES marker in the solution section of the listing file.

By default all equations are candidates for relaxation and weighted equally but none of the variables can be relaxed. This default behavior can be modified by assigning relaxation preferences to variable bounds and constraints. These preferences can be conveniently specified with the dot option FeasPref. A negative or zero preference means that the associated bound or constraint is not to be modified. The weighted penalty function is constructed from these preferences. The larger the preference, the more likely it will be that a given bound or constraint will be relaxed. However, it is not necessary to specify a unique preference for each bound or range. In fact, it is conventional to use only the values 0 (zero) and 1 (one) except when your knowledge of the problem suggests assigning explicit preferences.

Preferences can be specified through a CPLEX solver option file. The syntax is:

(variable or equation) .feaspref (value)

For example, suppose we have a GAMS declaration:

   Set i /i1*i5/;
Set j /j2*j4/;
variable v(i,j); equation e(i,j);


Then, the relaxation preference in the cplex.opt file can be specified by:

feasopt 1
v.feaspref            1
v.feaspref('i1',*)    2
v.feaspref('i1','j2') 0

e.feaspref(*,'j1')    0
e.feaspref('i5','j4') 2


First we turn the feasible relaxation on. Furthermore, we specify that all variables v(i,j) have preference of 1, except variables over set element i1, which have a preference of 2. The variable over set element i1 and j2 has preference 0. Note that preferences are assigned in a procedural fashion so that preferences assigned later overwrite previous preferences. The same syntax applies for assigning preferences to equations as demonstrated above. If you want to assign a preference to all variables or equations in a model, use the keywords variables or equations instead of the individual variable and equations names (e.g. variables.feaspref 1).

The parameter FeasOptMode allows different strategies in finding feasible relaxation in one or two phases. In its first phase, it attempts to minimize its relaxation of the infeasible model. That is, it attempts to find a feasible solution that requires minimal change. In its second phase, it finds an optimal solution (using the original objective) among those that require only as much relaxation as it found necessary in the first phase. Values of the parameter FeasOptMode indicate two aspects: (1) whether to stop in phase one or continue to phase two and (2) how to measure the relaxation (as a sum of required relaxations; as the number of constraints and bounds required to be relaxed; as a sum of the squares of required relaxations). Please check description of parameters FeasOpt and FeasOptMode for details. Also check example models feasopt* in the GAMS Model library.

# GAMS/Cplex Log File

Cplex reports its progress by writing to the GAMS log file as the problem solves. Normally the GAMS log file is directed to the computer screen.

The log file shows statistics about the presolve and continues with an iteration log.

For the primal simplex algorithm, the iteration log starts with the iteration number followed by the scaled infeasibility value. Once feasibility has been attained, the objective function value is listed instead. At the default value for option simdisplay there is a log line for each refactorization. The screen log has the following appearance:

Tried aggregator 1 time.
LP Presolve eliminated 2 rows and 39 columns.
Aggregator did 30 substitutions.
Reduced LP has 243 rows, 335 columns, and 3912 nonzeros.
Presolve time =    0.01 sec.
Using conservative initial basis.

Iteration log . . .
Iteration:     1    Scaled infeas =        193998.067174
Iteration:    29    Objective     =         -3484.286415
Switched to devex.
Iteration:    98    Objective     =         -1852.931117
Iteration:   166    Objective     =          -349.706562

Optimal solution found.

Objective :         901.161538


The iteration log for the dual simplex algorithm is similar, but the dual infeasibility and dual objective are reported instead of the corresponding primal values:

Tried aggregator 1 time.
LP Presolve eliminated 2 rows and 39 columns.
Aggregator did 30 substitutions.
Reduced LP has 243 rows, 335 columns, and 3912 nonzeros.
Presolve time =    0.01 sec.

Iteration log . . .
Iteration:     1   Scaled dual infeas =             3.890823
Iteration:    53   Dual objective     =          4844.392441
Iteration:   114   Dual objective     =          1794.360714
Iteration:   176   Dual objective     =          1120.183325
Iteration:   238   Dual objective     =           915.143030
Removing shift (1).

Optimal solution found.

Objective :         901.161538


The log for the network algorithm adds statistics about the extracted network and a log of the network iterations. The optimization is finished by one of the simplex algorithms and an iteration log for that is produced as well.

Tried aggregator 1 time.
LP Presolve eliminated 2 rows and 39 columns.
Aggregator did 30 substitutions.
Reduced LP has 243 rows, 335 columns, and 3912 nonzeros.
Presolve time =    0.01 sec.
Extracted network with 25 nodes and 116 arcs.
Extraction time =   -0.00 sec.
Iteration log . . .
Iteration:     0   Infeasibility     =          1232.378800 (-1.32326e+12)

Network - Optimal:  Objective =    1.5716820779e+03
Network time =    0.01 sec.  Iterations = 26 (24)

Iteration log . . .
Iteration:     1    Scaled infeas =        212696.154729
Iteration:    62    Scaled infeas =         10020.401232
Iteration:   142    Scaled infeas =          4985.200129
Switched to devex.
Iteration:   217    Objective     =         -3883.782587
Iteration:   291    Objective     =         -1423.126582

Optimal solution found.

Objective :         901.161538


The log for the barrier algorithm adds various algorithm specific statistics about the problem before starting the iteration log. The iteration log includes columns for primal and dual objective values and infeasibility values. A special log follows for the crossover to a basic solution.

Tried aggregator 1 time.
LP Presolve eliminated 2 rows and 39 columns.
Aggregator did 30 substitutions.
Reduced LP has 243 rows, 335 columns, and 3912 nonzeros.
Presolve time =    0.02 sec.
Number of nonzeros in lower triangle of A*A' = 6545
Using Approximate Minimum Degree ordering
Total time for automatic ordering = 0.01 sec.
Summary statistics for Cholesky factor:

Rows in Factor            = 243
Integer space required    = 578
Total non-zeros in factor = 8491
Total FP ops to factor    = 410889

Itn      Primal Obj        Dual Obj  Prim Inf Upper Inf  Dual Inf
0  -1.2826603e+06   7.4700787e+08  2.25e+10  6.13e+06  4.00e+05
1  -2.6426195e+05   6.3552653e+08  4.58e+09  1.25e+06  1.35e+05
2  -9.9117854e+04   4.1669756e+08  1.66e+09  4.52e+05  3.93e+04
3  -2.6624468e+04   2.1507018e+08  3.80e+08  1.04e+05  1.20e+04
4  -1.2104334e+04   7.8532364e+07  9.69e+07  2.65e+04  2.52e+03
5  -9.5217661e+03   4.2663811e+07  2.81e+07  7.67e+03  9.92e+02
6  -8.6929410e+03   1.4134077e+07  4.94e+06  1.35e+03  2.16e+02
7  -8.3726267e+03   3.1619431e+06  3.13e-07  6.84e-12  3.72e+01
8  -8.2962559e+03   3.3985844e+03  1.43e-08  5.60e-12  3.98e-02
9  -3.8181279e+03   2.6166059e+03  1.58e-08  9.37e-12  2.50e-02
10  -5.1366439e+03   2.8102021e+03  3.90e-06  7.34e-12  1.78e-02
11  -1.9771576e+03   1.5960442e+03  3.43e-06  7.02e-12  3.81e-03
12  -4.3346261e+02   8.3443795e+02  4.99e-07  1.22e-11  7.93e-04
13   1.2882968e+02   5.2138155e+02  2.22e-07  1.45e-11  8.72e-04
14   5.0418542e+02   5.3676806e+02  1.45e-07  1.26e-11  7.93e-04
15   2.4951043e+02   6.5911879e+02  1.73e-07  1.43e-11  5.33e-04
16   2.4666057e+02   7.6179064e+02  7.83e-06  2.17e-11  3.15e-04
17   4.6820025e+02   8.1319322e+02  4.75e-06  1.78e-11  2.57e-04
18   5.6081604e+02   7.9608915e+02  3.09e-06  1.98e-11  2.89e-04
19   6.4517294e+02   7.7729659e+02  1.61e-06  1.27e-11  3.29e-04
20   7.9603053e+02   7.8584631e+02  5.91e-07  1.91e-11  3.00e-04
21   8.5871436e+02   8.0198336e+02  1.32e-07  1.46e-11  2.57e-04
22   8.8146686e+02   8.1244367e+02  1.46e-07  1.84e-11  2.29e-04
23   8.8327998e+02   8.3544569e+02  1.44e-07  1.96e-11  1.71e-04
24   8.8595062e+02   8.4926550e+02  1.30e-07  2.85e-11  1.35e-04
25   8.9780584e+02   8.6318712e+02  1.60e-07  1.08e-11  9.89e-05
26   8.9940069e+02   8.9108502e+02  1.78e-07  1.07e-11  2.62e-05
27   8.9979049e+02   8.9138752e+02  5.14e-07  1.88e-11  2.54e-05
28   8.9979401e+02   8.9139850e+02  5.13e-07  2.18e-11  2.54e-05
29   9.0067378e+02   8.9385969e+02  2.45e-07  1.46e-11  1.90e-05
30   9.0112149e+02   8.9746581e+02  2.12e-07  1.71e-11  9.61e-06
31   9.0113610e+02   8.9837069e+02  2.11e-07  1.31e-11  7.40e-06
32   9.0113661e+02   8.9982723e+02  1.90e-07  2.12e-11  3.53e-06
33   9.0115644e+02   9.0088083e+02  2.92e-07  1.27e-11  7.35e-07
34   9.0116131e+02   9.0116262e+02  3.07e-07  1.81e-11  3.13e-09
35   9.0116154e+02   9.0116154e+02  4.85e-07  1.69e-11  9.72e-13
Barrier time =    0.39 sec.

Primal crossover.
Primal:  Fixing 13 variables.
12 PMoves:  Infeasibility  1.97677059e-06  Objective  9.01161542e+02
0 PMoves:  Infeasibility  0.00000000e+00  Objective  9.01161540e+02
Primal:  Pushed 1, exchanged 12.
Dual:  Fixing 3 variables.
2 DMoves:  Infeasibility  1.28422758e-36  Objective  9.01161540e+02
0 DMoves:  Infeasibility  1.28422758e-36  Objective  9.01161540e+02
Dual:  Pushed 3, exchanged 0.
Using devex.
Total crossover time =    0.02 sec.

Optimal solution found.

Objective :         901.161540


For MIP problems, during the branch and bound search, Cplex reports the node number, the number of nodes left, the value of the Objective function, the number of integer variables that have fractional values, the current best integer solution, the best relaxed solution at a node and an iteration count. The last column show the current optimality gap as a percentage. CPLEX logs an asterisk (*) in the left-most column for any node where it finds an integer-feasible solution or new incumbent. The + denotes an incumbent generated by the heuristic.

Tried aggregator 1 time.
MIP Presolve eliminated 1 rows and 1 columns.
Reduced MIP has 99 rows, 76 columns, and 419 nonzeros.
Presolve time =    0.00 sec.

Iteration log . . .
Iteration:     1   Dual objective     =             0.000000
Root relaxation solution time =    0.01 sec.

Nodes                                         Cuts/
Node  Left     Objective  IInf  Best Integer     Best Node    ItCnt     Gap

0     0        0.0000    24                      0.0000       40
*     0+    0        6.0000     0        6.0000        0.0000       40  100.00%
*    50+   50        4.0000     0        4.0000        0.0000      691  100.00%
100    99        2.0000    15        4.0000        0.4000     1448   90.00%
Fixing integer variables, and solving final LP..
Tried aggregator 1 time.
LP Presolve eliminated 100 rows and 77 columns.
All rows and columns eliminated.
Presolve time =    0.00 sec.

Solution satisfies tolerances.

MIP Solution    :            4.000000    (2650 iterations, 185 nodes)
Final LP        :            4.000000    (0 iterations)

Best integer solution possible :           1.000000
Absolute gap                   :                  3
Relative gap                   :                1.5


# Detailed Descriptions of CPLEX Options

These options should be entered in the options file after setting the GAMS ModelName.OptFile parameter to 1. The name of the options file is cplex.opt. The options file is case insensitive and the keywords should be given in full.

Use an Advanced Basis. GAMS/Cplex will automatically use an advanced basis from a previous solve statement. The GAMS BRatio option can be used to specify when not to use an advanced basis. The Cplex option AdvInd can be used to ignore a basis passed on by GAMS (it overrides BRatio).

Default: determined by GAMS Bratio

valuemeaning
0 Do not use advanced basis
1 Use advanced basis if available
2 Crash an advanced basis if available (use basis with presolve)

aggcutlim (integer): aggrigation limit for cut generation

Limits the number of constraints that can be aggregated for generating flow cover and mixed integer rounding cuts. For most purposes, the default will be satisfactory.

Default: 3

aggfill (integer): aggregator fill parameter

Aggregator fill limit. If the net result of a single substitution is more non-zeros than the setting of the AggFill parameter, the substitution will not be made.

Default: 10

aggind (integer): aggregator on/off

This option, when set to a nonzero value, will cause the Cplex aggregator to use substitution where possible to reduce the number of rows and columns in the problem. If set to a positive value, the aggregator will be applied the specified number of times, or until no more reductions are possible. At the default value of -1, the aggregator is applied once for linear programs and an unlimited number of times for mixed integer problems.

Default: -1

valuemeaning
-1 Once for LP, unlimited for MIP
0 Do not use
>0 Aggregator will be applied the specified number of times

Partitions the number of threads for CPLEX to use for auxiliary tasks while it solves the root node of a problem. On a system that offers N processors or N global threads, if you set this parameter to n, where N>n>0 then CPLEX uses at most n threads for auxiliary tasks and at most N-n threads to solve the root node. See also the parameter Threads.

Default: 0

valuemeaning
-1 Off: do not use additional threads for auxiliary tasks
0 Automatic: let CPLEX choose the number of threads to use
N>n>0 Use n threads for auxiliary root tasks

baralg (integer): algorithm selection

Selects which barrier algorithm to use. The default setting of 0 uses the infeasibility-estimate start algorithm for MIP subproblems and the standard barrier algorithm, option 3, for other cases. The standard barrier algorithm is almost always fastest. The alternative algorithms, options 1 and 2, may eliminate numerical difficulties related to infeasibility, but will generally be slower.

Default: 0

valuemeaning
0 Same as 1 for MIP subproblems, 3 otherwise
1 Infeasibility-estimate start
2 Infeasibility-constant start
3 standard barrier algorithm

barcolnz (integer): dense column handling

Determines whether or not columns are considered dense for special barrier algorithm handling. At the default setting of 0, this parameter is determined dynamically. Values above 0 specify the number of entries in columns to be considered as dense.

Default: 0

barcrossalg (integer): barrier crossover method

Selects which crossover method is used at the end of a barrier optimization. To turn off crossover set SolutionType to 2.

Default: 0

valuemeaning
0 Automatic
1 Primal crossover
2 Dual crossover

bardisplay (integer): progress display level

Determines the level of progress information to be displayed while the barrier method is running.

Default: 1

valuemeaning
0 No progress information
1 Display normal information
2 Display diagnostic information

barepcomp (real): convergence tolerance

Determines the tolerance on complementarity for convergence of the barrier algorithm. The algorithm will terminate with an optimal solution if the relative complementarity is smaller than this value.

Default: 1e-008

bargrowth (real): unbounded face detection

Used by the barrier algorithm to detect unbounded optimal faces. At higher values, the barrier algorithm will be less likely to conclude that the problem has an unbounded optimal face, but more likely to have numerical difficulties if the problem does have an unbounded face.

Default: 1e+012

baritlim (integer): iteration limit

Determines the maximum number of iterations for the barrier algorithm. When set to 0, no Barrier iterations occur, but problem setup occurs and information about the setup is displayed (such as Cholesky factorization information). When left at the default value, there is no explicit limit on the number of iterations.

Default: large

barmaxcor (integer): maximum correction limit

Specifies the maximum number of centering corrections that should be done on each iteration. Larger values may improve the numerical performance of the barrier algorithm at the expense of computation time. The default of -1 means the number is automatically determined.

Default: -1

barobjrng (real): maximum objective function

Determines the maximum absolute value of the objective function. The barrier algorithm looks at this limit to detect unbounded problems.

Default: 1e+020

barorder (integer): row ordering algorithm selection

Determines the ordering algorithm to be used by the barrier method. By default, Cplex attempts to choose the most effective of the available alternatives. Higher numbers tend to favor better orderings at the expense of longer ordering run times.

Default: 0

valuemeaning
0 Automatic
1 Approximate Minimum Degree (AMD)
2 Approximate Minimum Fill (AMF)
3 Nested Dissection (ND)

barqcpepcomp (real): convergence tolerance for the barrier optimizer for QCPs

Range: [1e-012, 1e+075]

Default: 1e-007

barstartalg (integer): barrier starting point algorithm

This option sets the algorithm to be used to compute the initial starting point for the barrier solver. The default starting point is satisfactory for most problems. Since the default starting point is tuned for primal problems, using the other starting points may be worthwhile in conjunction with the PreDual parameter.

Default: 1

valuemeaning
1 default primal, dual is 0
2 default primal, estimate dual
3 primal average, dual is 0
4 primal average, estimate dual

bbinterval (integer): best bound interval

Set interval for selecting a best bound node when doing a best estimate search. Active only when NodeSel is 2 (best estimate). Decreasing this interval may be useful when best estimate is finding good solutions but making little progress in moving the bound. Increasing this interval may help when the best estimate node selection is not finding any good integer solutions. Setting the interval to 1 is equivalent to setting NodeSel to 1.

Default: 7

bendersfeascuttol (real): Tolerance for whether a feasibility cut has been violated in Benders decomposition

Default: 1e-006

bendersoptcuttol (real): Tolerance for optimality cuts in Benders decomposition

Default: 1e-006

.benderspartition (integer): Benders partition

Default: 0

bendersstrategy (integer): Benders decomposition algorithm as a strategy

Given a formulation of a problem, CPLEX can decompose the model into a single master and (possibly multiple) subproblems. To do so, CPLEX can make use of annotations that you supply for your model. The strategy can be applied to mixed-integer linear programs (MILP). For certain types of problems, this approach offers significant performance improvements as subproblems can be solved in parallel.

For mixed integer programs (MIP), under certain conditions, CPLEX can apply Benders algorithm to improve the search to find more feasible solutions more quickly.

Default: 0

valuemeaning
-1 Off
Execute conventional branch and bound; ignore any Benders annotations. That is, do not use Benders algorithm even if a Benders partition of the current model is present
0 Automatic
If annotations specifying a Benders partition of the current model are available, CPLEX attempts to decompose the model. CPLEX uses the master as given by the annotations, and attempts to partition the subproblems further, if possible, before applying Benders algorithm to solve the model. If the user supplied annotations, but the annotations supplied do not lead to a complete decomposition into master and disjoint subproblems (that is, if the annotations are wrong in that sense), CPLEX produces an error.
1 Apply user annotations
CPLEX applies Benders algorithm to a decomposition based on annotations supplied by the user. If no annotations to decompose the model are available, this setting produces an error. If the user supplies annotations, but the supplied annotations do not lead to a complete partition of the original model into disjoint master and subproblems, then this setting produces an error.
2 Apply user annotations with automatic support for subproblems
CPLEX accepts the master as given and attempts to decompose the remaining elements into disjoint subproblems to assign to workers. It then solves the Benders decomposition of the model. If no annotations to decompose the model are available, this setting produces an error. If the user supplies annotations, but the supplied annotations do not lead to a complete partition of the original model into disjoint master and subproblems, then this setting produces an error.
3 Apply automatic decomposition
CPLEX ignores any annotation supplied with the model; CPLEX applies presolve; CPLEX then automatically generates a Benders partition, putting integer variables in master and continuous linear variables into disjoint subproblems. CPLEX then solves the Benders decomposition of the model. If the problem is a strictly linear program (LP), that is, there are no integer-constrained variables to put into master, then CPLEX reports an error. If the problem is a mixed integer linear program (MILP) where all variables are integer-constrained, (that is, there are no continuous linear variables to decompose into disjoint subproblems) then CPLEX reports an error.

bndstrenind (integer): bound strengthening

Use bound strengthening when solving mixed integer problems. Bound strengthening tightens the bounds on variables, perhaps to the point where the variable can be fixed and thus removed from consideration during the branch and bound algorithm. This reduction is usually beneficial, but occasionally, due to its iterative nature, takes a long time.

Default: -1

valuemeaning
-1 Determine automatically
0 Don't use bound strengthening
1 Use bound strengthening

bqpcuts (integer): boolean quadric polytope cuts for nonconvex QP or MIQP solved to global optimality

Default: 0

valuemeaning
-1 Do not generate BQP cuts
0 Determined automatically
1 Generate BQP cuts moderately
2 Generate BQP cuts aggressively
3 Generate BQP cuts very aggressively

brdir (integer): set branching direction

Used to decide which branch (up or down) should be taken first at each node.

Default: 0

valuemeaning
-1 Down branch selected first
0 Algorithm decides
1 Up branch selected first

bttol (real): backtracking limit

This option controls how often backtracking is done during the branching process. At each node, Cplex compares the objective function value or estimated integer objective value to these values at parent nodes; the value of the bttol parameter dictates how much relative degradation is tolerated before backtracking. Lower values tend to increase the amount of backtracking, making the search more of a pure best-bound search. Higher values tend to decrease the amount of backtracking, making the search more of a depth-first search. This parameter is used only once a first integer solution is found or when a cutoff has been specified.

Range: [0, 1]

Default: 0.9999

calcqcpduals (integer): calculate the dual values of a quadratically constrained problem

Default: 1

valuemeaning
0 Do not calculate dual values
1 Calculate dual values as long as it does not interfere with presolve reductions
2 Calculate dual values and disable any presolve reductions that would interfere

cliques (integer): clique cut generation

Determines whether or not clique cuts should be generated during optimization.

Default: 0

valuemeaning
-1 Do not generate clique cuts
0 Determined automatically
1 Generate clique cuts moderately
2 Generate clique cuts aggressively
3 Generate clique cuts very aggressively

clocktype (integer): clock type for computation time

Decides how computation times are measured for both reporting performance and terminating optimization when a time limit has been set. Small variations in measured time on identical runs may be expected on any computer system with any setting of this parameter. The default setting 0 (zero) allows CPLEX to choose wall clock time when other parameters invoke parallel optimization and to choose CPU time when other parameters enforce sequential (not parallel) optimization. GAMS/Cplex works with wall time on Windows also for sequential optimization unless this option instructs to measure time differently.

Default: 0

valuemeaning
0 Automatic
1 CPU time
2 Wall clock time

clonelog (integer): enable clone logs

The clone logs contain information normally recorded in the ordinary log file but inconvenient to send through the normal log channel in case of parallel execution. The information likely to be of most interest to you are special messages, such as error messages, that result from calls to the LP optimizers called for the subproblems. The clone log files are named cloneK.log, where K is the index of the clone, ranging from 0 (zero) to the number of threads minus one. Since the clones are created at each call to a parallel optimizer and discarded when it exits, the clone logs are opened at each call and closed at each exit. The clone log files are not removed when the clones themselves are discarded.

Default: 0

valuemeaning
-1 Clone log files off
0 Automatic
1 Clone log files on

coeredind (integer): coefficient reduction on/off

Coefficient reduction is a technique used when presolving mixed integer programs. The benefit is to improve the objective value of the initial (and subsequent) linear programming relaxations by reducing the number of non-integral vertexes. However, the linear programs generated at each node may become more difficult to solve.

Default: -1

valuemeaning
-1 Automatic
0 Do not use coefficient reduction
1 Reduce only to integral coefficients
2 Reduce all potential coefficients
3 Reduce aggressively with tilting

computeserver (string): address and port of Cplex remote object server

This option will use a remote machine to solve the model. The option is specified as name:port where name is the machine name or IP address of the remote server and port is the port number the Cplex remote server listen for work. On the remote server, a full Cplex installation (not just GAMS/Cplex) is required. On the server, one needs to start cplex -worker=tcpip -address=name:port with the same name/port as in this option.

covers (integer): cover cut generation

Determines whether or not cover cuts should be generated during optimization.

Default: 0

valuemeaning
-1 Do not generate cover cuts
0 Determined automatically
1 Generate cover cuts moderately
2 Generate cover cuts aggressively
3 Generate cover cuts very aggressively

The value of this parameter serves as a switch to turn on (or to turn off) CPLEX binding of multiple threads to multiple processors on platforms where this feature is available. Hexadecimal values of this parameter serve as a mask to specify to CPLEX which processors (or cores) to use in binding multiple threads to multiple processors. CPU binding is also sometimes known as processor affinity. CPU binding reduces the variability of CPLEX runs. On some occasions, running the same CPLEX on the same (non trivial) models would produce a big variation in runtime, e.g. 1000 seconds versus 900 seconds on a 12 core machine. These differences happen while CPLEX still gets exactly the same results and executes the exact same path, thanks to its completely deterministic algorithms. Running the same tests with CPU binding enabled reduced this variability in running time significantly.

If not set to off or auto CPLEX treats the value of this parameter as a string that resembles a hexadecimal number without the usual 0x prefix. A valid string consists of these elements: a) any digit from 0 (zero) through 9 (inclusive), b) any lower case character in the range a through f (inclusive), and c) any upper case character in the range A through F (inclusive). CPLEX rejects a string containing any other digits or characters than those.

When the value of this parameter is a valid string, each bit of this string corresponds to a central processing unit (CPU), that is, to a processor or core. The lowest order bit of the string corresponds to the first logical CPU, and the highest order corresponds to the last logical CPU. For example, 00000001 designates processor #0, 00000003 designates processors #0 and #1, FFFFFFFF designates all processors #0 through #31. CPLEX uses the ith CPU if and only if the ith bit of this string is set to 1 (one). Tip: For GNU/Linux users, this parameter behaves like the taskset command (except that this parameter lacks the prefix 0x).

If this CPU mask parameter is set to a valid string that designates a hexadecimal number, but global Threads count is set to 0 (zero), then CPLEX still starts as many threads as the number of cores on the machine, but only the cores enabled in the mask will be used.

For example, on a 16 core machine, consider the difference between the value "off" and the value ffff. If the value of this parameter is "off" CPLEX does no binding. If the value of this parameter is ffff, CPLEX binds threads to cores.

Default: auto

valuemeaning
auto CPLEX decides whether to bind threads to cores (or processors)
off CPLEX performs no binding
hex CPLEX binds the threads in round-robin fashion to the cores specified by the mask

craind (integer): crash strategy (used to obtain starting basis)

The crash option biases the way Cplex orders variables relative to the objective function when selecting an initial basis.

Default: 1

valuemeaning
-1 Primal: alternate ways of using objective coefficients. Dual: aggressive starting basis
0 Primal: ignore objective coefficients during crash. Dual: aggressive starting basis
1 Primal: alternate ways of using objective coefficients. Dual: default starting basis

cutlo (real): lower cutoff for tree search

Sets the lower cutoff tolerance. When the problem is a maximization problem, CPLEX cuts off or discards solutions that are less than the specified cutoff value. If the model has no solution with an objective value greater than or equal to the cutoff value, then CPLEX declares the model infeasible. In other words, setting the lower cutoff value c for a maximization problem is similar to adding this constraint to the objective function of the model: obj>=c.

This option overrides the GAMS Cutoff setting.

This parameter is not effective with FeasOpt. FeasOpt cannot analyze an infeasibility introduced by this parameter. If you want to analyze such a condition, add an explicit objective constraint to your model instead.

Default: -1e+075

cutpass (integer): maximum number of cutting plane passes

Sets the upper limit on the number of passes that will be performed when generating cutting planes on a mixed integer model.

Default: 0

valuemeaning
-1 None
0 Automatically determined
>0 Maximum passes to perform

cuts (string): default cut generation

Allows generation setting of all optional cuts at once. This is done by changing the meaning of the default value (0: automatic) for the various Cplex cut generation options. The options affected are Cliques, Covers, DisjCuts, FlowCovers, FlowPaths, FracCuts, GUBCovers, ImplBd, LiftProjCuts, MCFCuts, MIRCuts, and Symmetry.

Default: 0

valuemeaning
-1 Do not generate cuts
0 Determined automatically
1 Generate cuts moderately
2 Generate cuts aggressively
3 Generate cuts very aggressively
4 Generate cuts highly aggressively
5 Generate cuts extremely aggressively

cutsfactor (real): cut limit

This option limits the number of cuts that can be added. For values between zero and one inclusive (that is, in the range [0.0, 1.0], CPLEX generates no cuts.

For values strictly greater than 1.0 (one), CPLEX limits the number of rows in the model with cuts added.

The limit on this total is the product of CutsFactor times the original number of rows. If CPLEX has presolved the model, the original number of rows is the number of rows in the presolved model. (This behavior with respect to a presolved model is unchanged.)

CPLEX regards negative values of this parameter as equivalent to the default value -1.0. That is, a negative value specifies no particular limit on the number of cuts. CPLEX computes and dynamically adjusts such a limit automatically

Default: -1

cutup (real): upper cutoff for tree search

Sets the upper cutoff tolerance. When the problem is a minimization problem, CPLEX cuts off or discards any solutions that are greater than the specified upper cutoff value. If the model has no solution with an objective value less than or equal to the cutoff value, CPLEX declares the model infeasible. In other words, setting an upper cutoff value c for a minimization problem is similar to adding this constraint to the objective function of the model: obj<=c.

This option overrides the GAMS Cutoff setting.

This parameter is not effective with FeasOpt. FeasOpt cannot analyze an infeasibility introduced by this parameter. If you want to analyze such a condition, add an explicit objective constraint to your model instead.

Default: 1e+075

datacheck (integer): controls data consistency checking and modeling assistance

When the value of this parameter is set to level 2, CPLEX turns on both data consistency checking and modeling assistance. At this level, CPLEX issues warnings at the start of the optimization about disproportionate values (too large, too small) in coefficients, bounds, and righthand sides (RHS).

Default: 0

valuemeaning
0 Data checking off
1 Data checking on
2 Data checking and model assistance on

depind (integer): dependency checker on/off

This option determines if and when the dependency checker will be used.

Default: -1

valuemeaning
-1 Automatic
0 Turn off dependency checking
1 Turn on only at the beginning of preprocessing
2 Turn on only at the end of preprocessing
3 Turn on at the beginning and at the end of preprocessing

dettilim (real): deterministic time limit

Sets a time limit expressed in ticks, a unit to measure work done deterministically.

The length of a deterministic tick may vary by platform. Nevertheless, ticks are normally consistent measures for a given platform (combination of hardware and software) carrying the same load. In other words, the correspondence of ticks to clock time depends on the hardware, software, and the current load of the machine. For the same platform and same load, the ratio of ticks per second stays roughly constant, independent of the model solved. However, for very short optimization runs, the variation of this ratio is typically high.

Default: 1e+075

disjcuts (integer): disjunctive cuts generation

Determines whether or not to generate disjunctive cuts during optimization. At the default of 0, generation is continued only if it seems to be helping.

Default: 0

valuemeaning
-1 Do not generate disjunctive cuts
0 Determined automatically
1 Generate disjunctive cuts moderately
2 Generate disjunctive cuts aggressively
3 Generate disjunctive cuts very aggressively

divetype (integer): MIP dive strategy

The MIP traversal strategy occasionally performs probing dives, where it looks ahead at both children nodes before deciding which node to choose. The default (automatic) setting chooses when to perform a probing dive, and the other two settings direct Cplex when to perform probing dives: never or always.

Default: 0

valuemeaning
0 Automatic
1 Traditional dive
2 Probing dive
3 Guided dive

.divflt (real): solution pool range filter coefficients

A diversity filter for a solution pool (see option SolnPool) allows you generate solutions that are similar to (or different from) a set of reference values that you specify for a set of binary variables. In particular, you can use a diversity filter to generate more solutions that are similar to an existing solution or to an existing partial solution.

A diversity filter drives the search for multiple solutions toward new solutions that satisfy a measure of diversity specified in the filter. This diversity measure applies only to binary variables. Potential new solutions are compared to a reference set. This reference set is specified with this dot option. If no reference set is specified, the difference measure will be computed relative to the other solutions in the pool. The diversity measure is computed by summing the pair-wise absolute differences from solution and the reference values.

Default: 0

divfltlo (real): lower bound on diversity

Please check option DivFlt for general information on a diversity filter.

If you specify a lower bound on the diversity using DivFltLo, Cplex will look for solutions that are different from the reference values. In other words, you can say, Give me solutions that differ by at least this amount in this set of variables.

Default: mindouble

divfltup (real): upper bound on diversity

Please check option DivFlt for general information on a diversity filter.

If you specify an upper bound on diversity DivFltUp, Cplex will look for solutions similar to the reference values. In other words, you can say, Give me solutions that are close to this one, within this set of variables.

Default: maxdouble

dpriind (integer): dual simplex pricing

Pricing strategy for dual simplex method. Consider using dual steepest-edge pricing. Dual steepest-edge is particularly efficient and does not carry as much computational burden as the primal steepest-edge pricing.

Default: 0

valuemeaning
0 Determined automatically
1 Standard dual pricing
2 Steepest-edge pricing
3 Steepest-edge pricing in slack space
4 Steepest-edge pricing, unit initial norms
5 Devex pricing

eachcutlim (integer): sets a limit for each type of cut

This parameter allows you to set a uniform limit on the number of cuts of each type that Cplex generates. By default, the limit is a large integer; that is, there is no effective limit by default.

Tighter limits on the number of cuts of each type may benefit certain models. For example, a limit on each type of cut will prevent any one type of cut from being created in such large number that the limit on the total number of all types of cuts is reached before other types of cuts have an opportunity to be created. A setting of 0 means no cuts.

This parameter does not influence the number of Gomory cuts. For means to control the number of Gomory cuts, see also the fractional cut parameters: FracCand, FracCuts, and FracPass.

Default: 2100000000

epagap (real): absolute stopping tolerance

Synonym: optca

Absolute tolerance on the gap between the best integer objective and the objective of the best node remaining. When the value falls below the value of the epagap setting, the optimization is stopped. This option overrides GAMS OptCA which provides its initial value.

Default: GAMS OptCA

epgap (real): relative stopping tolerance

Synonym: optcr

Relative tolerance on the gap between the best integer objective and the objective of the best node remaining. When the value falls below the value of the epgap setting, the mixed integer optimization is stopped. Note the difference in the Cplex definition of the relative tolerance with the GAMS definition. This option overrides GAMS OptCR which provides its initial value.

Range: [0, 1]

Default: GAMS OptCR

epint (real): integrality tolerance

Integrality Tolerance. This specifies the amount by which an integer variable can be different than an integer and still be considered feasible.

Range: [0, 0.5]

Default: 1e-005

epmrk (real): Markowitz pivot tolerance

The Markowitz tolerance influences pivot selection during basis factorization. Increasing the Markowitz threshold may improve the numerical properties of the solution.

Range: [0.0001, 0.99999]

Default: 0.01

epopt (real): optimality tolerance

The optimality tolerance influences the reduced-cost tolerance for optimality. This option setting governs how closely Cplex must approach the theoretically optimal solution.

Range: [1e-009, 0.1]

Default: 1e-006

epper (real): perturbation constant

Perturbation setting. Highly degenerate problems tend to stall optimization progress. Cplex automatically perturbs the variable bounds when this occurs. Perturbation expands the bounds on every variable by a small amount thereby creating a different but closely related problem. Generally, the solution to the less constrained problem is easier to solve. Once the solution to the perturbed problem has advanced as far as it can go, Cplex removes the perturbation by resetting the bounds to their original values.

If the problem is perturbed more than once, the perturbation constant is probably too large. Reduce the epper option to a level where only one perturbation is required. Any value greater than or equal to 1.0e-8 is valid.

Default: 1e-006

eprhs (real): feasibility tolerance

Feasibility tolerance. This specifies the degree to which a problem's basic variables may violate their bounds. This tolerance influences the selection of an optimal basis and can be reset to a higher value when a problem is having difficulty maintaining feasibility during optimization. You may also wish to lower this tolerance after finding an optimal solution if there is any doubt that the solution is truly optimal. If the feasibility tolerance is set too low, Cplex may falsely conclude that a problem is infeasible.

Range: [1e-009, 0.1]

Default: 1e-006

feasopt (boolean): computes a minimum-cost relaxation to make an infeasible model feasible

With Feasopt turned on, a minimum-cost relaxation of the right hand side values of constraints or bounds on variables is computed in order to make an infeasible model feasible. It marks the relaxed right hand side values and bounds in the solution listing.

Several options are available for the metric used to determine what constitutes a minimum-cost relaxation which can be set by option FeasOptMode.

Feasible relaxations are available for all problem types with the exception of quadratically constraint problems.

Default: 0

valuemeaning
0 Turns Feasible Relaxation off
1 Turns Feasible Relaxation on

feasoptmode (integer): mode of FeasOpt

The parameter FeasOptMode allows different strategies in finding feasible relaxation in one or two phases. In its first phase, it attempts to minimize its relaxation of the infeasible model. That is, it attempts to find a feasible solution that requires minimal change. In its second phase, it finds an optimal solution (using the original objective) among those that require only as much relaxation as it found necessary in the first phase. Values of the parameter FeasOptMode indicate two aspects: (1) whether to stop in phase one or continue to phase two and (2) how to measure the minimality of the relaxation (as a sum of required relaxations; as the number of constraints and bounds required to be relaxed; as a sum of the squares of required relaxations).

Default: 0

valuemeaning
0 Minimize sum of relaxations
Minimize the sum of all required relaxations in first phase only
1 Minimize sum of relaxations and optimize
Minimize the sum of all required relaxations in first phase and execute second phase to find optimum among minimal relaxations
2 Minimize number of relaxations
Minimize the number of constraints and bounds requiring relaxation in first phase only
3 Minimize number of relaxations and optimize
Minimize the number of constraints and bounds requiring relaxation in first phase and execute second phase to find optimum among minimal relaxations
4 Minimize sum of squares of relaxations
Minimize the sum of squares of required relaxations in first phase only
5 Minimize sum of squares of relaxations and optimize
Minimize the sum of squares of required relaxations in first phase and execute second phase to find optimum among minimal relaxations

.feaspref (real): feasibility preference

You can express the costs associated with relaxing a bound or right hand side value during a FeasOpt run through the .feaspref option. The input value denotes the users willingness to relax a constraint or bound. More precisely, the reciprocal of the specified value is used to weight the relaxation of that constraint or bound. The user may specify a preference value less than or equal to 0 (zero), which denotes that the corresponding constraint or bound must not be relaxed.

Default: 1

flowcovers (integer): flow cover cut generation

Determines whether or not flow cover cuts should be generated during optimization.

Default: 0

valuemeaning
-1 Do not generate flow cover cuts
0 Determined automatically
1 Generate flow cover cuts moderately
2 Generate flow cover cuts aggressively

flowpaths (integer): flow path cut generation

Determines whether or not flow path cuts should be generated during optimization. At the default of 0, generation is continued only if it seems to be helping.

Default: 0

valuemeaning
-1 Do not generate flow path cuts
0 Determined automatically
1 Generate flow path cuts moderately
2 Generate flow path cuts aggressively

fpheur (integer): feasibility pump heuristic

Controls the use of the feasibility pump heuristic for mixed integer programming (MIP) models.

Default: 0

valuemeaning
-1 Turns Feasible Pump heuristic off
0 Automatic
1 Apply the feasibility pump heuristic with an emphasis on finding a feasible solution
2 Apply the feasibility pump heuristic with an emphasis on finding a feasible solution with a good objective value

fraccand (integer): candidate limit for generating Gomory fractional cuts

Limits the number of candidate variables for generating Gomory fractional cuts.

Default: 200

fraccuts (integer): Gomory fractional cut generation

Determines whether or not Gomory fractional cuts should be generated during optimization.

Default: 0

valuemeaning
-1 Do not generate Gomory fractional cuts
0 Determined automatically
1 Generate Gomory fractional cuts moderately
2 Generate Gomory fractional cuts aggressively

fracpass (integer): maximum number of passes for generating Gomory fractional cuts

Sets the upper limit on the number of passes that will be performed when generating Gomory fractional cuts on a mixed integer model. Ignored if parameter FracCuts is set to a nonzero value.

Default: 0

valuemeaning
0 0 Automatically determined
>0 Maximum passes to perform

freegamsmodel (boolean): preserves memory by dumping the GAMS model instance representation temporarily to disk

In order to provide the maximum amount of memory to the solver this option dumps the internal representation of the model instance temporarily to disk and frees memory. This option only works with SolveLink=0 and only for models without quadratic constraints for CplexD only.

Default: 0

gubcovers (integer): GUB cover cut generation

Determines whether or not GUB (Generalized Upper Bound) cover cuts should be generated during optimization. The default of 0 indicates that the attempt to generate GUB cuts should continue only if it seems to be helping.

Default: 0

valuemeaning
-1 Do not generate GUB cover cuts
0 Determined automatically
1 Generate GUB cover cuts moderately
2 Generate GUB cover cuts aggressively

heurfreq (integer): heuristic frequency

This option specifies how often to apply the node heuristic. Setting to a positive number applies the heuristic at the requested node interval.

Default: 0

valuemeaning
-1 Do not use the node heuristic
0 Determined automatically

iis (boolean): run the IIS finder if the problem is infeasible

Find an IIS (Irreducably Inconsistent Set of constraints) and write an IIS report to the GAMS solution listing if the model is found to be infeasible. IIS is available for LP problems only.

Default: 0

implbd (integer): implied bound cut generation

Determines whether or not implied bound cuts should be generated during optimization.

Default: 0

valuemeaning
-1 Do not generate implied bound cuts
0 Determined automatically
1 Generate implied bound cuts moderately
2 Generate implied bound cuts aggressively

interactive (boolean): allow interactive option setting after a Control-C

When set to yes, options can be set interactively after interrupting Cplex with a Control-C. Options are entered just as if they were being entered in the cplex.opt file. Control is returned to Cplex by entering continue. The optimization can be aborted by entering abort. This option can only be used when running from the command line. Moreover, the GAMS option InteractiveSolver needs to be set to 1.

Default: 0

intsollim (integer): maximum number of integer solutions

This option limits the MIP optimization to finding only this number of mixed integer solutions before stopping.

Default: large

itlim (integer): iteration limit

Synonym: iterlim

The iteration limit option sets the maximum number of iterations before the algorithm terminates, without reaching optimality. This Cplex option overrides the GAMS IterLim option. Any non-negative integer value is valid.

Default: GAMS IterLim

lbheur (boolean): local branching heuristic

This parameter lets you control whether Cplex applies a local branching heuristic to try to improve new incumbents found during a MIP search. By default, this parameter is off. If you turn it on, Cplex will invoke a local branching heuristic only when it finds a new incumbent. If Cplex finds multiple incumbents at a single node, the local branching heuristic will be applied only to the last one found.

Default: 0

valuemeaning
0 Off
1 Apply local branching heuristic to new incumbent

liftprojcuts (integer): lift-and-project cuts

Default: 0

valuemeaning
-1 Do not generate lift-and-project cuts
0 Determined automatically
1 Generate lift-and-project cuts moderately
2 Generate lift-and-project cuts aggressively
3 Generate lift-and-project cuts very aggressively

localimplied (integer): generation of locally valid implied bound cuts

Default: 0

valuemeaning
-1 Do not generate locally valid implied bound cuts
0 Determined automatically
1 Generate locally valid implied bound cuts moderately
2 Generate locally valid implied bound cuts aggressively
3 Generate locally valid implied bound cuts very aggressively

lpmethod (integer): algorithm to be used for LP problems

Specifies which LP algorithm to use. If left at the default value (0 for automatic), and a primal-feasible basis is available, primal simplex will be used. If no primal-feasible basis is available, and Threads is equal to 1, dual simplex will be used. If Threads is greater than 1 and no primal-feasible basis is available, the concurrent option will be used.

Sifting may be useful for problems with many more variables than equations.

The concurrent option runs multiple methods in parallel. The first thread uses dual simplex. The second thread uses barrier. The next thread uses primal simplex. Remaining threads are used by the barrier run. If the aspect ratio (number of columns versus number of rows) is large, and if more than 10 threads are available, then concurrent optimization also invokes sifting on the LP. The solution is returned by first method to finish.

Default: 0

valuemeaning
0 Automatic
1 Primal Simplex
2 Dual Simplex
3 Network Simplex
4 Barrier
5 Sifting
6 Concurrent

mcfcuts (integer): multi-commodity flow cut generation

Specifies whether Cplex should generate multi-commodity flow (MCF) cuts in a problem where Cplex detects the characteristics of a multi-commodity flow network with arc capacities. By default, Cplex decides whether or not to generate such cuts. To turn off generation of such cuts, set this parameter to -1. Cplex is able to recognize the structure of a network as represented in many real-world models. When it recognizes such a network structure, Cplex is able to generate cutting planes that usually help solve such problems. In this case, the cuts that Cplex generates state that the capacities installed on arcs pointing into a component of the network must be at least as large as the total flow demand of the component that cannot be satisfied by flow sources within the component.

Default: 0

valuemeaning
-1 Do not generate MCF cuts
0 Determined automatically
1 Generate MCF cuts moderately
2 Generate MCF cuts aggressively

memoryemphasis (boolean): reduces use of memory

This parameter lets you indicate to Cplex that it should conserve memory where possible. When you set this parameter to its non default value, Cplex will choose tactics, such as data compression or disk storage, for some of the data computed by the barrier and MIP optimizers. Of course, conserving memory may impact performance in some models. Also, while solution information will be available after optimization, certain computations that require a basis that has been factored (for example, for the computation of the condition number Kappa) may be unavailable.

Default: 0

valuemeaning
0 Do not conserve memory
1 Conserve memory where possible

mipdisplay (integer): progress display level

The amount of information displayed during MIP solution increases with increasing values of this option.

Default: 4

valuemeaning
0 No display
1 Display integer feasible solutions
2 Displays nodes under mipinterval control
3 Same as 2 but adds information on cuts
4 Same as 3 but adds LP display for the root node
5 Same as 3 but adds LP display for all nodes

mipemphasis (integer): MIP solution tactics

This option controls the tactics for solving a mixed integer programming problem.

Default: 0

valuemeaning
0 Balance optimality and feasibility
1 Emphasize feasibility over optimality
2 Emphasize optimality over feasibility
3 Emphasize moving the best bound
4 Emphasize hidden feasible solutions

mipinterval (integer): progress display interval

Controls the frequency of node logging when the parameter <a MIPDisplay is set higher than 1 (one). Frequency must be an integer; it may be 0 (zero), positive, or negative. By default, CPLEX displays new information in the node log during a MIP solve at relatively high frequency during the early stages of solving a MIP model, and adds lines to the log at progressively longer intervals as solving continues. In other words, CPLEX logs information frequently in the beginning and progressively less often as it works. When the value is a positive integer n, CPLEX displays new incumbents, plus it displays a new line in the log every n nodes. When the value is a negative integer n, CPLEX displays new incumbents, and the negative value determines how much processing CPLEX does before it displays a new line in the node log. A negative value close to zero means that CPLEX displays new lines in the log frequently. A negative value far from zero means that CPLEX displays new lines in the log less frequently. In other words, a negative value of this parameter contracts or dilates the interval at which CPLEX displays information in the node log.

Default: 0

mipkappastats (integer): MIP kappa computation

MIP kappa summarizes the distribution of the condition number of the optimal bases CPLEX encountered during the solution of a MIP model. That summary may let you know more about the numerical difficulties of your MIP model. Because MIP kappa (as a statistical distribution) requires CPLEX to compute the condition number of the optimal bases of the subproblems during branch-and-cut search, you can compute the MIP kappa only when CPLEX solves the subproblem with its simplex optimizer. In other words, in order to obtain results with this parameter, you can not use the sifting optimizer nor the barrier without crossover to solve the subproblems. See the parameters StartAlg and SubAlg.

Computing the kappa of a subproblem has a cost. In fact, computing MIP kappa for the basis matrices can be computationally expensive and thus generally slows down the solution of a problem. Therefore, the setting 0 (automatic) tells CPLEX generally not to compute MIP kappa, but in cases where the parameter NumericalEmphasis is turned on, CPLEX computes MIP kappa for a sample of subproblems. The value 1 (sample) leads to a negligible performance degradation on average, but can slow down the branch-and-cut exploration by as much as 10% on certain models. The value 2 (full) leads to a 2% performance degradation on average, but can significantly slow the branch-and-cut exploration on certain models. In practice, the value 1 (sample) is a good trade-off between performance and accuracy of statistics. If you need very accurate statistics, then use value 2 (full).

In case CPLEX is instructed to compute a MIP kappa distribution, the parameter Quality is automatically turned on.

Default: -1

valuemeaning
-1 No MIP kappa statistics; default
0 Automatic: let CPLEX decide
1 Compute MIP kappa for a sample of subproblems
2 Compute MIP kappa for all subproblems

mipordind (boolean): priority list on/off

Synonym: prioropt

Use priorities. Priorities should be assigned based on your knowledge of the problem. Variables with higher priorities will be branched upon before variables of lower priorities. This direction of the tree search can often dramatically reduce the number of nodes searched. For example, consider a problem with a binary variable representing a yes/no decision to build a factory, and other binary variables representing equipment selections within that factory. You would naturally want to explore whether or not the factory should be built before considering what specific equipment to purchased within the factory. By assigning a higher priority to the build/no build decision variable, you can force this logic into the tree search and eliminate wasted computation time exploring uninteresting portions of the tree. When set at 0 (default), the MIPOrdInd option instructs Cplex not to use priorities for branching. When set to 1, priority orders are utilized.

Note: Priorities are assigned to discrete variables using the .prior suffix in the GAMS model. Lower .prior values mean higher priority. The .prioropt model suffix has to be used to signal GAMS to export the priorities to the solver.

Default: GAMS PriorOpt

valuemeaning
0 Do not use priorities for branching
1 Priority orders are utilized

mipordtype (integer): priority order generation

This option is used to select the type of generic priority order to generate when no priority order is present.

Default: 0

valuemeaning
0 None
1 decreasing cost magnitude
2 increasing bound range
3 increasing cost per coefficient count

mipsearch (integer): search strategy for mixed integer programs

Sets the search strategy for a mixed integer program. By default, Cplex chooses whether to apply dynamic search or conventional branch and cut based on characteristics of the model.

Default: 0

valuemeaning
0 Automatic
1 Apply traditional branch and cut strategy
2 Apply dynamic search

mipstart (integer): use mip starting values

This option controls the use of advanced starting values for mixed integer programs. A setting of 1 indicates that the values should be checked to see if they provide an integer feasible solution before starting optimization.

Default: 0

valuemeaning
0 do not use the values
1 set discrete variable values and use auto mipstart level
2 set all variable values and use check feasibility mipstart level
3 set discrete variable values and use solve fixed mipstart level
4 set discrete variable values and use solve sub-MIP mipstart level
5 set discrete variable values and use solve repair-MIP mipstart level
6 set discrete variable values and use no checks at all

miptrace (string): filename of MIP trace file

miptracenode (integer): node interval when a trace record is written

Default: 100

miptracetime (real): time interval when a trace record is written

Default: 1

miqcpstrat (integer): MIQCP relaxation choice

This option controls how MIQCPs are solved. For some models, the setting 2 may be more effective than 1. You may need to experiment with this parameter to determine the best setting for your model.

Default: 0

valuemeaning
0 Automatic
1 QCP relaxation
Cplex will solve a QCP relaxation of the model at each node.
2 LP relaxation
Cplex will solve a LP relaxation of the model at each node.

mircuts (integer): mixed integer rounding cut generation

Determines whether or not to generate mixed integer rounding (MIR) cuts during optimization. At the default of 0, generation is continued only if it seems to be helping.

Default: 0

valuemeaning
-1 Do not generate MIR cuts
0 Determined automatically
1 Generate MIR cuts moderately
2 Generate MIR cuts aggressively

mpslongnum (boolean): MPS file format precision of numeric output

Determines the precision of numeric output in the MPS file formats. When this parameter is set to its default value 1 (one), numbers are written to MPS files in full-precision; that is, up to 15 significant digits may be written. The setting 0 (zero) writes files that correspond to the standard MPS format, where at most 12 characters can be used to represent a value. This limit may result in loss of precision.

Default: 1

valuemeaning
0 Use limited MPS precision
1 Use full-precision

names (boolean): load GAMS names into Cplex

This option causes GAMS names for the variables and equations to be loaded into Cplex. These names will then be used for error messages, log entries, and so forth. Setting names to no may help if memory is very tight.

Default: 1

netdisplay (integer): network display level

This option controls the log for network iterations.

Default: 2

valuemeaning
0 No network log.
1 Displays true objective values
2 Displays penalized objective values

netepopt (real): optimality tolerance for the network simplex method

This optimality tolerance influences the reduced-cost tolerance for optimality when using the network simplex method. This option setting governs how closely Cplex must approach the theoretically optimal solution.

Range: [1e-011, 0.1]

Default: 1e-006

neteprhs (real): feasibility tolerance for the network simplex method

This feasibility tolerance determines the degree to which the network simplex algorithm will allow a flow value to violate its bounds.

Range: [1e-011, 0.1]

Default: 1e-006

netfind (integer): attempt network extraction

Specifies the level of network extraction to be done.

Default: 2

valuemeaning
1 Extract pure network only
2 Try reflection scaling
3 Try general scaling

netitlim (integer): iteration limit for network simplex

Iteration limit for the network simplex method.

Default: large

netppriind (integer): network simplex pricing

Network simplex pricing algorithm. The default of 0 (currently equivalent to 3) shows best performance for most problems.

Default: 0

valuemeaning
0 Automatic
1 Partial pricing
2 Multiple partial pricing
3 Multiple partial pricing with sorting

nodefileind (integer): node storage file indicator

Specifies how node files are handled during MIP processing. Used when parameter WorkMem has been exceeded by the size of the branch and cut tree. If set to 0 when the tree memory limit is reached, optimization is terminated. Otherwise a group of nodes is removed from the in-memory set as needed. By default, Cplex transfers nodes to node files when the in-memory set is larger than 128 MBytes, and it keeps the resulting node files in compressed form in memory. At settings 2 and 3, the node files are transferred to disk. They are stored under a directory specified by parameter WorkDir and Cplex actively manages which nodes remain in memory for processing.

Default: 1

valuemeaning
0 No node files
1 Node files in memory and compressed
2 Node files on disk
3 Node files on disk and compressed

nodelim (integer): maximum number of nodes to solve

Synonym: nodlim

The maximum number of nodes solved before the algorithm terminates, without reaching optimality. This option overrides the GAMS NodLim model suffix. When this parameter is set to 0 (this is only possible through an option file), Cplex completes processing at the root; that is, it creates cuts and applies heuristics at the root. When this parameter is set to 1 (one), it allows branching from the root; that is, nodes are created but not solved.

Default: GAMS NodLim

nodesel (integer): node selection strategy

This option is used to set the rule for selecting the next node to process when backtracking.

Default: 1

valuemeaning
0 Depth-first search
This chooses the most recently created node.
1 Best-bound search
This chooses the unprocessed node with the best objective function for the associated LP relaxation.
2 Best-estimate search
This chooses the node with the best estimate of the integer objective value that would be obtained once all integer infeasibilities are removed.
3 Alternate best-estimate search

numericalemphasis (boolean): emphasizes precision in numerically unstable or difficult problems

This parameter lets you indicate to Cplex that it should emphasize precision in numerically difficult or unstable problems, with consequent performance trade-offs in time and memory.

Default: 0

valuemeaning
0 Off
1 Exercise extreme caution in computation

objdif (real): overrides GAMS Cheat parameter

Synonym: cheat

A means for automatically updating the cutoff to more restrictive values. Normally the most recently found integer feasible solution objective value is used as the cutoff for subsequent nodes. When this option is set to a positive value, the value will be subtracted from (added to) the newly found integer objective value when minimizing (maximizing). This forces the MIP optimization to ignore integer solutions that are not at least this amount better than the one found so far. The option can be adjusted to improve problem solving efficiency by limiting the number of nodes; however, setting this option at a value other than zero (the default) can cause some integer solutions, including the true integer optimum, to be missed. Negative values for this option will result in some integer solutions that are worse than or the same as those previously generated, but will not necessarily result in the generation of all possible integer solutions. This option overrides the GAMS Cheat parameter.

Default: 0

objllim (real): objective function lower limit

Setting a lower objective function limit will cause Cplex to halt the optimization process once the minimum objective function value limit has been exceeded.

Default: -1e+075

objrng (string): do objective ranging

Calculate sensitivity ranges for the specified GAMS variables. Unlike most options, ObjRng can be repeated multiple times in the options file. Sensitivity range information will be produced for each GAMS variable named. Specifying all will cause range information to be produced for all variables. Range information will be printed to the beginning of the solution listing in the GAMS listing file unless option RngRestart is specified.

Default: no objective ranging is done

objulim (real): objective function upper limit

Setting an upper objective function limit will cause Cplex to halt the optimization process once the maximum objective function value limit has been exceeded.

Default: 1e+075

optimalitytarget (integer): type of optimality that Cplex targets

This parameter sSpecifies the type of solution that CPLEX attempts to compute with respect to the optimality of that solution when CPLEX solves a continuous (QP) or mixed integer (MIQP) quadratic model. In other words, the variables of the model can be continuous or mixed integer and continuous; the objective function includes a quadratic term, and perhaps the objective function is not positive semi-definite (non PSD). This parameter does not apply to quadratically constrained mixed integer problems (MIQCP); that is, this parameter does not apply to mixed integer problems that include a quadratic term among the constraints.

Default: 0

valuemeaning
0 Automatic
CPLEX first attempts to compute a provably optimal solution. If CPLEX cannot compute a provably optimal solution because the objective function is not convex, CPLEX will return with an error (Q is not PSD).
1 Search for a globally optimal solution to a convex model
CPLEX searches for a globally optimal solution to a convex model. In problems of type QP or MIQP, this setting interacts with linearization switch QToLin for QP, MIQP
2 Search for a solution that satisfies first-order optimality conditions no optimality guarantee
CPLEX first attempt to compute a provably optimal solution. If CPLEX cannot compute a provably optimal solution because the objective function is not convex, CPLEX searches for a solution that satisfies first-order optimality conditions but is not necessarily globally optimal.
3 Search for a globally optimal solution regardless of convexity
If the problem type is QP, CPLEX first changes the problem type to MIQP. CPLEX then solves the problem (whether originally QP or MIQP) to global optimality. In problems of type QP or MIQP, this setting interacts with with linearization switch QToLin for QP, MIQP. With this setting information about dual values is not available for the solution.

parallelmode (integer): parallel optimization mode

Sets the parallel optimization mode. Possible modes are automatic, deterministic, and opportunistic.

In this context, deterministic means that multiple runs with the same model at the same parameter settings on the same platform will reproduce the same solution path and results. In contrast, opportunistic implies that even slight differences in timing among threads or in the order in which tasks are executed in different threads may produce a different solution path and consequently different timings or different solution vectors during optimization executed in parallel threads. When running with multiple threads, the opportunistic setting entails less synchronization between threads and consequently may provide better performance.

In deterministic mode, Cplex applies as much parallelism as possible while still achieving deterministic results. That is, when you run the same model twice on the same platform with the same parameter settings, you will see the same solution and optimization run.

More opportunities to exploit parallelism are available if you do not require determinism. In other words, Cplex can find more opportunities for parallelism if you do not require an invariant, repeatable solution path and precisely the same solution vector. To use all available parallelism, you need to select the opportunistic parallel mode. In this mode, Cplex will utilize all opportunities for parallelism in order to achieve best performance.

However, in opportunistic mode, the actual optimization may differ from run to run, including the solution time itself. A truly parallel deterministic algorithm is available only for MIP optimization. Only opportunistic parallel algorithms (barrier and concurrent optimizers) are available for continuous models. (Each of the simplex algorithms runs sequentially on a continuous model.) Consequently, when parallel mode is set to deterministic, both barrier and concurrent optimizers are restricted to run only sequentially, not in parallel.

A GAMS/Cplex run will use deterministic mode unless explicitly specified.

If ParallelMode is explicitly set to 0 (automatic) the settings of this parallel mode parameter interact with settings of the Threads parameter. Let the result number of threads available to Cplex be n (note that negative values for the threads parameter are possible to exclude work on some cores).

n=0: Cplex uses maximum number of threads (determined by the computing platform) in deterministic mode unless ParallelMode is set to -1 (opportunistic).

n=1: Cplex runs sequential.

n>1: Cplex uses maximum number of threads (determined by the computing platform) in opportunistic mode unless ParallelMode is set to 1 (deterministic).

Here is is list of possible value:

Default: 1

valuemeaning
-1 Enable opportunistic parallel search mode
0 Automatic
1 Enable deterministic parallel search mode

perind (boolean): force initial perturbation

Perturbation Indicator. If a problem automatically perturbs early in the solution process, consider starting the solution process with a perturbation by setting PerInd to 1. Manually perturbing the problem will save the time of first allowing the optimization to stall before activating the perturbation mechanism, but is useful only rarely, for extremely degenerate problems.

Default: 0

valuemeaning
0 not automatically perturbed
1 automatically perturbed

perlim (integer): number of stalled iterations before perturbation

Perturbation limit. The number of stalled iterations before perturbation is invoked. The default value of 0 means the number is determined automatically.

Default: 0

polishafterdettime (real): deterministic time before starting to polish a feasible solution

Default: 1e+075

polishafterepagap (real): absolute MIP gap before starting to polish a feasible solution

Solution polishing can yield better solutions in situations where good solutions are otherwise hard to find. More time-intensive than other heuristics, solution polishing is actually a variety of branch-and-cut that works after an initial solution is available. In fact, it requires a solution to be available for polishing, either a solution produced by branch-and-cut, or a MIP start supplied by a user. Because of the high cost entailed by solution polishing, it is not called throughout branch-and-cut like other heuristics. Instead, solution polishing works in a second phase after a first phase of conventional branch-and-cut. As an additional step after branch-and-cut, solution polishing can improve the best known solution. As a kind of branch-and-cut algorithm itself, solution polishing focuses solely on finding better solutions. Consequently, it may not prove optimality, even if the optimal solution has indeed been found. Like the RINS heuristic, solution polishing explores neighborhoods of previously found solutions by solving subMIPs.

Sets an absolute MIP gap (that is, the difference between the best integer objective and the objective of the best node remaining) after which CPLEX stops branch-and-cut and begins polishing a feasible solution. The default value is such that CPLEX does not invoke solution polishing by default.

Default: 0

polishafterepgap (real): relative MIP gap before starting to polish a solution

Sets a relative MIP gap after which CPLEX will stop branch-and-cut and begin polishing a feasible solution. The default value is such that CPLEX does not invoke solution polishing by default.

Default: 0

polishafterintsol (integer): MIP integer solutions to find before starting to polish a feasible solution

Sets the number of integer solutions to find before CPLEX stops branch-and-cut and begins to polish a feasible solution. The default value is such that CPLEX does not invoke solution polishing by default.

Default: 2100000000

polishafternode (integer): nodes to process before starting to polish a feasible solution

Sets the number of nodes processed in branch-and-cut before CPLEX starts solution polishing, if a feasible solution is available.

Default: 2100000000

polishaftertime (real): time before starting to polish a feasible solution

Tells CPLEX how much time in seconds to spend during mixed integer optimization before CPLEX starts polishing a feasible solution. The default value is such that CPLEX does not start solution polishing by default.

Default: 1e+075

populatelim (integer): limit of solutions generated for the solution pool by populate method

Limits the number of solutions generated for the solution pool during each call to the populate procedure. Populate stops when it has generated PopulateLim solutions. A solution is counted if it is valid for all filters (see DivFlt and consistent with the relative and absolute pool gap parameters (see SolnPoolGap and SolnPoolAGap), and has not been rejected by the incumbent checking routine (see UserIncbCall), whether or not it improves the objective of the model. This parameter does not apply to MIP optimization generally; it applies only to the populate procedure.

If you are looking for a parameter to control the number of solutions stored in the solution pool, consider the parameter SolnPoolCapacity instead.

Populate will stop before it reaches the limit set by this parameter if it reaches another limit, such as a time or node limit set by the user.

Default: 20

ppriind (integer): primal simplex pricing

Pricing algorithm. Likely to show the biggest impact on performance. Look at overall solution time and the number of Phase I and total iterations as a guide in selecting alternate pricing algorithms. If you are using the dual Simplex method use DPriInd to select a pricing algorithm. If the number of iterations required to solve your problem is approximately the same as the number of rows in your problem, then you are doing well. Iteration counts more than three times greater than the number of rows suggest that improvements might be possible.

Default: 0

valuemeaning
-1 Reduced-cost pricing
This is less compute intensive and may be preferred if the problem is small or easy. This option may also be advantageous for dense problems (say 20 to 30 nonzeros per column).
0 Hybrid reduced-cost and Devex pricing
1 Devex pricing
This may be useful for more difficult problems which take many iterations to complete Phase I. Each iteration may consume more time, but the reduced number of total iterations may lead to an overall reduction in time. Tenfold iteration count reductions leading to threefold speed improvements have been observed. Do not use devex pricing if the problem has many columns and relatively few rows. The number of calculations required per iteration will usually be disadvantageous.
2 Steepest edge pricing
If devex pricing helps, this option may be beneficial. Steepest-edge pricing is computationally expensive, but may produce the best results on exceptionally difficult problems.
3 Steepest edge pricing with slack initial norms
This reduces the computationally intensive nature of steepest edge pricing.
4 Full pricing

predual (integer): give dual problem to the optimizer

Solve the dual. Some linear programs with many more rows than columns may be solved faster by explicitly solving the dual. The PreDual option will cause Cplex to solve the dual while returning the solution in the context of the original problem. This option is ignored if presolve is turned off.

Default: 0

valuemeaning
-1 do not give dual to optimizer
0 automatic
1 give dual to optimizer

preind (boolean): turn presolver on/off

Perform Presolve. This helps most problems by simplifying, reducing and eliminating redundancies. However, if there are no redundancies or opportunities for simplification in the model, if may be faster to turn presolve off to avoid this step. On rare occasions, the presolved model, although smaller, may be more difficult than the original problem. In this case turning the presolve off leads to better performance. Specifying 0 turns the aggregator off as well.

Default: 1

prelinear (boolean): linear reduction indicator

If only linear reductions are performed, each variable in the original model can be expressed as a linear form of variables in the presolved model.

Default: 1

prepass (integer): number of presolve applications to perform

Number of MIP presolve applications to perform. By default, Cplex determines this automatically. Specifying 0 turns off the presolve but not the aggregator. Set PreInd to 0 to turn both off.

Default: -1

valuemeaning
-1 Determined automatically
0 No presolve
>0 Number of MIP presolve applications to perform

preslvnd (integer): node presolve selector

Indicates whether node presolve should be performed at the nodes of a mixed integer programming solution. Node presolve can significantly reduce solution time for some models. The default setting is generally effective.

Default: 0

valuemeaning
-1 No node presolve
0 Automatic
1 Force node presolve
2 Perform probing on integer-infeasible variables

pricelim (integer): pricing candidate list

Size for the pricing candidate list. Cplex dynamically determines a good value based on problem dimensions. Only very rarely will setting this option manually improve performance. Any non-negative integer values are valid.

Default: 0, in which case it is determined automatically

printoptions (boolean): list values of all options to GAMS listing file

Write the values of all options to the GAMS listing file. Valid values are no or yes.

Default: 0

probe (integer): perform probing before solving a MIP

Determines the amount of probing performed on a MIP. Probing can be both very powerful and very time consuming. Setting the value to 1 can result in dramatic reductions or dramatic increases in solution time depending on the particular model.

Default: 0

valuemeaning
-1 No probing
0 Automatic
1 Limited probing
2 More probing
3 Full probing

probedettime (real): deterministic time spent probing

Default: 1e+075

probetime (real): time spent probing

Limits the amount of time in seconds spent probing.

Default: 1e+075

Determines whether Cplex will attempt to adjust a MIQP formulation, in which all the variables appearing in the quadratic term are binary. When this feature is active, adjustments will be made to the elements of a quadratic matrix that is not nominally positive semi-definite (PSD, as required by Cplex for all QP formulations), to make it PSD, and will also attempt to tighten an already PSD matrix for better numerical behavior. The default setting of 1 means yes but you can turn it off if necessary; most models should benefit from the default setting.

Default: 1

valuemeaning
0 Off
1 On

qpmethod (integer): algorithm to be used for QP problems

Specifies which QP algorithm to use.

At the default of 0 (automatic), barrier is used for QP problems and dual simplex for the root relaxation of MIQP problems.

Default: 0

valuemeaning
0 Automatic
1 Primal Simplex
2 Dual Simplex
3 Network Simplex
4 Barrier
5 Sifting
6 Concurrent dual, barrier, and primal

qtolin (integer): linearization of the quadratic terms in the objective function of a QP or MIQP model

This parameter switches on or off linearization of the quadratic terms in the objective function of a quadratic program or of a mixed integer quadratic program.

In a convex mixed integer quadratic program, this parameter controls whether Cplex linearizes the product of binary variables in the objective function during presolve. In a nonconvex quadratic program or mixed integer quadratic program solved to global optimality according to OptimalityTarget, this parameter controls how Cplex linearizes the product of bounded variables in the objective function during presolve.

This parameter interacts with the existing parameter OptimalityTarget: When the solution target type is set to 1 (that is, Cplex searches for a globally optimal solution to a convex model), then in a convex MIQP, this parameter tells Cplex to replace the product of a binary variable and a bounded linear variable by a linearly constrained variable. When the solution target type is set to 3, then in a nonconvex QP or nonconvex MIQP, this parameter controls the initial relaxation.

Default: -1

valuemeaning
-1 Automatic
0 Off, Cplex does not linearize quadratic terms in the objective
1 On, Cplex linearizes quadratic terms in the objective

quality (boolean): write solution quality statistics

Write solution quality statistics to the listing file. If set to yes, the statistics appear after the Solve Summary and before the Solution Listing.

Default: 0

rampupdettimelimit (real): limits the amount of time in deterministic ticks spent during ramp up of distributed parallel optimization

This parameters specifies a limit on the amount of time measured in deterministic ticks to spend in the ramp up phase of distributed parallel optimization. This parameter is effective only when the ramp up duration parameter has a value of 0 (zero) or 1 (one), where 0 (zero) designates the default automatic value that CPLEX decides the ramp up duration, and 1 (one) designates dynamic ramp up. See ramp up duration for more detail about the conditions for time limits in ramp up.

The value 0 (zero) specifies that no time should be spent in ramp up.

Any positive number strictly greater than zero specifies a time limit in deterministic ticks.

Default: 1e+075

rampupduration (integer): customizes ramp up for distributed parallel optimization

During the ramp up phase of distributed parallel optimization, each worker applies different parameter settings to the same problem as the other workers. In other words, there is a competition among the workers to process the greatest number of nodes in parallel in the search tree of the distributed problem. At any given time, each worker is a candidate to be the winner of this competition.

This parameter enables you to customize the ramp up phase for your model. Its value has an impact on both timing parameters: time spent in ramp up during distributed parallel optimization and deterministic time spent in ramp up during distributed parallel optimization.

When the value of this parameter is -1, CPLEX turns off ramp up and ignores both of the parameters time spent in ramp up during distributed parallel optimization and deterministic time spent in ramp up during distributed parallel optimization. CPLEX directly begins distributed parallel tree search.

When the value of this parameter is 2, CPLEX observes ramp up with an infinite horizon. CPLEX ignores both of the parameters time spent in ramp up during distributed parallel optimization and deterministic time spent in ramp up during distributed parallel optimization. CPLEX never switches to distributed parallel tree search. This situation is also known as concurrent mixed integer programming (concurrent MIP).

When the value of this parameter is 1 (one), CPLEX considers the values of both time spent in ramp up during distributed parallel optimization and deterministic time spent in ramp up during distributed parallel optimization.

• If both ramp up timing parameters are at their default value (effectively, an infinite amount of time), then CPLEX terminates ramp up according to internal criteria before switching to distributed parallel tree search.
• If one or both of the ramp up timing parameters is set to a non default finite value, CPLEX observes that time limit by executing ramp up for that given amount of time. If the two time limits differ, CPLEX observes the smaller time limit before terminating ramp up and switching to distributed parallel tree search.

When the value of this parameter remains at its default, 0 (zero), CPLEX considers the values of both timing parameters time spent in ramp up during distributed parallel optimization and deterministic time spent in ramp up during distributed parallel optimization.

• If at least one of the ramp up timing parameters is set to a finite value, then CPLEX behaves as it does when the value of this parameter is 1 (one): first ramping up, then switching to distributed parallel tree search.
• If both of the ramp up timing parameters are at their default value (effectively an infinite amount of time), then CPLEX behaves as it does when the value of this parameter is 2: concurrent MIP.

Default: 0

valuemeaning
-1 Turns off ramp up
0 Automatic
1 Dynamically switch to distributed tree search
2 Infinite horizon for ramp up AKA concurrent MIP optimization

rampuptimelimit (real): limits the amount of time in seconds spent during ramp up of distributed parallel optimization

This parameters specifies a limit on the amount of time in seconds to spend in the ramp up phase of distributed parallel optimization. This parameter is effective only when the ramp up duration parameter has a value of 0 (zero) or 1 (one), where 0 (zero) designates the default automatic value that CPLEX decides the ramp up duration, and 1 (one) designates dynamic ramp up. See ramp up duration for more detail about the conditions for time limits in ramp up.

The value 0 (zero) specifies that no time should be spent in ramp up.

Any positive number strictly greater than zero specifies a time limit in seconds.

Default: 1e+075

randomseed (integer): sets the random seed differently for diversity of solutions

Default: changes with each Cplex release

The GAMS/Cplex solution pool options cover the basic use of diversity and range filters for producing multiple solutions. If you need multiple filters, weights on diversity filters or other advanced uses of solution pool filters, you could produce a Cplex filter file with your favorite editor or the GAMS Put Facility and read this into GAMS/Cplex using this option.

reduce (integer): primal and dual reduction type

Determines whether primal reductions, dual reductions, or both, are performed during preprocessing. It is occasionally advisable to do only one or the other when diagnosing infeasible or unbounded models.

Default: 3

valuemeaning
0 No primal or dual reductions
1 Only primal reductions
2 Only dual reductions
3 Both primal and dual reductions

reinv (integer): refactorization frequency

Refactorization Frequency. This option determines the number of iterations between refactorizations of the basis matrix. The default should be optimal for most problems. Cplex's performance is relatively insensitive to changes in refactorization frequency. Only for extremely large, difficult problems should reducing the number of iterations between refactorizations be considered. Any non-negative integer value is valid.

Default: 0, in which case it is determined automatically

relaxfixedinfeas (boolean): accept small infeasibilties in the solve of the fixed problem

Sometimes the solution of the fixed problem of a MIP does not solve to optimality due to small (dual) infeasibilities. The default behavior of the GAMS/Cplex link is to return the primal solution values only. If the option is set to 1, the small infeasibilities are ignored and a full solution including the dual values are reported back to GAMS.

Default: 0

valuemeaning
0 Off
1 On

relaxpreind (integer): presolve for initial relaxation on/off

This option will cause the Cplex presolve to be invoked for the initial relaxation of a mixed integer program (according to the other presolve option settings). Sometimes, additional reductions can be made beyond any MIP presolve reductions that may already have been done.

Default: -1

valuemeaning
-1 Automatic
0 do not presolve initial relaxation
1 use presolve on initial relaxation

relobjdif (real): relative cheat parameter

The relative version of the ObjDif option. Ignored if ObjDif is non-zero.

Default: 0

repairtries (integer): try to repair infeasible MIP start

This parameter lets you indicate to Cplex whether and how many times it should try to repair an infeasible MIP start that you supplied. The parameter has no effect if the MIP start you supplied is feasible. It has no effect if no MIP start was supplied.

Default: 0

valuemeaning
-1 None: do not try to repair
0 Automatic
>0 Maximum tries to perform

repeatpresolve (integer): reapply presolve at root after preprocessing

This integer parameter tells Cplex whether to re-apply presolve, with or without cuts, to a MIP model after processing at the root is otherwise complete.

Default: -1

valuemeaning
-1 Automatic
0 Turn off represolve
1 Represolve without cuts
2 Represolve with cuts
3 Represolve with cuts and allow new root cuts

rerun (string): rerun problem if presolve infeasible or unbounded

The Cplex presolve can sometimes diagnose a problem as being infeasible or unbounded. When this happens, GAMS/Cplex can, in order to get better diagnostic information, rerun the problem with presolve turned off. The GAMS solution listing will then mark variables and equations as infeasible or unbounded according to the final solution returned by the simplex algorithm. The IIS option can be used to get even more diagnostic information. The rerun option controls this behavior. Valid values are auto, yes, no and nono. The value of auto is equivalent to no if names are successfully loaded into Cplex and option IIS is set to no. In that case the Cplex messages from presolve help identify the cause of infeasibility or unboundedness in terms of GAMS variable and equation names. If names are not successfully loaded, rerun defaults to yes. Loading of GAMS names into Cplex is controlled by option Names. The value of nono only affects MIP models for which Cplex finds a feasible solution in the branch-and-bound tree but the fixed problem turns out to be infeasible. In this case the value nono also disables the rerun without presolve, while the value of no still tries this run. Feasible integer solution but an infeasible fixed problem happens in few cases and mostly with badly scaled models. If you experience this try more aggressive scaling (ScaInd) or tightening the integer feasibility tolerance EPInt. If the fixed model is infeasible only the primal solution is returned to GAMS. You can recognize this inside GAMS by checking the marginal of the objective defining constraint which is always nonzero.

Default: yes

valuemeaning
auto Automatic
yes Rerun infeasible models with presolve turned off
no Do not rerun infeasible models
nono Do not rerun infeasible fixed MIP models

rhsrng (string): do right-hand-side ranging

Calculate sensitivity ranges for the specified GAMS equations. Unlike most options, RHSRng can be repeated multiple times in the options file. Sensitivity range information will be produced for each GAMS equation named. Specifying all will cause range information to be produced for all equations. Range information will be printed to the beginning of the solution listing in the GAMS listing file unless option RngRestart is specified.

Default: no right-hand-side ranging is done

rinsheur (integer): relaxation induced neighborhood search frequency

Cplex implements a heuristic known a Relaxation Induced Neighborhood Search (RINS) for MIP and MIQCP problems. RINS explores a neighborhood of the current incumbent to try to find a new, improved incumbent. It formulates the neighborhood exploration as a MIP, a subproblem known as the subMIP, and truncates the subMIP solution by limiting the number of nodes explored in the search tree.

Parameter RINSHeur controls how often RINS is invoked. A value of 100, for example, means that RINS is invoked every hundredth node in the tree.

Default: 0

valuemeaning
-1 Disable RINS
0 Automatic

rngrestart (string): write GAMS readable ranging information file

Write ranging information, in GAMS readable format, to the file named. Options ObjRng and RHSRng are used to specify which GAMS variables or equations are included.

Default: ranging information is printed to the listing file

rtlcuts (integer): Reformulation Linearization Technique (RLT) cuts

This parameter controls the addition of cuts based on the Reformulation Linearization Technique (RLT) for nonconvex quadratic programs (QP) or mixed integer quadratic programs (MIQP) solved to global optimality. That is, the OptimalityTarget parameter must be set to 3. The RTLCuts option is not controlled by the option Cuts.

Default: 0

valuemeaning
-1 Do not generate RTL cuts
0 Determined automatically
1 Generate RTL cuts moderately
2 Generate RTL cuts aggressively
3 Generate RTL cuts very aggressively

scaind (integer): matrix scaling on/off

This option influences the scaling of the problem matrix.

Default: 0

valuemeaning
-1 No scaling
0 Standard scaling
An equilibration scaling method is implemented which is generally very effective.
1 Modified, more aggressive scaling method
This method can produce improvements on some problems. This scaling should be used if the problem is observed to have difficulty staying feasible during the solution process.

siftalg (integer): sifting subproblem algorithm

Sets the algorithm to be used for solving sifting subproblems.

Default: 0

valuemeaning
0 Automatic
1 Primal simplex
2 Dual simplex
3 Network simplex
4 Barrier

siftdisplay (integer): sifting display level

Determines the amount of sifting progress information to be displayed.

Default: 1

valuemeaning
0 No display
1 Display major iterations
2 Display LP subproblem information

siftitlim (integer): limit on sifting iterations

Sets the maximum number of sifting iterations that may be performed if convergence to optimality has not been reached.

Default: large

simdisplay (integer): simplex display level

This option controls what Cplex reports (normally to the screen) during optimization. The amount of information displayed increases as the setting value increases.

Default: 1

valuemeaning
0 No iteration messages are issued until the optimal solution is reported
1 An iteration log message will be issued after each refactorization
Each entry will contain the iteration count and scaled infeasibility or objective value.
2 An iteration log message will be issued after each iteration
The variables, slacks and artificials entering and leaving the basis will also be reported.

singlim (integer): limit on singularity repairs

The singularity limit setting restricts the number of times Cplex will attempt to repair the basis when singularities are encountered. Once the limit is exceeded, Cplex replaces the current basis with the best factorizable basis that has been found. Any non-negative integer value is valid.

Default: 10

solnpool (string): solution pool file name

The solution pool enables you to generate and store multiple solutions to a MIP problem. The option expects a GDX filename. This GDX file name contains the information about the different solutions generated by Cplex. Inside your GAMS program you can process the GDX file and read the different solution point files. Please check the GAMS/Cplex solver guide document and the example model solnpool.gms from the GAMS model library.

solnpoolagap (real): absolute tolerance for the solutions in the solution pool

Sets an absolute tolerance on the objective bound for the solutions in the solution pool. Solutions that are worse (either greater in the case of a minimization, or less in the case of a maximization) than the objective of the incumbent solution according to this measure are not kept in the solution pool.

Values of the solution pool absolute gap and the solution pool relative gap SolnPoolGap may differ: For example, you may specify that solutions must be within 15 units by means of the solution pool absolute gap and also within 1% of the incumbent by means of the solution pool relative gap. A solution is accepted in the pool only if it is valid for both the relative and the absolute gaps.

The solution pool absolute gap parameter can also be used as a stopping criterion for the populate procedure: if populate cannot enumerate any more solutions that satisfy this objective quality, then it will stop. In the presence of both an absolute and a relative solution pool gap parameter, populate will stop when the smaller of the two is reached.

Default: 1e+075

solnpoolcapacity (integer): limits of solutions kept in the solution pool

Limits the number of solutions kept in the solution pool. At most, SolnPoolCapacity solutions will be stored in the pool. Superfluous solutions are managed according to the replacement strategy set by the solution pool replacement parameter SolnPoolReplace.

The optimization (whether by MIP optimization or the populate procedure) will not stop if more than SolnPoolCapacity are generated. Instead, stopping criteria are regular node and time limits and PopulateLim, SolnPoolGap and SolnPoolAGap.

Default: 2100000000

solnpoolgap (real): relative tolerance for the solutions in the solution pool

Sets a relative tolerance on the objective bound for the solutions in the solution pool. Solutions that are worse (either greater in the case of a minimization, or less in the case of a maximization) than the incumbent solution by this measure are not kept in the solution pool.

Values of the solution pool absolute gap SolnPoolAGap and the solution pool relative gap may differ: For example, you may specify that solutions must be within 15 units by means of the solution pool absolute gap and within 1% of the incumbent by means of the solution pool relative gap. A solution is accepted in the pool only if it is valid for both the relative and the absolute gaps.

The solution pool relative gap parameter can also be used as a stopping criterion for the populate procedure: if populate cannot enumerate any more solutions that satisfy this objective quality, then it will stop. In the presence of both an absolute and a relative solution pool gap parameter, populate will stop when the smaller of the two is reached.

Default: 1e+075

solnpoolintensity (integer): solution pool intensity for ability to produce multiple solutions

Controls the trade-off between the number of solutions generated for the solution pool and the amount of time or memory consumed. This parameter applies both to MIP optimization and to the populate procedure.

Values from 1 to 4 invoke increasing effort to find larger numbers of solutions. Higher values are more expensive in terms of time and memory but are likely to yield more solutions.

Default: 0

valuemeaning
0 Automatic
Its default value, 0 , lets Cplex choose which intensity to apply.
1 Mild: generate few solutions quickly
For value 1, the performance of MIP optimization is not affected. There is no slowdown and no additional consumption of memory due to this setting. However, populate will quickly generate only a small number of solutions. Generating more than a few solutions with this setting will be slow. When you are looking for a larger number of solutions, use a higher value of this parameter.
2 Moderate: generate a larger number of solutions
For value 2, some information is stored in the branch and cut tree so that it is easier to generate a larger number of solutions. This storage has an impact on memory used but does not lead to a slowdown in the performance of MIP optimization. With this value, calling populate is likely to yield a number of solutions large enough for most purposes. This value is a good choice for most models.
3 Aggressive: generate many solutions and expect performance penalty
For value 3, the algorithm is more aggressive in computing and storing information in order to generate a large number of solutions. Compared to values 1 and 2, this value will generate a larger number of solutions, but it will slow MIP optimization and increase memory consumption. Use this value only if setting this parameter to 2 does not generate enough solutions.
4 Very aggressive: enumerate all practical solutions
For value 4, the algorithm generates all solutions to your model. Even for small models, the number of possible solutions is likely to be huge; thus enumerating all of them will take time and consume a large quantity of memory.

solnpoolmerge (string): solution pool file name for merged solutions

Similar to solnpool this option enables you to generate and store multiple solutions to a MIP problem. The option expects a GDX filename. This GDX file contains all variables with an additional first index (determined through SolnPoolPrefix) as parameters (Cplex only reports the primal solution). Inside your GAMS program you can process the GDX file and read all solutions in one read operation. Please check the GAMS/Cplex solver guide document for further solution pool options and the example model solmpool.gms from the GAMS model library.

solnpoolnumsym (integer): maximum number of variable symbols when writing merged solutions

Default: 10

solnpoolpop (integer): methods to populate the solution pool

Regular MIP optimization automatically adds incumbents to the solution pool as they are discovered. Cplex also provides a procedure known as populate specifically to generate multiple solutions. You can invoke this procedure either as an alternative to the usual MIP optimizer or as a successor to the MIP optimizer. You can also invoke this procedure many times in a row in order to explore the solution space differently (see option SolnPoolPopRepeat). In particular, you may invoke this procedure multiple times to find additional solutions, especially if the first solutions found are not satisfactory.

Default: 1

valuemeaning
1 Just collect the incumbents found during regular optimization
2 Calls the populate procedure

solnpoolpopdel (string): file with solution numbers to delete from the solution pool

After the GAMS program specified in SolnPoolPopRepeat determined to continue the search for alternative solutions, the file specified by this option is read in. The solution numbers present in this file will be delete from the solution pool before the populate routine is called again. The file is automatically deleted by the GAMS/Cplex link after processing.

solnpoolpoprepeat (string): method to decide if populating the solution should be repeated

After the termination of the populate procedure (see option SolnPoolPop). The GAMS program specified in this option will be called which can examine the solutions in the solution pool and can decide to run the populate procedure again. If the GAMS program terminates normally (not compilation or execution time error) the search for new alternative solutions will be repeated.

solnpoolprefix (string): file name prefix for GDX solution files

Default: soln

solnpoolreplace (integer): strategy for replacing a solution in the solution pool

Default: 0

valuemeaning
0 Replace the first solution (oldest) by the most recent solution; first in, first out
1 Replace the solution which has the worst objective
2 Replace solutions in order to build a set of diverse solutions

solutiontype (integer): type of solution (basic or non basic) for an LP or QP

Specifies the type of solution (basic or non basic) that CPLEX attempts to compute for a linear program (LP) or for a quadratic program (QP). In this context, basic means having to do with the basis, and non basic applies to the variables and constraints not participating in the basis.

By default (that is, when the value of this parameter is 0 (zero) automatic), CPLEX seeks a basic solution (that is, a solution with a basis) for all linear programs (LP) and for all quadratic programs (QP).

When the value of this parameter is 1 (one), CPLEX seeks a basic solution, that is, a solution that includes a basis with a basic status for variables and constraints. In other words, CPLEX behaves the same way for the values 0 (zero) and 1 (one) of this parameter.

When the value of this parameter is 2, CPLEX seeks a pair of primal-dual solution vectors. This setting does not prevent CPLEX from producing status information, but in seeking a pair of primal-dual solution vectors, CPLEX possibly may not produce basic status information; that is, it is possible that CPLEX does not produce status information about which variables and constraints participate in the basis at this setting.

Do not use the deprecated value -1 (minus one) of the parameter barrier crossover algorithm to turn off crossover of the barrier algorithm but use this parameter to indicate that a primal-dual pair is sufficient.

Default: 0

valuemeaning
0 Automatic
1 Basic solution
2 primal-dual pair

solvefinal (boolean): switch to solve the problem with fixed discrete variables

Sometimes the solution process after the branch-and-cut that solves the problem with fixed discrete variables takes a long time and the user is interested in the primal values of the solution only. In these cases, solvefinal can be used to turn this final solve off. Without the final solve no proper marginal values are available and only zeros are returned to GAMS.

Default: 1

valuemeaning
0 Do not solve the fixed problem
1 Solve the fixed problem and return duals

startalg (integer): MIP starting algorithm

Selects the algorithm to use for the initial relaxation of a MIP.

Default: 0

valuemeaning
0 Automatic
1 Primal simplex
2 Dual simplex
3 Network simplex
4 Barrier
5 Sifting
6 Concurrent

strongcandlim (integer): size of the candidates list for strong branching

Limit on the length of the candidate list for strong branching (VarSel = 3).

Default: 10

strongitlim (integer): limit on iterations per branch for strong branching

Limit on the number of iterations per branch in strong branching (VarSel = 3). The default value of 0 causes the limit to be chosen automatically which is normally satisfactory. Try reducing this value if the time per node seems excessive. Try increasing this value if the time per node is reasonable but Cplex is making little progress.

Default: 0

subalg (integer): algorithm for subproblems

Strategy for solving linear sub-problems at each node.

Default: 0

valuemeaning
0 Automatic
1 Primal simplex
2 Dual simplex
3 Network optimizer followed by dual simplex
4 Barrier with crossover
5 Sifting

submipnodelim (integer): limit on number of nodes in an RINS subMIP

Controls the number of nodes explored in an RINS subMIP. See option RINSHeur.

Default: 500

symmetry (integer): symmetry breaking cuts

Determines whether symmetry breaking cuts may be added, during the preprocessing phase, to a MIP model.

Default: -1

valuemeaning
-1 Automatic
0 Turn off symmetry breaking
1 Moderate level of symmetry breaking
2 Aggressive level of symmetry breaking
3 Very aggressive level of symmetry breaking
4 Highly aggressive level of symmetry breaking
5 Extremely aggressive level of symmetry breaking

Default number of parallel threads allowed for any solution method. Non-positive values are interpreted as the number of cores to leave free so setting threads to 0 uses all available cores while setting threads to -1 leaves one core free for other tasks. Cplex does not understand negative values for the threads parameter. GAMS/Cplex will translate this is a non-negative number by applying the following formula: max(1,number of cores-|threads|)

Default: GAMS Threads

tilim (real): overrides the GAMS ResLim option

Synonym: reslim

The time limit setting determines the amount of time in seconds that Cplex will continue to solve a problem. This Cplex option overrides the GAMS ResLim option. Any non-negative value is valid.

Default: GAMS ResLim

trelim (real): maximum space in memory for tree

Sets an absolute upper limit on the size (in megabytes) of the branch and cut tree. If this limit is exceeded, Cplex terminates optimization.

Default: 1e+075

tuning (string): invokes parameter tuning tool

Invokes the Cplex parameter tuning tool. The mandatory value following the keyword specifies a GAMS/Cplex option file. All options found in this option file will be used but not modified during the tuning. A sequence of file names specifying existing problem files may follow the option file name. The files can be in LP, MPS or SAV format. Cplex will tune the parameters either for the problem provided by GAMS (no additional problem files specified) or for the suite of problems listed after the GAMS/Cplex option file name without considering the problem provided by GAMS (use option WriteSav to create a SAV file of the problem provided by GAMS and include this name in the list of problems). The result of such a run is the updated GAMS/Cplex option file with a tuned set of parameters. The solver and model status returned to GAMS will be NORMAL COMPLETION and NO SOLUTION. More details on Cplex tuning can be found on IBM's web page. Tuning is incompatible with the BCH facility and other advanced features of GAMS/Cplex.

tuningdettilim (real): tuning deterministic time limit per model or suite

Default: 1e+007

tuningdisplay (integer): level of information reported by the tuning tool

Specifies the level of information reported by the tuning tool as it works.

Default: 1

valuemeaning
0 Turn off display
1 Display standard minimal reporting
2 Display standard report plus parameter settings being tried
3 Display exhaustive report and log

tuningmeasure (integer): measure for evaluating progress for a suite of models

Controls the measure for evaluating progress when a suite of models is being tuned. Choices are mean average and minmax of time to compare different parameter sets over a suite of models

Default: 1

valuemeaning
1 mean average
2 minmax

tuningrepeat (integer): number of times tuning is to be repeated on perturbed versions

Specifies the number of times tuning is to be repeated on perturbed versions of a given problem. The problem is perturbed automatically by Cplex permuting its rows and columns. This repetition is helpful when only one problem is being tuned, as repeated perturbation and re-tuning may lead to more robust tuning results. This parameter applies to only one problem in a tuning session.

Default: 1

tuningtilim (real): tuning time limit per model or suite

Sets a time limit per model and per test set (that is, suite of models).

As an example, suppose that you want to spend an overall amount of time tuning the parameter settings for a given model, say, 2000 seconds. Also suppose that you want Cplex to make multiple attempts within that overall time limit to tune the parameter settings for your model. Suppose further that you want to set a time limit on each of those attempts, say, 200 seconds per attempt. In this case you need to specify an overall time limit of 2000 using GAMS option reslim or Cplex option TiLim and tuningtilim to 200.

Default: 0.2*GAMS ResLim

usercutcall (string): the GAMS command line to call the cut generator

usercutfirst (integer): calls the cut generator for the first n nodes

Default: 10

usercutfreq (integer): determines the frequency of the cut generator model calls

Default: 10

usercutinterval (integer): determines the interval when to apply the multiplier for the frequency of the cut generator model calls

Default: 100

usercutmult (integer): determines the multiplier for the frequency of the cut generator model calls

Default: 2

usercutnewint (boolean): calls the cut generator if the solver found a new integer feasible solution

Default: 1

usergdxin (string): the name of the GDX file read back into Cplex

Default: bchin.gdx

usergdxname (string): the name of the GDX file exported from the solver with the solution at the node

Default: bchout.gdx

usergdxnameinc (string): the name of the GDX file exported from the solver with the incumbent solution

Default: bchout_i.gdx

usergdxprefix (string): prefixes usergdxin, usergdxname, and usergdxnameinc

usergdxsol (string): the name of the GDX file exported by Cplex to store the solution of extra columns

Default: bchsol.gdx

userheurcall (string): the GAMS command line to call the heuristic

userheurfirst (integer): calls the heuristic for the first n nodes

Default: 10

userheurfreq (integer): determines the frequency of the heuristic model calls

Default: 10

userheurinterval (integer): determines the interval when to apply the multiplier for the frequency of the heuristic model calls

Default: 100

userheurmult (integer): determines the multiplier for the frequency of the heuristic model calls

Default: 2

userheurnewint (boolean): calls the heuristic if the solver found a new integer feasible solution

Default: 1

userheurobjfirst (integer): Similar to UserHeurFirst but only calls the heuristic if the relaxed objective promises an improvement

Default: 0

userincbcall (string): the GAMS command line to call the incumbent checking program

userincbicall (string): the GAMS command line to call the incumbent reporting program

userjobid (string): postfixes lf, o on call adds –userjobid to the call. Postfixes gdxname, gdxnameinc and gdxin

userkeep (boolean): calls gamskeep instead of gams

Default: 0

varsel (integer): variable selection strategy at each node

This option is used to set the rule for selecting the branching variable at the node which has been selected for branching. The default value of 0 allows Cplex to select the best rule based on the problem and its progress.

Default: 0

valuemeaning
-1 Branch on variable with minimum infeasibility
This rule may lead more quickly to a first integer feasible solution, but will usually be slower overall to reach the optimal integer solution.
0 Branch variable automatically selected
1 Branch on variable with maximum infeasibility
This rule forces larger changes earlier in the tree, which tends to produce faster overall times to reach the optimal integer solution.
2 Branch based on pseudo costs
Generally, the pseudo-cost setting is more effective when the problem contains complex trade-offs and the dual values have an economic interpretation.
3 Strong Branching
This setting causes variable selection based on partially solving a number of subproblems with tentative branches to see which branch is most promising. This is often effective on large, difficult problems.
4 Branch based on pseudo reduced costs

workdir (string): directory for working files

The name of an existing directory into which Cplex may store temporary working files. Used for MIP node files and by out-of-core Barrier.

Default: current or project directory

workmem (real): memory available for working storage

Upper limit on the amount of memory, in megabytes, that Cplex is permitted to use for working files. See parameter WorkDir.

Default: 128

writebas (string): produce a Cplex basis file

Write a basis file.

writeflt (string): produce a Cplex solution pool filter file

Write the diversity filter to a Cplex FLT file.

writelp (string): produce a Cplex LP file

Write a file in Cplex LP format.

writemps (string): produce a Cplex MPS file

Write an MPS problem file.

writemst (string): produce a Cplex mst file

Write a Cplex MST (containing the MIP start) file.

writeord (string): produce a Cplex ord file

Write a Cplex ORD (containing priority and branch direction information) file.

writeparam (string): produce a Cplex parameter file with all active options

Write a Cplex parameter (containing all modified Cplex options) file.

writepre (string): produce a Cplex LP/MPS/SAV file of the presolved problem

Synonym: writepremps

Write a Cplex LP, MPS, or SAV file of the presolved problem. The file extension determines the problem format. For example, WritePre presolved.lp creates a file presolved.lp in Cplex LP format.

writesav (string): produce a Cplex binary problem file

Write a binary problem file.

zerohalfcuts (integer): zero-half cuts

Decides whether or not to generate zero-half cuts for the problem. The value 0, the default, specifies that the attempt to generate zero-half cuts should continue only if it seems to be helping. If the dual bound of your model does not make sufficient progress, consider setting this parameter to 2 to generate zero-half cuts more aggressively.

Default: 0

valuemeaning
-1 Off
0 Automatic
1 Generate zero-half cuts moderately
2 Generate zero-half cuts aggressively