LINDO and LINDOGlobal

Lindo Systems, Inc.

# Introduction

GAMS/LINDO finds guaranteed globally optimal solutions to general nonlinear problems with continuous and/or discrete variables. GAMS/LINDO supports most mathematical functions, including functions that are nonsmooth, such as abs(x) and or even discontinuous, such as floor(x). Nonlinear solvers employing methods like successive linear programming (SLP) or generalized reduced gradient (GRG) return a local optimal solution to an NLP problem. However, many practical nonlinear models are non-convex and have more than one local optimal solution. In some applications, the user may want to find a global optimal solution.

The LINDO global optimization procedure(GOP) employs branch-and-cut methods to break an NLP model down into a list of subproblems. Each subproblem is analyzed and either a) is shown to not have a feasible or optimal solution, or b) an optimal solution to the subproblem is found, e.g., because the subproblem is shown to be convex, or c) the subproblem is further split into two or more subproblems which are then placed on the list. Given appropriate tolerances, after a finite, though possibly large number of steps a solution provably global optimal to tolerances is returned. Traditional nonlinear solvers can get stuck at suboptimal, local solutions. This is no longer the case when using the global solver.

GAMS/LINDO can automatically linearize a number of nonlinear relationships, such as max(x,y), through the addition of constraints and integer variables, so the transformed linearized model is mathematically equivalent to the original nonlinear model. Keep in mind, however, that each of these strategies will require additional computation time. Thus, formulating models, so they are convex and contain a single extremum, is desirable. In order to decrease required computing power and time it is also possible to disable the global solver and use GAMS/LINDO like a regular nonlinear solver.

GAMS/LINDO has a multistart feature that restarts the standard (non-global) nonlinear solver from a number of intelligently generated points. This allows the solver to find a number of locally optimal points and report the best one found. This alternative can be used when global optimization is costly. A user adjustable parameter controls the maximum number of multistarts to be performed.

LINDO automatically detects problem type and uses an appropriate solver, e.g., if you submit an LP model to LINDO, it will be solved as an LP at LP speed, regardless of what you said in the "solve using" statement. With the NLP parameter NLP_QUADCHK turned on, LINDO can detect hidden quadratic expressions and automatically recognize convex QCPs, as well as second-order cones (SOCP), like in Value-at-Risk models, allowing dramatically faster solution times via the barrier solver. When such models have integer variables, LINDO would use the barrier solver to solve all subproblems leading to significantly improved solution times when compared to the case with the standard NLP solver.

## Licensing and software requirements

In order to use GAMS/LINDOGlobal, two licenses are required: a GAMS/LINDOGlobal license and a GAMS/CONOPT license. The additional CONOPT license requirement exists because LINDOGlobal uses CONOPT to solve the nonlinear subproblems. The GAMS/LINDOGlobal license places upper limits on the model size of 3,000 variables and 2,000 constraints.

To use GAMS/LINDO, only a GAMS/LINDO license is required. It imposes no upper limit on the model size and includes the capability to solve stochastic models (see section Stochastic Programming (SP) in GAMS/Lindo ).

Neither the GAMS/LINDO nor the GAMS/LINDOGlobal license includes the Barrier solver option. The Barrier option is enabled via a separate license for the GAMS/MOSEK barrier solver.

## Running GAMS/LINDO

GAMS/LINDO is capable of solving models of the following types: EMP (stochastic), LP, MIP, RMIP, NLP, DNLP, QCP, MIQCP, RMINLP and MINLP. If GAMS/LINDO is not specified as the default solver for these models, it can be invoked by issuing one of the following command before the solve statement:

option xxx=lindo;
option xxx=lindoglobal;


where xxx is one of: EMP, LP, MIP, RMIP, NLP, DNLP, QCP, MIQCP, RMINLP, or MINLP.

You can also find global optima to math programs with equilibrium or complementarity constraints, type MPEC, by using the GAMS/NLPEC translator in conjunction with LINDO. You use NLPEC to translate complementarities into standard mathematical statements, e.g. h*y = 0, and then use LINDO as the DNLP(Discontinuous Nonlinear) solver to solve the translated model. The following little GAMS model illustrates:

   $TITLE simple mpec example variable f, x1, x2, y1, y2; positive variable y1; y2.lo = -1; y2.up = 1; equations cost, g, h1, h2; cost.. f =E= x1 + x2; g.. sqr(x1) + sqr(x2) =L= 1; h1.. x1 =G= y1 - y2 + 1; h2.. x2 + y2 =N= 0; * declare h and y complementary model example / cost, g, h1.y1, h2.y2 /; option mpec=nlpec; option dnlp=lindo; solve example using mpec min f;  # Supported nonlinear functions GAMS/LINDO supports most nonlinear functions in global mode, including +, -, *, /, floor, modulo, sign, min, max, sqr, exp, power, ln, log, sqrt, abs, cos, sin, tan, cosh, sinh, tanh, arccos, arcsin, arctan and logic expressions AND, OR, NOT, and IF. Be aware that using highly nonconvex functions may lead to long solve times. # Diagnosis of Infeasible or Unbounded Models GAMS/LINDO offers two diagnostic tools, that can help users debug infeasible or unbounded optimization models. These tools can be called after the solver reports an infeasible or unbounded status for the model. When activating IIS Lindo finds an irreducible infeasible set (IIS) of constraints, whereas setting IUS, makes Lindo find an irreducible unbounded set (IUS) of variables. An IIS is a set of constraints that are infeasible taken together, but every strict subset is feasible. Similarly, an IUS is a set of unbounded variables such that fixing any one of them would make the model bounded. The IIS or IUS portion of the model will generally be much smaller than the original model. Thus, the user can track down formulation or data entry errors quickly. By isolating the source of infeasibility or unboundedness, the user can correct the model data such as right-hand side values, objective coefficients, senses of the constraints, and column bounds. Note that the IUS option is available for LPs only. ## Infeasible Models GAMS/Lindo's IIS option activates the IIS finder, after a model was tried to be solved and the solver returned a "no feasible solution" message. For an LP, if an infeasible basis is not resident in the solver, the IIS finder cannot initiate the process to isolate an IIS. This can occur if the infeasibility is detected in the pre-solver before a basis is created, or the barrier solver has terminated without performing a basis crossover. To obtain an IIS for such cases, the pre-solve option will be turned off automatically and the model gets optimized again. The constraints and bounds in the IIS are further classified into two disjoint sets: a necessary set and a sufficient set. The sufficient set refers to a crucial subset of the IIS in the sense that removing any one of its members from the entire model renders the model feasible. Note that not all infeasible models have sufficient sets. The necessary set contains those constraints and bounds that are likely to contribute to the overall infeasibility of the entire model. Thus, the necessary set requires a correction in at least one member to make the original model feasible. A constraint that has been marked as sufficient has a high probability of containing an error. In fact, if the model contains only one bad coefficient, the constraint containing it will be marked as sufficient. To control the level of analysis when locating an IIS, one can set the option IIS_ANALYZE_LEVEL. ## Unbounded Linear Programs GAMS/Lindo's IUS option is similar to the IIS option, except that it is used to track down the source of an unbounded solution in a linear program. This tool analyzes the model and isolates an "irreducibly unbounded set" (IUS) of variables. As in the infeasibility case, the IUS is partitioned into sufficient and necessary sets to indicate the role of the member variables for the unboundedness of the overall model. The variables in the sufficient set are crucial in the sense that fixing any of these variables makes the overall model bounded. However, fixing the variables in the necessary set does not ensure that there are no other sets of unbounded variables that cause unboundedness for the overall model. To control the level of analysis when locating an IUS, one can set the option IUS_ANALYZE_LEVEL. # GAMS/LINDO output The log output below is obtained for the NLP model mhw4d.gms from the GAMS model library using LINDOs global solver. LINDO 24Nov11 23.8.0 WIN 30200.30202 VS8 x86/MS Windows LINDO Driver Lindo Systems Inc, www.lindo.com Lindo API version 7.0.1.372 built on Nov 3 2011 21:49:01 Barrier Solver Version 6.0.0.114, Nonlinear Solver Version 3.15B Platform Windows x86 Number of constraints: 3 le: 0, ge: 0, eq: 3, rn: 0 (ne:0) Number of variables : 5 lb: 0, ub: 0, fr: 5, bx: 0 (fx:0) Number of nonzeroes : 8 density=0.0053(%) Nonlinear variables : 5 Nonlinear constraints: 4 Nonlinear nonzeroes : 5+5 Starting global optimization ... Number of nonlinear functions/operators: 3 EP_MULTIPLY EP_POWER EP_SQR Starting GOP presolve ... First Call Local Solver Find local solution, objvalue = 27.871905 Pre-check unboundedness Computing reduced bound... Searching for a better solution... Starting reformulation ... Model Input Operation Atomic Convex Number of variables : 5 6 20 20 Number of constraints: 3 4 18 46 integer variables : 0 0 0 0 nonlinear variables : 5 5 9 0 Starting global search ... Initial upper bound on objective: +2.931083e-002 Initial lower bound on objective: -3.167052e+022 #NODEs BOXES LOWER BOUND UPPER BOUND RGAP TIME(s) 1 1 -3.167052e+022 +2.931083e-002 1.0e+000 0 (*N) 19 17 -2.136461e+000 +2.931083e-002 1.0e+000 0 (*I) 22 20 -1.848574e-001 +2.931083e-002 2.1e-001 0 (*I) 23 21 +2.416053e-003 +2.931083e-002 2.7e-002 0 (*F) Terminating global search ... Global optimum found Objective value : 0.0293108307216 Best Bound : 0.00241605257558 Factors (ok,stb) : 522 (100.00,99.81) Simplex iterations : 2503 Barrier iterations : 0 Nonlinear iterations : 433 Box iterations : 23 Total number of boxes : 21 Max. Depth : 5 First solution time (sec.) : 0 Best solution time (sec.) : 0 Total time (sec.) : 0  After determining the different kinds of nonlinear operators LINDO tries to linearize these within the presolving. When a feasible starting point is found the optimization starts and the log provides information about the progress. At the end it is reported if an optimum could be found and then the results as well as the used resources are summarized. The following flags can be seen in the progress log: Flag Description (*FP) found a new MIP solution with feasibility pump (*SBB) found a new MIP solution in tree reorder (*SE) found a new MIP solution in simple enumeration (*AB) found a new MIP solution in advanced branching (*AH) found a new MIP solution with advanced heuristics (*C) found a new MIP solution after cuts added (*T) found a new MIP solution on the top (*SRH) found a new MIP solution in simple rounding heuristics (*SB) found a new MIP solution in strong branching (*K) found a new MIP solution in knapsack enumerator (*) found a new MIP solution normal branching (*?-) found a new MIP solution with advanced heuristics (level$>\$10)
(*N) found a new incumbent GOP solution
(*I) stored a box with the incumbent solution into the GOP solution list
(*F) determined the final GOP status

# The GAMS/LINDO Options

GAMS/LINDO offers a diverse range of user-adjustable parameters to control the behavior of its solvers. While the default values of these parameters work best for most purposes, there may be cases the users prefer to work with different settings for a subset of the available parameters. This section gives a list of available GAMS/LINDO parameters, categorized by type, along with their brief descriptions. A more detailed description is given in the section that follows.

## GAMS/LINDO Options File

In order to set GAMS/LINDO options, you need to set up an option file lindo.opt or lindoglobal.opt in your GAMS project directory. You must indicate in the model that you want to use the option file by inserting before the solve statement, the line:

  <modelname>.optfile = 1;


where

<modelname>


is the name of the model referenced in the model statement. The option file is in plain text format containing a single GAMS/LINDO option per line. Each option identifier is followed by its target value with space or tab characters separating them. The lines starting with * character are treated as comments.

A sample option file lindo.opt looks like below

    * Use(1) or Disable(0) global optimization for NLP/MINLP models
USEGOP               0

* Enable Multistart NLP solver
NLP_SOLVER           9

* Allow a maximum of 3 multistart attempts
NLP_MAXLOCALSEARCH   3

* Set an overall time limit of 200 secs.
SOLVER_TIMLMT      200


# Summary of GAMS/Lindo Options

## General Options

Option Description Default
DECOMPOSITION_TYPE decomposition to be performed on a linear or mixed integer model 1
FIND_BLOCK graph partitioning method to find block structures 0
FIND_SYMMETRY_LEVEL specifies the symmetry finding level. -1
FIND_SYMMETRY_PRINT_LEVEL specifies print level for symmetry finding 0
INSTRUCT_SUBOUT flag to specify how to deal with fixed variables in the instruction list -1
MULTITHREAD_MODE threading mode -1
NUM_THREADS number of parallel threads to be used GAMS Threads
PROFILER_LEVEL specifies the profiler level to break down the total cpu time into. 0
SOLVER_CONCURRENT_OPTMODE controls if simplex and interior-point optimizers will run concurrently 0
SOLVER_CUTOFFVAL solver will exit if optimal solution is worse than this 0
SOLVER_FEASTOL feasibility tolerance 1e-7
SOLVER_IPMSOL basis crossover flag for barrier solver 0
SOLVER_IUSOL flag for computing basic solution for infeasible model 0
SOLVER_METHOD specifies the method to use when generic solver is invoked 0
SOLVER_MODE controls some of the advanced strategies when solving LPs 1
SOLVER_OPTTOL dual feasibility tolerance 1e-7
SOLVER_PRE_ELIM_FILL fill-in introduced by the eliminations during pre-solve 1000
SOLVER_RESTART starting basis flag 0
SOLVER_TIMLMT time limit in seconds for continous solver GAMS ResLim
SOLVER_USECUTOFFVAL flag for using cutoff value 0
TUNER_PRINT_LEVEL specifies the amount of print to do during parameter tuning 1

## LP Options

Option Description Default
LP_AIJ_ZEROTOL coefficient matrix zero tolerance 2.22045e-16
LP_BIGM big-M for phase-I 1e6
LP_BNDINF big-M to truncate lower and upper bounds in single phase dual-simplex 1e15
LP_DPSWITCH specifies whether LP primal-dual simplex switch is enabled or not 1
LP_DRATIO controls the dual min-ratio strategy 1
LP_DYNOBJFACT Dynamic obj factor 0.75
LP_DYNOBJMODE Dynamic obj mode 0
LP_ITRLMT simplex iteration limit infinity
LP_PIV_BIGTOL simplex maximum pivot tolerance 1e-5
LP_PIV_ZEROTOL simplex pivot zero tolerance 1e-8
LP_PPARTIAL primal simplex partial pricing method 0
LP_PRELEVEL controls the amount and type of LP pre-solving 126
LP_RATRANGE controls the number of pivot-candidates to consider when searching for a stable pivot in LU decomposition 4
LP_SCALE scaling flag 1
LP_SPRINT_COLFACT maximum number of columns in Sprint as a factor of number of rows 10
LP_SPRINT_MAXPASS maximum number of passes in Sprint method 100
LP_SPRINT_SUB LP method for subproblem in Sprint method 0
PROB_TO_SOLVE controls whether the explicit primal or dual form of the given LP problem will be solved 0
SPLEX_DPRICING pricing option for dual simplex method -1
SPLEX_DUAL_PHASE controls the dual simplex strategy 0
SPLEX_PPRICING pricing option for primal simplex method -1
SPLEX_REFACFRQ number of simplex iterations between two consecutive basis re-factorizations 100

## IPM Options

Option Description Default
IPM_BASIS_REL_TOL_S maximum relative dual bound violation allowed in an optimal basic solution 1e-12
IPM_BASIS_TOL_S maximum absolute dual bound violation in an optimal basic solution 1e-7
IPM_BASIS_TOL_X maximum absolute primal bound violation allowed in an optimal basic solution 1e-7
IPM_BI_LU_TOL_REL_PIV relative pivot tolerance used in the LU factorization in the basis identification procedure 1e-2
IPM_CHECK_CONVEXITY flag to check convexity of a quadratic program using barrier solver 1
IPM_CO_TOL_DFEAS dual feasibility tolerance for Conic solver 1e-8
IPM_CO_TOL_INFEAS maximum bound infeasibility tolerance for Conic solver 1e-12
IPM_CO_TOL_MU_RED optimality tolerance for Conic solver 1e-8
IPM_CO_TOL_PFEAS primal feasibility tolerance for Conic solver 1e-8
IPM_MAX_ITERATIONS ipm iteration limit 1000
IPM_NUM_THREADS number of threads to run the interiorpoint optimizer on 1
IPM_OFF_COL_TRH extent for detecting the offending columns in the Jacobian of the constraint matrix 40
IPM_TOL_DFEAS dual feasibility tolerance 1e-8
IPM_TOL_DSAFE controls the initial dual starting point 1
IPM_TOL_INFEAS infeasibility tolerance 1e-10
IPM_TOL_MU_RED relative complementarity gap tolerance 1e-16
IPM_TOL_PATH how close to follow the central path 1e-8
IPM_TOL_PFEAS primal feasibility tolerance 1e-8
IPM_TOL_PSAFE controls the initial primal starting point 1
IPM_TOL_REL_STEP relative step size to the boundary 0.9999

## MIP Options

Option Description Default
MIP_ABSCUTTOL MIP absolute cut tolerance -1.0
MIP_ABSOPTTOL MIP absolute optimality tolerance GAMS OptCA
MIP_ADDCUTOBJTOL required objective improvement to continue generating cuts 1.5625e-5
MIP_ADDCUTPER percentage of constraint cuts that can be added 0.75
MIP_ADDCUTPER_TREE percentage of constraint cuts that can be added at child nodes 0.5
MIP_AGGCUTLIM_TOP max number of constraints involved in derivation of aggregation cut at root node -1
MIP_AGGCUTLIM_TREE max number of constraints involved in derivation of aggregation cut at tree nodes -1
MIP_ANODES_SWITCH_DF threshold on active nodes for switching to depth-first search 50000
MIP_AOPTTIMLIM time in seconds beyond which the relative optimality tolerance will be applied 100
MIP_BIGM_FOR_INTTOL threshold for which coefficient of a binary variable would be considered as big-M 1e8
MIP_BRANCHDIR first branching direction 0
MIP_BRANCHRULE rule for choosing the variable to branch 0
MIP_BRANCH_LIMIT limit on the total number of branches to be created during branch and bound -1
MIP_BRANCH_PRIO controls how variable selection priorities are set and used 0
MIP_CONCURRENT_REOPTMODE specifies the concurrent optimization mode with warm start 0
MIP_CONCURRENT_STRATEGY controls the concurrent MIP strategy -1
MIP_CONCURRENT_TOPOPTMODE specifies the concurrent optimization mode with cold start 0
MIP_CUTDEPTH threshold value for the depth of nodes in the branch and bound tree 8
MIP_CUTFREQ frequency of invoking cut generation at child nodes 10
MIP_CUTLEVEL_TOP combination of cut types to try at the root node when solving a MIP 57342
MIP_CUTLEVEL_TREE combination of cut types to try at child nodes in the branch and bound tree when solving a MIP 53246
MIP_CUTOFFOBJ defines limit for branch and bound 1e30
MIP_CUTTIMLIM time to be spent in cut generation -1
MIP_DELTA near-zero value used in linearizing nonlinear expressions 1e-6
MIP_DUAL_SOLUTION flag for computing dual solution of LP relaxation 0
MIP_FIXINIT_ITRLIM iteration limit of the LP solved after fixing integer variables to their initial values -1
MIP_FP_HEU_MODE specifies the feasibility-pump (FP) heuristic mode 0
MIP_FP_ITRLIM iteration limit for feasibility pump heuristic 500
MIP_FP_MODE mode for the feasibility pump heuristic -1
MIP_FP_OPT_METHOD optimization and reoptimization method for feasibility pump heuristic 0
MIP_FP_PROJECTION type of objective function of LPs in projection step of the feasibility pump heuristic 0
MIP_FP_TIMLIM time limit for feasibility pump heuristic 1800
MIP_FP_WEIGTH weight of the objective function in the feasibility pump 1
MIP_GENERAL_MODE general strategy in solving MIPs 0
MIP_HEULEVEL specifies heuristic used to find integer solution 3
MIP_HEUMINTIMLIM minimum time in seconds to be spent in finding heuristic solutions 0
MIP_HEU_DROP_OBJ flag for whether to use without OBJ heuristic 0
MIP_HEU_MODE heuristic used in MIP solver 0
MIP_INTTOL absolute integer feasibility tolerance 1e-6
MIP_ITRLIM iteration limit for branch and bound infinity
MIP_KBEST_USE_GOP specifies whether to use gop solver in MIP KBest 0
MIP_KEEPINMEM flag for keeping LP bases in memory 1
MIP_LBIGM Big-M value used in linearizing nonlinear expressions 10000
MIP_LSOLTIMLIM time limit until finding a new integer solution -1
MIP_MAKECUT_INACTIVE_COUNT threshold for times a cut could remain active after successive reoptimization 10
MIP_MAXCUTPASS_TOP number passes to generate cuts on the root node 200
MIP_MAXCUTPASS_TREE number passes to generate cuts on the child nodes 2
MIP_MAXNONIMP_CUTPASS number of passes allowed in cut-generation that does not improve current relaxation 3
MIP_MAXNUM_MIP_SOL_STORAGE maximum number of k-best solutions to store 1
MIP_MINABSOBJSTEP value to update cutoff value each time a mixed integer solution is found 0
MIP_NODESELRULE specifies the node selection rule 0
MIP_NUM_THREADS number of parallel threads to use by the parallel MIP solver 1
MIP_PARA_FP flag for whether to use parallelization on the feasibility pump heuristic 1
MIP_PARA_FP_MODE flag for the mode of parallel feasibility pump 0
MIP_PARA_INIT_NODE number of initial nodes for MIP parallelization -1
MIP_PARA_ITR_MODE flag for iteration mode in MIP parallelization 1
MIP_PARA_RND_ITRLMT iteration limit of each round in MIP parallelization, it is a weighted combination of simplex and barrier iterations 2.0
MIP_PARA_SUB flag for whether to use MIP parallelization on subproblems solved in MIP preprocessing 1
MIP_PEROPTTOL MIP relative optimality tolerance in effect after MIP_AOPTTIMLIM seconds 1e-5
MIP_PERSPECTIVE_REFORM flag for whether to use Perspective Reformulation 1
MIP_POLISH_ALPHA_TARGET proportion solutions in the pool to initiate a polishing-task at the current node 0.6
MIP_POLISH_MAX_BRANCH_COUNT maximum number of branches to polish 2000
MIP_POLISH_NUM_BRANCH_NEXT number of branches to polish in the next round 4000
MIP_PREHEU_DFE_VSTLIM limit for the variable visit in depth first enumeration 200
MIP_PREHEU_LEVEL heuristic level for the prerelax solver 0
MIP_PREHEU_TC_ITERLIM iteration limit for the two change heuristic 30000000
MIP_PREHEU_VAR_SEQ sequence of the variable considered by the prerelax heuristic -1
MIP_PRELEVEL controls the amount and type of MIP pre-solving at root node 3070
MIP_PRELEVEL_TREE amount and type of MIP pre-solving at tree nodes 1214
MIP_PRE_ELIM_FILL controls fill-in introduced by eliminations during pre-solve 100
MIP_PSEUDOCOST_RULE specifies the rule in pseudocost computations for variable selection 0
MIP_PSEUDOCOST_WEIGT weight in pseudocost computations for variable selection 1.5625e-05
MIP_REDCOSTFIX_CUTOFF cutoff value as a percentage of the reduced costs 0.9
MIP_REDCOSTFIX_CUTOFF_TREE cutoff value as a percentage of the reduced costs at tree nodes 0.9
MIP_RELINTTOL relative integer feasibility tolerance 8e-6
MIP_RELOPTTOL MIP relative optimality tolerance GAMS OptCR
MIP_REOPT optimization method to use when doing reoptimization 0
MIP_SCALING_BOUND maximum difference between bounds of an integer variable for enabling scaling 10000
MIP_SOLLIM integer solution limit for MIP solver -1
MIP_SOLVERTYPE optimization method to use when solving mixed-integer models 0
MIP_STRONGBRANCHDONUM minimum number of variables to try the strong branching on 3
MIP_STRONGBRANCHLEVEL depth from the root in which strong branching is used 10
MIP_SWITCHFAC_SIM_IPM_ITER specifies the (positive) factor that multiplies the number of constraints to impose an iteration limit to simplex method and trigger a switch over to the barrier method -1
MIP_SWITCHFAC_SIM_IPM_TIME factor that multiplies the number of constraints to impose a time limit to simplex method and trigger a switch over to the barrier method -1
MIP_SYMMETRY_MODE specifies mip symmetry handling methods 0
MIP_SYMMETRY_NONZ limit on number of nonzeros to look for symmetries 50000
MIP_TIMLIM time limit in seconds for integer solver GAMS ResLim
MIP_TOPOPT optimization method to use when there is no previous basis 0
MIP_TREEREORDERLEVEL tree reordering level 10
MIP_TREEREORDERMODE tree reordering mode 1
MIP_USECUTOFFOBJ flag for using branch and bound limit 1
MIP_USE_CUTS_HEU controls if cut generation is enabled during MIP heuristics -1
MIP_USE_ENUM_HEU frequency of enumeration heuristic 4
MIP_USE_INT_ZERO_TOL controls if all MIP calculations would be based on absolute integer feasibility tolarance 0

## NLP Options

Option Description Default
NLP_AUTODERIV defining type of computing derivatives 0
NLP_AUTOHESS flag for using Second Order Automatic Differentiation for solving NLP 0
NLP_CONIC_REFORM determines if to explore conic reformulation 1
NLP_CONOPT_VER specifies the CONOPT version to be used in NLP optimizations 3
NLP_CUTOFFOBJ as soon as any multi-start thread achieves this value all threads stop -1e30
NLP_DERIV_DIFFTYPE flag indicating the technique used in computing derivatives with finite differences 0
NLP_FEASCHK how to report results when solution satisfies tolerance of scaled but not original model 1
NLP_FEASTOL feasibility tolerance for nonlinear constraints 1e-6
NLP_INF numeric infinity for nonlinear models 1e30
NLP_IPM2GRG switch from IPM solver to GRG solver when IPM fails due to numerical errors 1
NLP_ITERS_PER_LOGLINE number of nonlinear iterations to elapse before next progress message 10
NLP_ITRLMT nonlinear iteration limit GAMS IterLim
NLP_LINEARZ extent to which the solver will attempt to linearize nonlinear models -1
NLP_LINEARZ_WB_CONSISTENT determines if linearization process is consistent with WB/excel calculation 0
NLP_MAXLOCALSEARCH maximum number of local searches 5
NLP_MAXLOCALSEARCH_TREE maximum number of multistarts 1
NLP_MAX_RETRY maximum number refinement retries to purify the final NLP solution 5
NLP_MSW_EUCDIST_THRES euclidean distance threshold in multistart search 0.001
NLP_MSW_FILTMODE filtering mode to exclude certain domains during sampling in multistart search -1
NLP_MSW_MAXNOIMP maximum number of consecutive populations to generate without any improvements -1
NLP_MSW_MAXPOP maximum number of populations to generate in multistart search -1
NLP_MSW_MAXREF maximum number of reference points to generate trial points in multistart search -1
NLP_MSW_NORM norm to measure the distance between two points in multistart search 2
NLP_MSW_NUM_THREADS number of parallel threads to be used when solving an NLP model with the multistart solver 1
NLP_MSW_OVERLAP_RATIO rate of replacement in successive populations 0.1
NLP_MSW_POXDIST_THRES penalty function neighborhood threshold in multistart search 0.01
NLP_MSW_PREPMODE preprocessing strategies in multistart solver -1
NLP_MSW_RG_SEED random number generator seed for the multistart solver 1019
NLP_MSW_RMAPMODE specifies the mode to map reference points in the unit cube into the original space -1
NLP_MSW_SOLIDX index of the multistart solution to be loaded 0
NLP_MSW_XKKTRAD_FACTOR KKT solution neighborhood factor in multistart search 0.85
NLP_MSW_XNULRAD_FACTOR initial solution neighborhood factor in multistart search 0.5
NLP_PRELEVEL controls the amount and type of NLP pre-solving 126
NLP_PSTEP_FINITEDIFF value of the step length in computing the derivatives using finite differences 5e-7
NLP_QUADCHK flag for checking if NLP is quadratic 1
NLP_REDGTOL tolerance for the gradients of nonlinear functions 1e-7
NLP_SOLVER type of nonlinear solver 7
NLP_SOLVE_AS_LP flag indicating if the nonlinear model will be solved as an LP 0
NLP_STALL_ITRLMT iteration limit before a sequence of non-improving NLP iterations is declared as stalling 100
NLP_STARTPOINT flag for using initial starting solution for NLP 1
NLP_SUBSOLVER type of nonlinear subsolver 1
NLP_USECUTOFFOBJ flag to use parameter NLP_CUTOFFOBJ 0
NLP_USE_CRASH flag for using simple crash routines for initial solution 0
NLP_USE_LINDO_CRASH flag for using advanced crash routines for initial solution 1
NLP_USE_SDP flag to use SDP solver for POSD constraint 1
NLP_USE_SELCONEVAL flag for using selective constraint evaluations for solving NLP 1
NLP_USE_SLP flag for using sequential linear programming step directions for updating solution 1
NLP_USE_STEEPEDGE flag for using steepest edge directions for updating solution 0

## Global Options

Option Description Default
GOP_ABSOPTTOL absolute optimality tolerance GAMS OptCA
GOP_ALGREFORMMD algebraic reformulation rule for a GOP 18
GOP_BBSRCHMD node selection rule in GOP branch-and-bound 1
GOP_BNDLIM max magnitude of variable bounds used in GOP convexification 1e10
GOP_BOXTOL minimal width of variable intervals 1e-6
GOP_BRANCHMD direction to branch first when branching on a variable 5
GOP_BRANCH_LIMIT limit on the total number of branches to be created in GOP tree -1
GOP_CMINLP flag indicating if GOP exploits convex MINLP model 0
GOP_CONIC_REFORM flag indicating if GOP explore conic reformulation 1
GOP_CORELEVEL strategy of GOP branch-and-bound 14
GOP_DECOMPPTMD decomposition point selection rule in GOP branch-and-bound 1
GOP_DELTATOL delta tolerance in GOP convexification 1e-7
GOP_FLTTOL floating-point tolerance 1e-10
GOP_HEU_MODE heuristic used in global solver 0
GOP_ITRLIM GOP iteration limit infinity
GOP_ITRLIM_IPM total barrier iteration limit summed over all branches in GOP -1
GOP_ITRLIM_NLP total nonlinear iteration limit summed over all branches in GOP -1
GOP_ITRLIM_SIM total simplex iteration limit summed over all branches in GOP -1
GOP_LIM_MODE flag indicating which heuristic limit on sub-solver in GOP is based 1
GOP_LINEARZ flag indicating if GOP exploits linearizable model 1
GOP_LSOLBRANLIM branch limit until finding a new nonlinear solution -1
GOP_MAXWIDMD maximum width flag for the global solution 0
GOP_MULTILINEAR flag indicating if GOP exploits multi linear feature 1
GOP_NUM_THREADS number of parallel threads to be used when solving a nonlinear model with the global optimization solver 1
GOP_OBJ_THRESHOLD threshold of objective value in the GOP solver -1e+30
GOP_OPTCHKMD criterion used to certify the global optimality 2
GOP_OPT_MODE mode for GOP optimization 1
GOP_POSTLEVEL amount and type of GOP postsolving 6
GOP_PRELEVEL amount and type of GOP presolving 30
GOP_QUADMD flag indicating if GOP exploits quadratic feature -1
GOP_QUAD_METHOD specifies if the GOP solver should solve the model as a QP when applicable -1
GOP_RELBRNDMD reliable rounding in the GOP branch-and-bound 0
GOP_RELOPTTOL relative optimality tolerance GAMS OptCR
GOP_SOLLIM integer solution limit for GOP branch-and-bound -1
GOP_SUBOUT_MODE substituting out fixed variables 1
GOP_TIMLIM time limit in seconds for GOP branch-and-bound GAMS ResLim
GOP_USEBNDLIM max magnitude of variable bounds flag for GOP convexification 2
GOP_WIDTOL maximal width of variable intervals 1e-4
USEGOP use global optimization 1

## SP Options

Option Description Default
CORE_ORDER_BY_STAGE order nontemporal models or not 1
EMPINFOFILE Path and name of file containing additional EMP-SP information as randvar, jrandvar, stage etc.
REPORTEVSOL solve and report the expected value solution 0
SAMP_CDSINC correlation matrix diagonal shift increment 1e-6
SAMP_NCM_CUTOBJ objective cutoff (target) value to stop the nearest correlation matrix (NCM) subproblem 1e-30
SAMP_NCM_DSTORAGE flag to enable or disable sparse mode in NCM computations -1
SAMP_NCM_ITERLIM iteration limit for NCM method 100
SAMP_NCM_METHOD bitmask to enable methods for solving the nearest correlation matrix (NCM) subproblem 5
SAMP_NCM_OPTTOL optimality tolerance for NCM method 1e-7
SAMP_NUM_THREADS specifies the number of parallel threads to be used when sampling 0
SAMP_RG_BUFFER_SIZE specifies the buffer size for random number generators in running in parallel mode 0
SAMP_SCALE flag to enable scaling of raw sample data 0
STOC_ABSOPTTOL absolute optimality tolerance (w.r.t lower and upper bounds on the true objective) to stop the solver GAMS OptCA
STOC_ADD_MPI flag to use add-instructions mode when building deteq 0
STOC_ALD_DUAL_FEASTOL dual feasibility tolerance for ALD 1e-4
STOC_ALD_DUAL_STEPLEN dual step length for ALD 0.9
STOC_ALD_INNER_ITER_LIM inner loop iteration limit for ALD 1000
STOC_ALD_OUTER_ITER_LIM outer loop iteration limit for ALD 200
STOC_ALD_PRIMAL_FEASTOL primal feasibility tolerance for ALD 1e-4
STOC_ALD_PRIMAL_STEPLEN primal step length for ALD 0.5
STOC_AUTOAGGR flag to enable or disable autoaggregation 1
STOC_BENCHMARK_SCEN benchmark scenario to compare EVPI and EVMU against -2
STOC_BIGM big-M value for linearization and penalty functions 1e7
STOC_BUCKET_SIZE bucket size in Benders decomposition -1
STOC_CALC_EVPI flag to enable or disable calculation of EVPI 1
STOC_CORRELATION_TYPE correlation type associated with correlation matrix 0
STOC_DEQOPT method to solve the DETEQ problem 0
STOC_DETEQ_TYPE type of deterministic equivalent -1
STOC_DS_SUBFORM subproblem formulation to use in DirectSearch -1
STOC_ELIM_FXVAR flag to enable elimination of fixed variables from deteq MPI 1
STOC_INFBND value to truncate infinite bounds at non-leaf nodes 1e9
STOC_ITER_LIM iteration limit for stochastic solver infinity
STOC_MAP_MPI2LP flag to specify whether stochastic parameters in MPI will be mapped as LP matrix elements 0
STOC_MAX_NUMSCENS maximum number of scenarios before forcing automatic sampling 40000
STOC_METHOD stochastic optimization method to solve the model -1
STOC_NAMEDATA_LEVEL name data level 1
STOC_NODELP_PRELEVEL presolve level solving node-models 0
STOC_NSAMPLE_PER_STAGE list of sample sizes per stage (starting at stage 2)
STOC_NSAMPLE_SPAR common sample size per stochastic parameter -1
STOC_NSAMPLE_STAGE common sample size per stage -1
STOC_NUM_THREADS number of parallel threads 1
STOC_RELOPTTOL relative optimality tolerance (w.r.t lower and upper bounds on the true objective) to stop the solver GAMS OptCR
STOC_REL_DSTEPTOL dual-step tolerance 1e-7
STOC_REL_PSTEPTOL primal-step tolerance 1e-8
STOC_REOPT reoptimization method to solve the node-models 0
STOC_RG_SEED seed to initialize the random number generator 1031
STOC_SAMP_CONT_ONLY flag to restrict sampling to continuous stochastic parameters only or not 1
STOC_SBD_MAXCUTS max cuts to generate for master problem -1
STOC_SBD_NUMCANDID maximum number of candidate solutions to generate at SBD root -1
STOC_SBD_OBJCUTFLAG flag to enable objective cut in SBD master problem 1
STOC_SBD_OBJCUTVAL RHS value of objective cut in SBD master problem 1e-30
STOC_SHARE_BEGSTAGE stage beyond which node-models are shared -1
STOC_TIME_LIM time limit for stochastic solver GAMS ResLim
STOC_TOPOPT optimization method to solve the root problem 0
STOC_VARCONTROL_METHOD sampling method for variance reduction 1
STOC_WSBAS warm start basis for wait-see model -1
SVR_LS_ANTITHETIC Sample variance reduction map to Lindo Antithetic algorithm
SVR_LS_LATINSQUARE Sample variance reduction map to Lindo Latin Square algorithm
SVR_LS_MONTECARLO Sample variance reduction map to Lindo Montecarlo algorithm

## IIS and IUS Options

Option Description Default
IIS run the IIS finder if the problem is infeasible 0
IIS_ANALYZE_LEVEL controls the level of analysis when locating an IIS 1
IIS_GETMODE flag that controls whether variable bounds in the IIS should be retrieved or the integer restrictions 0
IIS_INFEAS_NORM specifies the norm to measure infeasibilities in IIS search 0
IIS_ITER_LIMIT the iteration limit for IIS search -1
IIS_METHOD specifies the method to use in analyzing infeasible models to locate an IIS 0
IIS_PRINT_LEVEL specifies the amount of print to do during IIS search 2
IIS_REOPT specifies which optimization method to use when starting from a given basis 0
IIS_TIME_LIMIT the time limit for IIS search -1
IIS_TOPOPT specifies which optimization method to use when there is no previous basis 0
IIS_USE_EFILTER flag that controls whether the Elastic Filter should be enabled as the supplementary filter in analyzing infeasible models 0
IIS_USE_GOP flag that controls whether the global optimizer should be enabled in analyzing infeasible NLP models 0
IIS_USE_SFILTER flag indicating is sensitivity filter will be used during IIS search 1
IUS run the IUS finder if the problem is unbounded 0
IUS_ANALYZE_LEVEL controls the level of analysis when locating an IUS 2

Option Description Default
CHECKRANGE calculate feasible range for variables range.gdx
WRITEDEMPI write deterministic equivalent in MPI format
WRITEDEMPS write deterministic equivalent in MPS format
WRITEMPI write (S)MPI file of processed model
WRITEMPS write (S)MPS file of processed model

# Detailed Descriptions of GAMS/Lindo Options

CHECKRANGE (string): calculate feasible range for variables

If this option is set, Lindo calculates the feasible range (determined by an upper and lower bound) for every variable in each equation while all other variables are fixed to their level. If set, the value of this option defines the name of the GDX file where the results are written to. For every combination of equation- and variable block there will be one symbol in the format EquBlock_VarBlock(equ_Ind_1, ..., equ_Ind_M, var_Ind_1, ..., var_Ind_N, directions).

Default: range.gdx

CORE_ORDER_BY_STAGE (integer): order nontemporal models or not

Order nontemporal models or not.

Default: 1

DECOMPOSITION_TYPE (integer): decomposition to be performed on a linear or mixed integer model

This refers to the type of decomposition to be performed on a linear or mixed integer model.

Default: 1

value meaning
0 Solver decides which type of decomposition to use
1 Solver does not perform any decompositions and uses the original model
2 Attempt total decomposition
3 Decomposed model will have dual angular structure
4 Decomposed model will have block angular structure
5 Decomposed model will have both dual and block angular structure

EMPINFOFILE (string): Path and name of file containing additional EMP-SP information as randvar, jrandvar, stage etc.

FIND_BLOCK (integer): graph partitioning method to find block structures

Specifies the graph partitioning method to find block structures.

Default: 0

value meaning
0 Use an edge-weight minimizing graph partitioning heuristic
1 Use a vertex-weight minimizing graph partitioning heuristic

FIND_SYMMETRY_LEVEL (integer): specifies the symmetry finding level.

Default: -1

value meaning
-1 Solver decides
0 Finding orbit only without MIP preprocessing
1 Finding orbit only with MIP preprocessing
2 Finding generators without MIP preprocessing
3 Finding generators with MIP preprocessing
4 Finding the first generator without MIP preprocessing
5 Finding the first generator with MIP preprocessing

FIND_SYMMETRY_PRINT_LEVEL (integer): specifies print level for symmetry finding

Default: 0

value meaning
0 Nothing printed
+2 General information
+4 Time information
+8 Orbit information
+16 Partition information

GOP_ABSOPTTOL (real): absolute optimality tolerance

Synonym: ABSOPTTOL

This value is the GOP absolute optimality tolerance. Solutions must beat the incumbent by at least this amount to become the new best solution.

Default: GAMS OptCA

GOP_ALGREFORMMD (integer): algebraic reformulation rule for a GOP

Synonym: ALGREFORMMD

This controls the algebraic reformulation rule for a GOP. The algebraic reformulation and analysis is very crucial in building a tight convex envelope to enclose the nonlinear/nonconvex functions. A lower degree of overestimation on convex envelopes helps increase the convergence rate to the global optimum.

Default: 18

value meaning
+2 Rearrange and collect terms
+4 Expand all parentheses
+8 Retain nonlinear functions
+16 Selectively expand parentheses

GOP_BBSRCHMD (integer): node selection rule in GOP branch-and-bound

Synonym: BBSRCHMD

This specifies the node selection rule for choosing between all active nodes in the GOP branch-and-bound tree when solving global optimization programs.

Default: 1

value meaning
0 Depth first search
1 Choose node with worst bound

GOP_BNDLIM (real): max magnitude of variable bounds used in GOP convexification

Synonym: BNDLIM

This value specifies the maximum magnitude of variable bounds used in the GOP convexification. Any lower bound smaller than the negative of this value will be treated as the negative of this value. Any upper bound greater than this value will be treated as this value. This helps the global solver focus on more productive domains.

Default: 1e10

GOP_BOXTOL (real): minimal width of variable intervals

Synonym: BOXTOL

This value specifies the minimal width of variable intervals in a box allowed to branch.

Default: 1e-6

GOP_BRANCHMD (integer): direction to branch first when branching on a variable

Synonym: BRANCHMD

This specifies the direction to branch first when branching on a variable. The branch variable is selected as the one that holds the largest magnitude in the measure.

Default: 5

value meaning
0 Absolute width
1 Locally relative width
2 Globally relative width
3 Globally relative distance from the convex minimum to the bounds
4 Absolute violation between the function and its convex envelope at the convex minimum
5 Relative violation between the function and its convex envelope at the convex minimum

GOP_BRANCH_LIMIT (integer): limit on the total number of branches to be created in GOP tree

Synonym: BRANCH_LIMIT

This is the limit on the total number of branches to be created during branch-and- bound in GOP tree. The default value is -1, which means no limit is imposed. If the branch limit is reached and a feasible solution was found, it will be installed as the incumbent (best known) solution.

Range: {-1, ..., ∞}

Default: -1

GOP_CMINLP (integer): flag indicating if GOP exploits convex MINLP model

Default: 0

value meaning
0 Off
1 On

GOP_CONIC_REFORM (integer): flag indicating if GOP explore conic reformulation

Default: 1

value meaning
0 Off
1 On

GOP_CORELEVEL (integer): strategy of GOP branch-and-bound

Synonym: CORELEVEL

This controls the strategy of GOP branch-and-bound procedure.

Default: 14

value meaning
+2 LP convex relaxation
+4 NLP solving
+8 Box Branching

GOP_DECOMPPTMD (integer): decomposition point selection rule in GOP branch-and-bound

Synonym: DECOMPPTMD

This specifies the decomposition point selection rule. In the branch step of GOP branch-and-bound, a branch point M is selected to decompose the selected variable interval [Lb, Ub] into two subintervals, [Lb, M] and [M, Ub].

Default: 1

value meaning
0 Mid-point
1 Local minimum or convex minimum

GOP_DELTATOL (real): delta tolerance in GOP convexification

Synonym: DELTATOL

This value is the delta tolerance in the GOP convexification. It is a measure of how closely the additional constraints added as part of convexification should be satisfied.

Default: 1e-7

GOP_FLTTOL (real): floating-point tolerance

Synonym: FLTTOL

This value is the GOP floating-point tolerance. It specifies the maximum rounding errors in the floating-point computation.

Default: 1e-10

GOP_HEU_MODE (integer): heuristic used in global solver

Synonym: HEU_MODE

This specifies the heuristic used in the global solver to find a good solution. Typically, if a heuristic is used, this will put more efforts in searching for good solutions, and less in bound tightening.

Default: 0

value meaning
0 No heuristic is used
1 A simple heuristic is used

GOP_ITRLIM (real): GOP iteration limit

Synonym: ITRLIM

This is the total iteration limit (including simplex, barrier and nonlinear iteration) summed over branches in GOP. The default value is -1, which means no iteration limit is imposed. If this limit is reached, GOP will stop.

Range: [-1, ∞]

Default: infinity

GOP_ITRLIM_IPM (real): total barrier iteration limit summed over all branches in GOP

Synonym: ITRLIM_IPM

This is the total barrier iteration limit summed over all branches in GOP. The default value is -1, which means no iteration limit is imposed. If this limit is reached, GOP will stop.

Range: [-1, ∞]

Default: -1

GOP_ITRLIM_NLP (real): total nonlinear iteration limit summed over all branches in GOP

Synonym: ITRLIM_NLP

This is the total nonlinear iteration limit summed over all branches in GOP. The default value is -1, which means no iteration limit is imposed. If this limit is reached, GOP will stop.

Range: [-1, ∞]

Default: -1

GOP_ITRLIM_SIM (real): total simplex iteration limit summed over all branches in GOP

Synonym: ITRLIM_SIM

This is the total simplex iteration limit summed over all branches in GOP. The default value is -1, which means no iteration limit is imposed. If this limit is reached, GOP will stop.

Range: [-1, ∞]

Default: -1

GOP_LIM_MODE (integer): flag indicating which heuristic limit on sub-solver in GOP is based

Synonym: LIM_MODE

This is a flag indicating which heuristic limit on sub-solver in GOP is based.

Default: 1

value meaning
0 No limit
1 Time based limit
2 Iteration based limit
3 Both time and iteration based limit

GOP_LINEARZ (integer): flag indicating if GOP exploits linearizable model

This is a flag indicating if GOP exploits linearizable model.

Default: 1

value meaning
0 Exploit lineariable model
1 Do not exploit lineariable model

GOP_LSOLBRANLIM (integer): branch limit until finding a new nonlinear solution

Synonym: LSOLBRANLIM

This value controls the branch limit until finding a new nonlinear solution since the last nonlinear solution is found. The default value is -1, which means no branch limit is imposed.

Range: {-1, ..., ∞}

Default: -1

GOP_MAXWIDMD (integer): maximum width flag for the global solution

Synonym: MAXWIDMD

This is the maximum width flag for the global solution. The GOP branch-and-bound may continue contracting a box with an incumbent solution until its maximum width is smaller than GOP_WIDTOL.

Default: 0

value meaning
0 The maximum width criterion is suppressed
1 The maximum width criterion is performed

GOP_MULTILINEAR (integer): flag indicating if GOP exploits multi linear feature

This is a flag indicating if GOP exploits multi linear feature.

Default: 1

value meaning
0 Off
1 On

GOP_NUM_THREADS (integer): number of parallel threads to be used when solving a nonlinear model with the global optimization solver

This value specifies the number of parallel threads to be used when solving a nonlinear model with the global optimization solver.

Default: 1

GOP_OBJ_THRESHOLD (real): threshold of objective value in the GOP solver

This value specifies the threshold of objective value in the GOP solver. For min problem, if current incumbent solution is less than the threshold GOP solver will stop.

Range: [-1e+30, ∞]

Default: -1e+30

GOP_OPTCHKMD (integer): criterion used to certify the global optimality

Synonym: OPTCHKMD

This specifies the criterion used to certify the global optimality. When this value is 0, the absolute deviation of objective lower and upper bounds should be smaller than GOP_ABSOPTTOL at the global optimum. When its value is 1, the relative deviation of objective lower and upper bounds should be smaller than GOP_RELOPTTOL at the global optimum. 2 means either absolute or relative tolerance is satisfied at global optimum.

Default: 2

GOP_OPT_MODE (integer): mode for GOP optimization

Synonym: OPT_MODE

This specifies the mode for GOP optimization.

Default: 1

value meaning
0 Global search for a feasible solution (thus a feasibility certificate)
1 Global search for an optimal solution
2 Global search for an unboundedness certificate

GOP_POSTLEVEL (integer): amount and type of GOP postsolving

Synonym: POSTLEVEL

This controls the amount and type of GOP post-solving. The default value is: 6 = 2+4 meaning to do both of the below options.

Default: 6

value meaning
+2 Apply LSgetBestBound
+4 Reoptimize variable bounds

GOP_PRELEVEL (integer): amount and type of GOP presolving

Synonym: PRELEVEL

This controls the amount and type of GOP pre-solving. The default value is: 30 = 2+4+8+16 meaning to do all of the below options.

Default: 30

value meaning
+2 Initial local optimization
+4 Initial linear constraint propagation
+8 Recursive linear constraint propagation
+16 Recursive nonlinear constraint propagation

Default: -1

value meaning
-1 Solver decides
0 No
1 Yes

GOP_QUAD_METHOD (integer): specifies if the GOP solver should solve the model as a QP when applicable

Default: -1

value meaning
-1 Solver decides
0 General GOP solver
1 Specified QP solver

GOP_RELBRNDMD (integer): reliable rounding in the GOP branch-and-bound

Synonym: RELBRNDMD

This controls the reliable rounding rule in the GOP branch-and-bound. The global solver applies many suboptimizations to estimate the lower and upper bounds on the global optimum. A rounding error or numerical instability could unintentionally cut off a good solution. A variety of reliable approaches are available to improve the precision.

Default: 0

value meaning
+2 Use smaller optimality or feasibility tolerances and appropriate presolving options
+4 Apply interval arithmetic to reverify the solution feasibility

GOP_RELOPTTOL (real): relative optimality tolerance

Synonyms: OPTTOL RELOPTTOL

This value is the GOP relative optimality tolerance. Solutions must beat the incumbent by at least this amount to become the new best solution.

Default: GAMS OptCR

GOP_SOLLIM (integer): integer solution limit for GOP branch-and-bound

Range: {-1, ..., ∞}

Default: -1

GOP_SUBOUT_MODE (integer): substituting out fixed variables

Synonym: SUBOUT_MODE

This is a flag indicating whether fixed variables are substituted out of the instruction list used in the global solver.

Default: 1

value meaning
0 Do not substitute out fixed variables
1 Substitute out fixed variables

GOP_TIMLIM (integer): time limit in seconds for GOP branch-and-bound

Synonym: TIMLIM

This is the time limit in seconds for GOP branch-and-bound.

Range: {-1, ..., ∞}

Default: GAMS ResLim

GOP_USEBNDLIM (integer): max magnitude of variable bounds flag for GOP convexification

Synonym: USEBNDLIM

This value is a flag for the parameter GOP_BNDLIM.

Default: 2

value meaning
0 Do not use the bound limit on the variables
1 Use the bound limit right at the beginning of global optimization
2 Use the bound limit after the initial local optimization if selected

GOP_WIDTOL (real): maximal width of variable intervals

Synonym: WIDTOL

This value specifies the maximal width of variable intervals for a box to be considered as an incumbent box containing an incumbent solution. It is used when GOP_MAXWIDMD is set at 1.

Default: 1e-4

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

Default: 0

IIS_ANALYZE_LEVEL (integer): controls the level of analysis when locating an IIS

Default: 1

value meaning
+1 Search for necessary rows
+2 Search for necessary columns
+4 Search for sufficient rows
+8 Search for sufficient columns
+16 Consider integrality restrictions as the potential cause of infeasibilities and include it in the analysis
+32 Compute the underlying LTF matrix and use this as the basis of a ranking score to guide the IIS run
+64 If the underlying matrix is totally decomposable, rank blocks w.r.t their sizes and debug the smallest independent infeasible block
+128 Use the nonzero structure of the underlying matrix to compute a ranking score to guide the IIS run
+256 Treat iter/time limits as intractability

IIS_GETMODE (integer): flag that controls whether variable bounds in the IIS should be retrieved or the integer restrictions

Default: 0

value meaning
0 Variable bound
1 Integer restrictions

IIS_INFEAS_NORM (integer): specifies the norm to measure infeasibilities in IIS search

Default: 0

value meaning
0 Solver decides
1 Use L-1 norm
2 L-infinity norm

IIS_ITER_LIMIT (integer): the iteration limit for IIS search

Range: {-1, ..., ∞}

Default: -1

IIS_METHOD (integer): specifies the method to use in analyzing infeasible models to locate an IIS

Default: 0

value meaning
0 Default filter
1 Standard deletion filter
2 Standard additive filter
3 Generalized-binary-search filter
4 Depth-first-binary-search filter
5 Fast-scan filter
6 Standard elastic filter

IIS_PRINT_LEVEL (integer): specifies the amount of print to do during IIS search

Default: 2

IIS_REOPT (integer): specifies which optimization method to use when starting from a given basis

Default: 0

value meaning
0 Free
1 Primal Simplex
2 Dual Simplex
3 Barrier
4 NLP

IIS_TIME_LIMIT (integer): the time limit for IIS search

Range: {-1, ..., ∞}

Default: -1

IIS_TOPOPT (integer): specifies which optimization method to use when there is no previous basis

Default: 0

value meaning
0 Free
1 Primal Simplex
2 Dual Simplex
3 Barrier
4 NLP

IIS_USE_EFILTER (integer): flag that controls whether the Elastic Filter should be enabled as the supplementary filter in analyzing infeasible models

Default: 0

value meaning
-1 Solver decides
0 Do not use elastic filter
1 Use elastic filter

IIS_USE_GOP (integer): flag that controls whether the global optimizer should be enabled in analyzing infeasible NLP models

Default: 0

value meaning
-1 Solver decides
0 Do not use GOP
1 Use GOP

IIS_USE_SFILTER (integer): flag indicating is sensitivity filter will be used during IIS search

Default: 1

value meaning
-1 Solver decides
0 Do not use sensitivity filter
1 Use sensitivity filter

INSTRUCT_SUBOUT (integer): flag to specify how to deal with fixed variables in the instruction list

This is a flag indicating whether 1) fixed variables are substituted out of the instruction list, 2) performing numerical calculation on constant numbers and replacing with the results.

Default: -1

value meaning
-1 Solver decides
0 Substitutions will not be performed
1 Substitutions will be performed

IPM_BASIS_REL_TOL_S (real): maximum relative dual bound violation allowed in an optimal basic solution

Maximum relative dual bound violation allowed in an optimal basic solution.

Default: 1e-12

IPM_BASIS_TOL_S (real): maximum absolute dual bound violation in an optimal basic solution

Maximum absolute dual bound violation in an optimal basic solution.

Default: 1e-7

IPM_BASIS_TOL_X (real): maximum absolute primal bound violation allowed in an optimal basic solution

Maximum absolute primal bound violation allowed in an optimal basic solution.

Default: 1e-7

IPM_BI_LU_TOL_REL_PIV (real): relative pivot tolerance used in the LU factorization in the basis identification procedure

Relative pivot tolerance used in the LU factorization in the basis identification procedure.

Range: [0, 0.999999]

Default: 1e-2

IPM_CHECK_CONVEXITY (integer): flag to check convexity of a quadratic program using barrier solver

This is a flag to check convexity of a quadratic program using barrier solver.

Default: 1

value meaning
-1 Check convexity only without solving the model
0 Use barrier solver to check convexity
1 Do not use barrier solver to check convexity

IPM_CO_TOL_DFEAS (real): dual feasibility tolerance for Conic solver

Default: 1e-8

IPM_CO_TOL_INFEAS (real): maximum bound infeasibility tolerance for Conic solver

Maximum bound infeasibility tolerance for Conic solver.

Default: 1e-12

IPM_CO_TOL_MU_RED (real): optimality tolerance for Conic solver

Default: 1e-8

IPM_CO_TOL_PFEAS (real): primal feasibility tolerance for Conic solver

Default: 1e-8

IPM_MAX_ITERATIONS (integer): ipm iteration limit

Controls the maximum number of iterations allowed in the interior-point optimizer.

Default: 1000

Number of threads to run the interiorpoint optimizer on. This value should be less than or equal to the actual number of processors or cores on a multi-core system.

Default: 1

IPM_OFF_COL_TRH (integer): extent for detecting the offending columns in the Jacobian of the constraint matrix

Controls the extent for detecting the offending columns in the Jacobian of the constraint matrix. 0 means no offending columns will be detected. 1 means offending columns will be detected. In general, increasing the parameter value beyond the default value of 40 does not improve the result.

Default: 40

IPM_TOL_DFEAS (real): dual feasibility tolerance

Dual feasibility tolerance used for linear and quadratic optimization problems.

Default: 1e-8

IPM_TOL_DSAFE (real): controls the initial dual starting point

Controls the initial dual starting point used by the interior-point optimizer. If the interior-point optimizer converges slowly and/or the dual variables associated with constraint or variable bounds are very large, then it might be worthwhile to increase this value.

Range: [1e-4, ∞]

Default: 1

IPM_TOL_INFEAS (real): infeasibility tolerance

This is the tolerance to declare the model primal or dual infeasible using the interior-point optimizer. A smaller number means the optimizer gets more conservative about declaring the model infeasible.

Default: 1e-10

IPM_TOL_MU_RED (real): relative complementarity gap tolerance

Relative complementarity gap tolerance.

Default: 1e-16

IPM_TOL_PATH (real): how close to follow the central path

Controls how close the interior-point optimizer follows the central path. A large value of this parameter means the central path is followed very closely. For numerically unstable problems it might help to increase this parameter.

Range: [0, 0.5]

Default: 1e-8

IPM_TOL_PFEAS (real): primal feasibility tolerance

Primal feasibility tolerance used for linear and quadratic optimization problems.

Default: 1e-8

IPM_TOL_PSAFE (real): controls the initial primal starting point

Controls the initial primal starting point used by the interior-point optimizer. If the interior-point optimizer converges slowly and/or the constraint or variable bounds are very large, then it might be worthwhile to increase this value.

Range: [1e-2, ∞]

Default: 1

IPM_TOL_REL_STEP (real): relative step size to the boundary

Relative step size to the boundary for linear and quadratic optimization problems.

Range: [0, 0.999999]

Default: 0.9999

IUS (boolean): run the IUS finder if the problem is unbounded

Default: 0

IUS_ANALYZE_LEVEL (integer): controls the level of analysis when locating an IUS

Default: 2

value meaning
+2 Search for necessary columns
+8 Search for sufficient columns

LP_AIJ_ZEROTOL (real): coefficient matrix zero tolerance

Default: 2.22045e-16

LP_BIGM (real): big-M for phase-I

Default: 1e6

LP_BNDINF (real): big-M to truncate lower and upper bounds in single phase dual-simplex

Default: 1e15

LP_DPSWITCH (integer): specifies whether LP primal-dual simplex switch is enabled or not

Range: {0, ..., 1}

Default: 1

LP_DRATIO (integer): controls the dual min-ratio strategy

Range: {0, ..., 2}

Default: 1

LP_DYNOBJFACT (real): Dynamic obj factor

Range: [0, 1]

Default: 0.75

LP_DYNOBJMODE (integer): Dynamic obj mode

Default: 0

LP_ITRLMT (integer): simplex iteration limit

Synonym: SPLEX_ITRLMT

Range: {-1, ..., ∞}

Default: infinity

LP_PIV_BIGTOL (real): simplex maximum pivot tolerance

Default: 1e-5

LP_PIV_ZEROTOL (real): simplex pivot zero tolerance

Default: 1e-8

LP_PPARTIAL (integer): primal simplex partial pricing method

Range: {0, ..., 3}

Default: 0

LP_PRELEVEL (integer): controls the amount and type of LP pre-solving

This controls the amount and type of LP pre-solving to be used.

Default: 126

value meaning
+2 Simple pre-solving
+4 Probing
+8 Coefficient reduction
+16 Elimination
+32 Dual reductions
+64 Use dual information
+512 Maximum pass

LP_RATRANGE (integer): controls the number of pivot-candidates to consider when searching for a stable pivot in LU decomposition

Range: {1, ..., ∞}

Default: 4

LP_SCALE (integer): scaling flag

Synonym: SPLEX_SCALE

Default: 1

value meaning
0 Scaling is suppressed
1 Scaling is performed

LP_SPRINT_COLFACT (integer): maximum number of columns in Sprint as a factor of number of rows

Range: {1, ..., ∞}

Default: 10

LP_SPRINT_MAXPASS (integer): maximum number of passes in Sprint method

Range: {1, ..., ∞}

Default: 100

LP_SPRINT_SUB (integer): LP method for subproblem in Sprint method

Default: 0

MIP_ABSCUTTOL (real): MIP absolute cut tolerance

This is the MIP absolute cut tolerance. If the value is less than or equal to zero, it will use the internal decided tolerace, otherwise it will use this value as the abolute tolerace for adding cuts.

Range: [-1.0, ∞]

Default: -1.0

MIP_ABSOPTTOL (real): MIP absolute optimality tolerance

This is the MIP absolute optimality tolerance. Solutions must beat the incumbent by at least this absolute amount to become the new, best solution.

Default: GAMS OptCA

MIP_ADDCUTOBJTOL (real): required objective improvement to continue generating cuts

This specifies the minimum required improvement in the objective function for the cut generation phase to continue generating cuts.

Default: 1.5625e-5

This determines how many constraint cuts can be added as a percentage of the number of original rows in an integer programming model.

Default: 0.75

MIP_ADDCUTPER_TREE (real): percentage of constraint cuts that can be added at child nodes

This determines how many constraint cuts can be added at child nodes as a percentage of the number of original rows in an integer programming model.

Default: 0.5

MIP_AGGCUTLIM_TOP (integer): max number of constraints involved in derivation of aggregation cut at root node

This specifies an upper limit on the number of constraints to be involved in the derivation of an aggregation cut at the root node. The default is .1, which means that the solver will decide.

Range: {-1, ..., ∞}

Default: -1

MIP_AGGCUTLIM_TREE (integer): max number of constraints involved in derivation of aggregation cut at tree nodes

This specifies an upper limit on the number of constraints to be involved in the derivation of an aggregation cut at the tree nodes. The default is .1, which means that the solver will decide.

Range: {-1, ..., ∞}

Default: -1

MIP_ANODES_SWITCH_DF (integer): threshold on active nodes for switching to depth-first search

This specifies the threshold on active nodes for switching to depth-first search rule.

Default: 50000

MIP_AOPTTIMLIM (integer): time in seconds beyond which the relative optimality tolerance will be applied

This is the time in seconds beyond which the relative optimality tolerance, MIP_PEROPTTOL will be applied.

Default: 100

MIP_BIGM_FOR_INTTOL (real): threshold for which coefficient of a binary variable would be considered as big-M

This value specifies the threshold for which the coefficient of a binary variable would be considered as big-M (when applicable).

Default: 1e8

MIP_BRANCHDIR (integer): first branching direction

This specifies the direction to branch first when branching on a variable.

Default: 0

value meaning
0 Solver decides
1 Always branch up first
2 Always branch down first

MIP_BRANCHRULE (integer): rule for choosing the variable to branch

This specifies the rule for choosing the variable to branch on at the selected node.

Default: 0

value meaning
0 Solver decides
1 Basis rounding with pseudo reduced costs
2 Maximum infeasibility
3 Pseudo reduced costs only
4 Maximum coefficient only
5 Previous branching only

MIP_BRANCH_LIMIT (integer): limit on the total number of branches to be created during branch and bound

This is the limit on the total number of branches to be created during branch-and- bound. The default value is -1, which means no limit is imposed. If the branch limit is reached and a feasible integer solution was found, it will be installed as the incumbent (best known) solution.

Range: {-1, ..., ∞}

Default: -1

MIP_BRANCH_PRIO (integer): controls how variable selection priorities are set and used

This controls how variable selection priorities are set and used.

Default: 0

value meaning
0 If the user has specified priorities then use them Otherwise let LINDO API decide
1 If user has specified priorities then use them Overwrite users choices if necessary
2 If user has specified priorities then use them Otherwise do not use any priorities
3 Let LINDO API set the priorities and ignore any user specified priorities
4 Binaries always have higher priority over general integers

MIP_CONCURRENT_REOPTMODE (integer): specifies the concurrent optimization mode with warm start

Default: 0

value meaning
0 no concurrent runs
1 run concurrently if at least 2 threads exist
2 run concurrently

MIP_CONCURRENT_STRATEGY (integer): controls the concurrent MIP strategy

Default: -1

value meaning
-1 Solver decides
1 Defines built-in priority lists for each thread
3 Defines heuristic based strategies for each thread

MIP_CONCURRENT_TOPOPTMODE (integer): specifies the concurrent optimization mode with cold start

Default: 0

value meaning
0 no concurrent runs
1 run concurrently if at least 2 threads exist
2 run concurrently

MIP_CUTDEPTH (integer): threshold value for the depth of nodes in the branch and bound tree

This controls a threshold value for the depth of nodes in the B&B tree, so cut generation will be less likely at those nodes deeper than this threshold.

Default: 8

MIP_CUTFREQ (integer): frequency of invoking cut generation at child nodes

This controls the frequency of invoking cut generation at child nodes. The default value is 10, indicating that the MIP solver will try to generate cuts at every 10 nodes.

Default: 10

MIP_CUTLEVEL_TOP (integer): combination of cut types to try at the root node when solving a MIP

This controls the combination of cut types to try at the root node when solving a MIP. Bit settings are used to enable the various cut types.

Default: 57342

value meaning
+2 GUB cover
+4 Flow cover
+8 Lifting
+16 Plant location
+32 Disaggregation
+64 Knapsack cover
+128 Lattice
+256 Gomory
+512 Coefficient reduction
+1024 GCD
+2048 Obj integrality
+4096 Basis Cuts
+8192 Cardinality Cuts
+16384 Disjunk Cuts
+32768 Soft Knapsack Cuts

MIP_CUTLEVEL_TREE (integer): combination of cut types to try at child nodes in the branch and bound tree when solving a MIP

This controls the combination of cut types to try at child nodes in the B&B tree when solving a MIP.

Default: 53246

value meaning
+2 GUB cover
+4 Flow cover
+8 Lifting
+16 Plant location
+32 Disaggregation
+64 Knapsack cover
+128 Lattice
+256 Gomory
+512 Coefficient reduction
+1024 GCD
+2048 Obj integrality
+4096 Basis Cuts
+8192 Cardinality Cuts
+16384 Disjunk Cuts
+32768 Soft Knapsack Cuts

MIP_CUTOFFOBJ (real): defines limit for branch and bound

If this is specified, then any part of the branch-and-bound tree that has a bound worse than this value will not be considered. This can be used to reduce the running time if a good bound is known.

Default: 1e30

MIP_CUTTIMLIM (integer): time to be spent in cut generation

This controls the total time to be spent in cut generation throughout the solution of a MIP. The default value is -1, indicating that no time limits will be imposed when generating cuts.

Range: {-1, ..., ∞}

Default: -1

MIP_DELTA (real): near-zero value used in linearizing nonlinear expressions

This refers to a near-zero value used in linearizing nonlinear expressions.

Default: 1e-6

MIP_DUAL_SOLUTION (integer): flag for computing dual solution of LP relaxation

This flag controls whether the dual solution to the LP relaxation that yielded the optimal MIP solution will be computed or not.

Default: 0

value meaning
0 Do not calculate dual solution for LP relaxation
1 Calculate dual solution for LP relaxation

MIP_FIXINIT_ITRLIM (integer): iteration limit of the LP solved after fixing integer variables to their initial values

Range: {-1, ..., ∞}

Default: -1

MIP_FP_HEU_MODE (integer): specifies the feasibility-pump (FP) heuristic mode

Default: 0

value meaning
0 FP is disabled
1 Solver decides
2 Enable FP if no cutoff value or initial mip solution was defined
3 Enable FP independent of cutoff values and initial mip solutions
4 Same as 2 but also enable FP on child nodes in branch-bound tree
5 Same as 3 but also enable FP on child nodes in branch-bound tree

MIP_FP_ITRLIM (integer): iteration limit for feasibility pump heuristic

This is the iteration limit in seconds for feasibility pump heuristic. A value of -1 means no iteration limit is imposed.

Default: 500

MIP_FP_MODE (integer): mode for the feasibility pump heuristic

Controls the mode for the feasibility pump heuristic.

Default: -1

value meaning
-1 Solver decides
0 Off
1 On until the first solution
2 Try to get more than one solution

MIP_FP_OPT_METHOD (integer): optimization and reoptimization method for feasibility pump heuristic

This specifies optimization and reoptimization method for feasibility pump heuristic.

Default: 0

value meaning
0 Solver decides
1 Primal simplex
2 Dual simplex
3 Barrier

MIP_FP_PROJECTION (integer): type of objective function of LPs in projection step of the feasibility pump heuristic

Range: {0, ..., 1}

Default: 0

MIP_FP_TIMLIM (real): time limit for feasibility pump heuristic

This is the time limit in seconds for feasibility pump heuristic. A value of -1 implies no time limit is imposed.

Default: 1800

MIP_FP_WEIGTH (real): weight of the objective function in the feasibility pump

Controls the weight of the objective function in the feasibility pump.

Range: [0, 1]

Default: 1

MIP_GENERAL_MODE (integer): general strategy in solving MIPs

This value specifies the general strategy in solving MIPs.

Default: 0

value meaning
0 Solver decides
+2 Disable all time-driven events for reproducibility of runs
+16 Disable cut generation before branching

MIP_HEULEVEL (integer): specifies heuristic used to find integer solution

This specifies the heuristic used to find the integer solution. Possible values are: 0: No heuristic is used. 1: A simple heuristic is used. Typically, this will find integer solutions only on problems with a certain structure. However, it tends to be fast. 2: This is an advanced heuristic that tries to find a "good" integer solution fast. In general, a value of 2 seems to not increase the total solution time and will find an integer solution fast on many problems. A higher value may find an integer solution faster, or an integer solution where none would have been found with a lower level. Try level 3 or 4 on "difficult" problems where 2 does not help. Higher values cause more time to be spent in the heuristic. The value may be set arbitrarily high. However, >20 is probably not worthwhile. MIP_HEUMINTIMLIM controls the time to be spent in searching heuristic solutions.

Default: 3

MIP_HEUMINTIMLIM (integer): minimum time in seconds to be spent in finding heuristic solutions

This specifies the minimum time in seconds to be spent in finding heuristic solutions to the MIP model. MIP_HEULEVEL controls the heuristic used to find the integer solution.

Default: 0

MIP_HEU_DROP_OBJ (integer): flag for whether to use without OBJ heuristic

This is a flag for whether to use without OBJ heuristic.

Default: 0

value meaning
0 Off
1 On

MIP_HEU_MODE (integer): heuristic used in MIP solver

This controls the MIP heuristic mode.

Default: 0

value meaning
0 Solver decides when to stop the heuristic
1 Solver uses a pre-specified time limit to stop the heuristic.
2 Solver uses a pre-specified iteration limit to stop the heuristic

MIP_INTTOL (real): absolute integer feasibility tolerance

An integer variable is considered integer feasible if the absolute difference from the nearest integer is smaller than this.

Default: 1e-6

MIP_ITRLIM (real): iteration limit for branch and bound

This is the total LP iteration limit summed over all branches for branch-and-bound. Range for The default value is -1, which means no iteration limit is imposed. If this iteration limit is reached, branch-and-bound will stop and the best feasible integer solution found will be installed as the incumbent (best known) solution.

Range: [-1, ∞]

Default: infinity

MIP_KBEST_USE_GOP (integer): specifies whether to use gop solver in MIP KBest

Default: 0

value meaning
0 No
1 Yes

MIP_KEEPINMEM (integer): flag for keeping LP bases in memory

If this is set to 1, the integer pre-solver will try to keep LP bases in memory. This typically gives faster solution times, but uses more memory. Setting this parameter to 0 causes the pre-solver to erase bases from memory.

Default: 1

value meaning
0 Do not keep LP bases in memory
1 Keep LP bases in memory

MIP_LBIGM (real): Big-M value used in linearizing nonlinear expressions

This refers to the Big-M value used in linearizing nonlinear expressions.

Default: 10000

MIP_LSOLTIMLIM (integer): time limit until finding a new integer solution

Range: {-1, ..., ∞}

Default: -1

MIP_MAKECUT_INACTIVE_COUNT (integer): threshold for times a cut could remain active after successive reoptimization

This value specifies the threshold for the times a cut could remain active after successive reoptimization during branch-and-bound. If the count is larger than the specified level the solver will inactive the cut.

Default: 10

MIP_MAXCUTPASS_TOP (integer): number passes to generate cuts on the root node

This controls the number passes to generate cuts on the root node. Each of these passes will be followed by a reoptimization and a new batch of cuts will be generated at the new solution.

Default: 200

MIP_MAXCUTPASS_TREE (integer): number passes to generate cuts on the child nodes

This controls the number passes to generate cuts on the child nodes. Each of these passes will be followed by a reoptimization and a new batch of cuts will be generated at the new solution.

Default: 2

MIP_MAXNONIMP_CUTPASS (integer): number of passes allowed in cut-generation that does not improve current relaxation

This controls the maximum number of passes allowed in cut-generation that does not improve the current relaxation.

Default: 3

MIP_MAXNUM_MIP_SOL_STORAGE (integer): maximum number of k-best solutions to store

This specifies the maximum number of k-best solutions to store. Possible values are positive integers.

Default: 1

MIP_MINABSOBJSTEP (real): value to update cutoff value each time a mixed integer solution is found

This specifies the value to update the cutoff value each time a mixed integer solution is found.

Default: 0

MIP_NODESELRULE (integer): specifies the node selection rule

This specifies the node selection rule for choosing between all active nodes in the branch-and-bound tree when solving integer programs.Possible selections are: 0: Solver decides (default). 1: Depth first search. 2: Choose node with worst bound. 3: Choose node with best bound. 4: Start with best bound. If no improvement in the gap between best bound and best integer solution is obtained for some time, switch to: if (number of active nodes<10000) Best estimate node selection (5). else Worst bound node selection (2). 5: Choose the node with the best estimate, where the new objective estimate is obtained using pseudo costs. 6: Same as (4), but start with the best estimate.

Default: 0

value meaning
0 Solver decides
1 Depth first search
2 Choose node with worst bound
3 Choose node with best bound
4 Start with best bound
5 Choose the node with the best estimate
6 Same as 4 but start with the best estimate

MIP_NUM_THREADS (integer): number of parallel threads to use by the parallel MIP solver

This parameter specifies the number of parallel threads to use by the parallel MIP solver. Possible values are positive integers. The default is 1 implying that the parallel solver is disabled.

Range: {1, ..., ∞}

Default: 1

MIP_PARA_FP (integer): flag for whether to use parallelization on the feasibility pump heuristic

This is a flag for whether to use parallelization on the feasibility pump heuristic.

Default: 1

value meaning
0 Off
1 On

MIP_PARA_FP_MODE (integer): flag for the mode of parallel feasibility pump

This is a flag for the mode of parallel feasibility pump.

Default: 0

value meaning
0 Terminate when all threads finish
1 Terminate as soon as the master thread finishes

MIP_PARA_INIT_NODE (real): number of initial nodes for MIP parallelization

This value specifies the number of initial nodes for MIP parallelization.

Range: [-1, ∞]

Default: -1

MIP_PARA_ITR_MODE (integer): flag for iteration mode in MIP parallelization

This is a flag for iteration mode in MIP parallelization.

Default: 1

value meaning
0 Each thread terminates as soon as arrives iteration limit
1 Each thread terminates until all threads get iteration limit

MIP_PARA_RND_ITRLMT (real): iteration limit of each round in MIP parallelization, it is a weighted combination of simplex and barrier iterations

This value specifies the iteration limit of each round in MIP parallelization, it is a weighted combination of simplex and barrier iterations.

Default: 2.0

MIP_PARA_SUB (integer): flag for whether to use MIP parallelization on subproblems solved in MIP preprocessing

This is a flag for whether to use MIP parallelization on subproblems solved in MIP preprocessing.

Default: 1

value meaning
0 Off
1 On

MIP_PEROPTTOL (real): MIP relative optimality tolerance in effect after MIP_AOPTTIMLIM seconds

This is the MIP relative optimality tolerance that will be in effect after T seconds following the start. The value T should be specified using the MIP_AOPTTIMLIM parameter.

Default: 1e-5

MIP_PERSPECTIVE_REFORM (integer): flag for whether to use Perspective Reformulation

This is the flag for wether to use Persective Reformulation.

Default: 1

value meaning
0 Off
1 On

MIP_POLISH_ALPHA_TARGET (real): proportion solutions in the pool to initiate a polishing-task at the current node

This value specifies the proportion solutions in the pool to initiate a polishing-task at the current node.

Range: [0.01, 0.99]

Default: 0.6

MIP_POLISH_MAX_BRANCH_COUNT (integer): maximum number of branches to polish

This value specifies the maximum number of branches to polish.

Default: 2000

MIP_POLISH_NUM_BRANCH_NEXT (integer): number of branches to polish in the next round

This value specifies the number of branches to polish in the next round.

Default: 4000

MIP_PREHEU_DFE_VSTLIM (integer): limit for the variable visit in depth first enumeration

Limit for the variable visit in depth first enumeration.

Default: 200

MIP_PREHEU_LEVEL (integer): heuristic level for the prerelax solver

The heuristic level for the prerelax solver.

Default: 0

value meaning
0 Nothing
1 One-change
2 One-change and two-change
3 Depth first enumeration

MIP_PREHEU_TC_ITERLIM (integer): iteration limit for the two change heuristic

Iteration limit for the two change heuristic.

Default: 30000000

MIP_PREHEU_VAR_SEQ (integer): sequence of the variable considered by the prerelax heuristic

The sequence of the variable considered by the prerelax heuristic.

Default: -1

value meaning
-1 Backward
1 Forward

MIP_PRELEVEL (integer): controls the amount and type of MIP pre-solving at root node

This controls the amount and type of MIP pre-solving at root node.

Default: 3070

value meaning
+2 Simple pre-solving
+4 Probing
+8 Coefficient reduction
+16 Elimination
+32 Dual reductions
+64 Use dual information
+128 Binary row presolving
+256 Row aggregation
+512 Coef Probe Lifting
+1024 Maximum pass
+2048 Similar row

MIP_PRELEVEL_TREE (integer): amount and type of MIP pre-solving at tree nodes

This controls the amount and type of MIP pre-solving at tree nodes.

Default: 1214

value meaning
+2 Simple pre-solving
+4 Probing
+8 Coefficient reduction
+16 Elimination
+32 Dual reductions
+64 Use dual information
+128 Binary row presolving
+256 Row aggregation
+512 Coef Probe Lifting
+1024 Maximum pass

MIP_PRE_ELIM_FILL (integer): controls fill-in introduced by eliminations during pre-solve

This is a nonnegative value that controls the fill-in introduced by the eliminations during pre-solve. Smaller values could help when the total nonzeros in the presolved model is significantly more than the original model.

Default: 100

MIP_PSEUDOCOST_RULE (integer): specifies the rule in pseudocost computations for variable selection

This specifies the rule in pseudocost computations for variable selection.

Default: 0

value meaning
0 Solver decides
1 Only use min pseudo cost
2 Only use max pseudo cost
3 Use quadratic score function and the pseudo cost weigth
4 Same as 3 without quadratic score

MIP_PSEUDOCOST_WEIGT (real): weight in pseudocost computations for variable selection

This specifies the weight in pseudocost computations for variable selection.

Default: 1.5625e-05

MIP_REDCOSTFIX_CUTOFF (real): cutoff value as a percentage of the reduced costs

This specifies the cutoff value as a percentage of the reduced costs to be used in fixing variables when using the reduced cost fixing heuristic.

Default: 0.9

MIP_REDCOSTFIX_CUTOFF_TREE (real): cutoff value as a percentage of the reduced costs at tree nodes

This specifies the cutoff value as a percentage of the reduced costs to be used in fixing variables when using the reduced cost fixing heuristic at tree nodes.

Default: 0.9

MIP_RELINTTOL (real): relative integer feasibility tolerance

An integer variable is considered integer feasible if the difference between its value and the nearest integer value divided by the value of the nearest integer is less than this.

Default: 8e-6

MIP_RELOPTTOL (real): MIP relative optimality tolerance

This is the MIP relative optimality tolerance. Solutions must beat the incumbent by at least this relative amount to become the new, best solution.

Default: GAMS OptCR

MIP_REOPT (integer): optimization method to use when doing reoptimization

This specifies which optimization method to use when doing reoptimization from a given basis.

Default: 0

value meaning
0 Solver decides
1 Use primal method
2 Use dual simplex
3 Use barrier solver

MIP_SCALING_BOUND (integer): maximum difference between bounds of an integer variable for enabling scaling

This controls the maximum difference between the upper and lower bounds of an integer variable that will enable the scaling in the simplex solver when solving a subproblem in the branch-and-bound tree.

Default: 10000

MIP_SOLLIM (integer): integer solution limit for MIP solver

Range: {-1, ..., ∞}

Default: -1

MIP_SOLVERTYPE (integer): optimization method to use when solving mixed-integer models

This specifies the optimization method to use when solving mixed-integer models.

Default: 0

value meaning
0 Solver decides
1 Use Branch and Bound only
2 Use Enumeration and Knapsack solver only

MIP_STRONGBRANCHDONUM (integer): minimum number of variables to try the strong branching on

This value specifies the minimum number of variables, among all the candidates, to try the strong branching on.

Default: 3

MIP_STRONGBRANCHLEVEL (integer): depth from the root in which strong branching is used

This specifies the depth from the root in which strong branching is used. The default value of 10 means that strong branching is used on a level of 1 to 10 measured from the root. Strong branching finds the real bound for branching on a given variable, which, in most cases, requires a solution of a linear program and may therefore also be quite expensive in computing time. However, if used on nodes close to the root node of the tree, it also gives a much better bound for that part of the tree and can therefore reduce the size of the branch-and-bound tree.

Default: 10

MIP_SWITCHFAC_SIM_IPM_ITER (integer): specifies the (positive) factor that multiplies the number of constraints to impose an iteration limit to simplex method and trigger a switch over to the barrier method

Range: {-1, ..., ∞}

Default: -1

MIP_SWITCHFAC_SIM_IPM_TIME (real): factor that multiplies the number of constraints to impose a time limit to simplex method and trigger a switch over to the barrier method

This specifies the (positive) factor that multiplies the number of constraints to impose a time limit to simplex method and trigger a switch over to the barrier method. A value of -1.0 means that no time limit is imposed.

Range: [-1, ∞]

Default: -1

MIP_SYMMETRY_MODE (integer): specifies mip symmetry handling methods

Default: 0

value meaning
0 Do not use symmetries
1 Adding symmetry breaking cuts
2 Orbital fixing

MIP_SYMMETRY_NONZ (integer): limit on number of nonzeros to look for symmetries

Range: {0, ..., ∞}

Default: 50000

MIP_TIMLIM (integer): time limit in seconds for integer solver

This is the time limit in seconds for branch-and-bound. The default value is -1, which means no time limit is imposed. However, the value of SOLVER_TIMLMT will be applied to each continuous subproblem solve. If the value of this parameter is greater than 0, then the value of SOLVER_TIMLMT will be disregarded. If this time limit is reached and a feasible integer solution was found, it will be installed as the incumbent (best known) solution.

Range: {-1, ..., ∞}

Default: GAMS ResLim

MIP_TOPOPT (integer): optimization method to use when there is no previous basis

This specifies which optimization method to use when there is no previous basis.

Default: 0

value meaning
0 Solver decides
1 Use primal method
2 Use dual simplex
3 Use barrier solver

MIP_TREEREORDERLEVEL (integer): tree reordering level

This specifies the tree reordering level.

Default: 10

MIP_TREEREORDERMODE (integer): tree reordering mode

This specifies the tree reordering mode.

Default: 1

value meaning
1 Use tree reordering only for subproblems
2 Use tree reordering for subproblems and the main bnb loop only when LP status is infeasible
3 Not use tree reordering
4 Use tree reordering based on MIP_TREEREORDERLEVEL

MIP_USECUTOFFOBJ (integer): flag for using branch and bound limit

This is a flag for the parameter MIP_CUTOFFOBJ. If you do not want to lose the value of the parameter MIP_CUTOFFOBJ, this provides an alternative to disabling the cutoff objective.

Default: 1

value meaning
0 Do not use current cutoff value
1 Use current cutoff value

MIP_USE_CUTS_HEU (integer): controls if cut generation is enabled during MIP heuristics

This flag controls if cut generation is enabled during MIP heuristics. The default is -1 (i.e. the solver decides).

Default: -1

value meaning
-1 Solver decides
0 Do not use cut heuristic
1 Use cut heuristic

MIP_USE_ENUM_HEU (integer): frequency of enumeration heuristic

This specifies the frequency of enumeration heuristic.

Default: 4

value meaning
0 Off
1 Only at top (root) node without cuts
2 Both at top (root) and tree nodes without cuts
3 Same as 1 with cuts
4 Same as 2 with cuts

MIP_USE_INT_ZERO_TOL (integer): controls if all MIP calculations would be based on absolute integer feasibility tolarance

This flag controls if all MIP calculations would be based on the integrality tolarance specified by MIP_INTTOL.

Default: 0

value meaning
0 Do not base MIP calculations on MIP_INTTOL
1 Base MIP calculations on MIP_INTTOL

Default: -1

value meaning
-1 Solver decides
1 Try parallel mode but if it is not available try concurrent mode
2 Try parallel mode only
3 Try concurrent mode but if it is not available try parallel mode
4 Try concurrent mode only

NLP_AUTODERIV (integer): defining type of computing derivatives

This is a flag to indicate if automatic differentiation is the method of choice for computing derivatives and select the type of differentiation.

Default: 0

value meaning
0 Finite Differences approach will be used
1 Forward type of Automatic Differentiation will be used
2 Backward type of Automatic Differentiation will be used

NLP_AUTOHESS (integer): flag for using Second Order Automatic Differentiation for solving NLP

This is a flag to indicate if Second Order Automatic Differentiation will be performed in solving a nonlinear model. The second order derivatives provide an exact/precise Hessian matrix to the SQP algorithm, which may lead to less iterations and better solutions, but may also be quite expensive in computing time for some cases.

Default: 0

value meaning
0 Do not use Second Order Automatic Differentiation
1 Use Second Order Automatic Differentiation

NLP_CONIC_REFORM (integer): determines if to explore conic reformulation

Default: 1

value meaning
0 No
1 Yes

NLP_CONOPT_VER (integer): specifies the CONOPT version to be used in NLP optimizations

Range: {3, ..., 4}

Default: 3

NLP_CUTOFFOBJ (real): as soon as any multi-start thread achieves this value all threads stop

If the current best objective of the NLP being solved in a multistart run is better than this value, the solver will terminate early without exhausting the maximum number of multistarts. This is a way of saving computer time if the current best solution is sufficiently attractive.

Range: [-1e30, ∞]

Default: -1e30

NLP_DERIV_DIFFTYPE (integer): flag indicating the technique used in computing derivatives with finite differences

This is a flag indicating the technique used in computing derivatives with Finite Differences.

Default: 0

value meaning
0 The solver decides
1 Use forward differencing method
2 Use backward differencing method
3 Use center differencing method

NLP_FEASCHK (integer): how to report results when solution satisfies tolerance of scaled but not original model

This input parameter specifies how the NLP solver reports the results when an optimal or local-optimal solution satisfies the feasibililty tolerance (NLP_FEASTOL) of the scaled model but not the original (descaled) one.

Default: 1

value meaning
0 Perform no action accept the final solution
1 Declare the model status as FEASIBLE if maximum violation in the unscaled model is not higher than 10 times NLP_FEASTOL
2 Declare the model status as UNKNOWN if maximum violation in the unscaled model is higher than NLP_FEASTOL

NLP_FEASTOL (real): feasibility tolerance for nonlinear constraints

This is the feasibility tolerance for nonlinear constraints. A constraint is considered violated if the artificial, slack, or surplus variable associated with the constraint violates its lower or upper bounds by the feasibility tolerance.

Default: 1e-6

NLP_INF (real): numeric infinity for nonlinear models

Specifies the numeric infinity for nonlinear models. Possible values are positive real numbers. Smaller values could cause numerical problems.

nlp_ipm2grg This is a flag to switch from IPM solver to the standard NLP (GRG) solver when IPM fails due to numerical errors.

Default: 1e30

NLP_IPM2GRG (integer): switch from IPM solver to GRG solver when IPM fails due to numerical errors

Default: 1

value meaning
0 Do not switch
1 Switch

NLP_ITERS_PER_LOGLINE (integer): number of nonlinear iterations to elapse before next progress message

Number of nonlinear iterations to elapse before next progress message.

Range: {1, ..., ∞}

Default: 10

NLP_ITRLMT (integer): nonlinear iteration limit

This controls the iteration limit on the number of nonlinear iterations performed.

Range: {-1, ..., ∞}

Default: GAMS IterLim

NLP_LINEARZ (integer): extent to which the solver will attempt to linearize nonlinear models

This determines the extent to which the solver will attempt to linearize nonlinear models.

Default: -1

value meaning
-1 Solver decides
0 No linearization occurs
1 Linearize ABS, MAX, MIN and similar
2 Same as previous plus IF, AND, OR, NOT and all logical operators are linearized
4 Same as previoys plus Nonlinear operators involving integer/binary variables
256 Same as previous plus DIVIDE reformulation

NLP_LINEARZ_WB_CONSISTENT (integer): determines if linearization process is consistent with WB/excel calculation

Default: 0

value meaning
0 No
1 Yes

NLP_MAXLOCALSEARCH (integer): maximum number of local searches

This controls the maximum number of local searches (multistarts) when solving a NLP using the multistart solver.

Default: 5

NLP_MAXLOCALSEARCH_TREE (integer): maximum number of multistarts

Maximum number of multistarts (at tree nodes)

Default: 1

NLP_MAX_RETRY (integer): maximum number refinement retries to purify the final NLP solution

Maximum number refinement retries to purify the final NLP solution.

Range: {-1, ..., ∞}

Default: 5

NLP_MSW_EUCDIST_THRES (real): euclidean distance threshold in multistart search

Euclidean distance threshold in multistart search

Default: 0.001

NLP_MSW_FILTMODE (integer): filtering mode to exclude certain domains during sampling in multistart search

Filtering mode to exclude certain domains during sampling in multistart search.

Default: -1

value meaning
-1 Solver decides
+1 Filter-out the points around known KKT or feasible points previously visited
+2 Filter-out the points whose p are in the vicinity of p(x)
+4 Filter-out the points in the vicinity of x where x are initial points of all previous local optimizations
+8 Filter-out the points whose p(.) values are below a dynamic threshold tolerance

NLP_MSW_MAXNOIMP (integer): maximum number of consecutive populations to generate without any improvements

Maximum number of consecutive populations to generate without any improvements.

Range: {-1, ..., ∞}

Default: -1

NLP_MSW_MAXPOP (integer): maximum number of populations to generate in multistart search

Maximum number of populations to generate in multistart search.

Range: {-1, ..., ∞}

Default: -1

NLP_MSW_MAXREF (integer): maximum number of reference points to generate trial points in multistart search

Maximum number of reference points in the solution space to generate trial points in multistart search.

Range: {-1, ..., ∞}

Default: -1

NLP_MSW_NORM (integer): norm to measure the distance between two points in multistart search

Norm to measure the distance between two points in multistart search.

Range: {-1, ..., ∞}

Default: 2

NLP_MSW_NUM_THREADS (integer): number of parallel threads to be used when solving an NLP model with the multistart solver

This value specifies the number of parallel threads to be used when solving an NLP model with the multistart solver.

Default: 1

NLP_MSW_OVERLAP_RATIO (real): rate of replacement in successive populations

This value specifies the rate of replacement in successive populations. Higher values favors survival of points in the parent population.

Range: [0.0, 1.0]

Default: 0.1

NLP_MSW_POXDIST_THRES (real): penalty function neighborhood threshold in multistart search

Penalty function neighborhood threshold in multistart search

Default: 0.01

NLP_MSW_PREPMODE (integer): preprocessing strategies in multistart solver

This value specifies the preprocessing strategies in multistart solver.

Default: -1

value meaning
-1 Solver decides
+1 Truncate free variables
+2 Scale reference points to origin
+4 Enable expansive scaling of radius[k] by hit[k]
+8 Skewed sampling allowing values in the vicinity of origin.
+16 Get best bounds by presolver
+32 Get best bounds using GOP
+64 Enable sampling of free variables (not recommended)
+128 Collect sufficiently many trial points prior to local solves
+256 Enable power solver, trying several different local strategies
+512 Share presolver stack for large models

NLP_MSW_RG_SEED (integer): random number generator seed for the multistart solver

This value specified the random number generator seed for the multistart solver.

Default: 1019

NLP_MSW_RMAPMODE (integer): specifies the mode to map reference points in the unit cube into the original space

Default: -1

value meaning
-1 Solver decides
0 Use original variable bounds
1 Use min-max values over all sample points per each dimension
2 Use min-max values over all sample points over all dimensions

NLP_MSW_SOLIDX (integer): index of the multistart solution to be loaded

Index of the multistart solution to be loaded main solution structures.

Default: 0

NLP_MSW_XKKTRAD_FACTOR (real): KKT solution neighborhood factor in multistart search

KKT solution neighborhood factor in multistart search

Default: 0.85

NLP_MSW_XNULRAD_FACTOR (real): initial solution neighborhood factor in multistart search

Initial solution neighborhood factor in multistart search

Default: 0.5

NLP_PRELEVEL (integer): controls the amount and type of NLP pre-solving

This controls the amount and type of NLP pre-solving.

Default: 126

value meaning
+2 Simple pre-solving
+4 Probing
+8 Coefficient reduction
+16 Elimination
+32 Dual reductions
+64 Use dual information
+512 Maximum pass

NLP_PSTEP_FINITEDIFF (real): value of the step length in computing the derivatives using finite differences

This controls the value of the step length in computing the derivatives using finite differences.

Default: 5e-7

This is a flag indicating if the nonlinear model should be examined to check if it is a quadratic model.

Default: 1

value meaning
0 Do not check if NLP is quadratic
1 Check if NLP is quadratic

NLP_REDGTOL (real): tolerance for the gradients of nonlinear functions

This is the tolerance for the gradients of nonlinear functions. The (projected) gradient of a function is considered to be the zero-vector if its norm is below this tolerance.

Default: 1e-7

NLP_SOLVER (integer): type of nonlinear solver

This value determines the type of nonlinear solver.

Default: 7

value meaning
4 Solver decides
5 Uses Levenberg-Marquardt method to solve nonlinear least-squares problem
6 Uses Barrier solver for convex QCP models
7 Uses CONOPTs reduced gradient solver
8 Uses SLP solver
9 Uses CONOPT with multistart feature enabled

NLP_SOLVE_AS_LP (integer): flag indicating if the nonlinear model will be solved as an LP

This is a flag indicating if the nonlinear model will be solved as an LP. 1 means that an LP using first order approximations of the nonlinear terms in the model will be used when optimizing the model with the LSoptimize() function.

Default: 0

value meaning
0 NLP will not be solved as LP
1 NLP will be solved as LP

NLP_STALL_ITRLMT (integer): iteration limit before a sequence of non-improving NLP iterations is declared as stalling

This specifies the iteration limit before a sequence of non-improving NLP iterations is declared as stalling, thus causing the solver to terminate.

Default: 100

NLP_STARTPOINT (integer): flag for using initial starting solution for NLP

This is a flag indicating if the nonlinear solver should accept initial starting solutions.

Default: 1

value meaning
0 Do not use initial starting solution for NLP
1 Use initial starting solution for NLP

NLP_SUBSOLVER (integer): type of nonlinear subsolver

This controls the type of linear solver to be used for solving linear subproblems when solving nonlinear models.

Default: 1

value meaning
1 Primal simplex method
2 Dual simplex method
3 Barrier solver with or without crossover

NLP_USECUTOFFOBJ (integer): flag to use parameter NLP_CUTOFFOBJ

This is a flag for the parameter NLP_CUTOFFOBJ. The value of 0 means NLP_CUTOFFOBJ will be ignored, else it will be used as specified.

Default: 0

value meaning
-1 Solver decides
0 No
1 Yes

NLP_USE_CRASH (integer): flag for using simple crash routines for initial solution

This is a flag indicating if an initial solution will be computed using simple crash routines.

Default: 0

value meaning
0 Do not use simple crash routines
1 Use simple crash routines

NLP_USE_LINDO_CRASH (integer): flag for using advanced crash routines for initial solution

This is a flag indicating if an initial solution will be computed using advanced crash routines.

Default: 1

value meaning
0 Do not use advanced crash routines
1 Use advanced crash routines

NLP_USE_SDP (integer): flag to use SDP solver for POSD constraint

Default: 1

value meaning
0 No
1 Yes

NLP_USE_SELCONEVAL (integer): flag for using selective constraint evaluations for solving NLP

This is a flag indicating if selective constraint evaluations will be performed in solving a nonlinear model.

Default: 1

value meaning
0 Do not use selective constraint evaluations
1 Use selective constraint evaluations

NLP_USE_SLP (integer): flag for using sequential linear programming step directions for updating solution

This is a flag indicating if sequential linear programming step directions should be used in updating the solution.

Default: 1

value meaning
-1 Solver decides
0 Do not use sequential linear programming step directions
1 Use sequential linear programming step directions

NLP_USE_STEEPEDGE (integer): flag for using steepest edge directions for updating solution

This is a flag indicating if steepest edge directions should be used in updating the solution.

Default: 0

value meaning
0 Do not use steepest edge directions
1 Use steepest edge directions

Number of threads to use in the solver routine to be called. It is a solver-independent parameter which internally sets solver-specific threading parameters automatically. If the GAMS threads parameter is set to 0, the Lindo default will be used, which is 1.

Range: {1, ..., ∞}

Default: GAMS Threads

PROB_TO_SOLVE (integer): controls whether the explicit primal or dual form of the given LP problem will be solved

This flag controls whether the explicit primal or dual form of the given LP problem will be solved.

Default: 0

value meaning
0 Solver decides
1 Explicit primal form
2 Explicit dual form

PROFILER_LEVEL (integer): specifies the profiler level to break down the total cpu time into.

Specifies the profiler level to break down the total cpu time into.

Default: 0

value meaning
0 Profiler is off
+1 Enable for simplex solver
+2 Enable for integer solver
+4 Enable for multistart solver
+8 Enable for global solver

REPORTEVSOL (no value): solve and report the expected value solution

Default: 0

SAMP_CDSINC (real): correlation matrix diagonal shift increment

Correlation matrix diagonal shift increment.

Default: 1e-6

SAMP_NCM_CUTOBJ (real): objective cutoff (target) value to stop the nearest correlation matrix (NCM) subproblem

Objective cutoff (target) value to stop the nearest correlation matrix (NCM) subproblem.

Default: 1e-30

SAMP_NCM_DSTORAGE (integer): flag to enable or disable sparse mode in NCM computations

Flag to enable/disable sparse mode in NCM computations.

Range: {-1, ..., ∞}

Default: -1

SAMP_NCM_ITERLIM (integer): iteration limit for NCM method

Iteration limit for NCM method.

Default: 100

SAMP_NCM_METHOD (integer): bitmask to enable methods for solving the nearest correlation matrix (NCM) subproblem

Bitmask to enable methods for solving the nearest correlation matrix (NCM) subproblem.

Default: 5

SAMP_NCM_OPTTOL (real): optimality tolerance for NCM method

Optimality tolerance for NCM method.

Default: 1e-7

SAMP_NUM_THREADS (integer): specifies the number of parallel threads to be used when sampling

Default: 0

SAMP_RG_BUFFER_SIZE (integer): specifies the buffer size for random number generators in running in parallel mode

Default: 0

SAMP_SCALE (integer): flag to enable scaling of raw sample data

Flag to enable scaling of raw sample data.

Default: 0

SOLVER_CONCURRENT_OPTMODE (integer): controls if simplex and interior-point optimizers will run concurrently

Controls if simplex and interior-point optimizers will run concurrently, 0 means no concurrent runs will be performed, 1 means both optimizers will run concurrently if at least two threads exist in system, 2 means both optimizers will run concurrently.

Default: 0

value meaning
0 no concurrent runs
1 run concurrently if at least 2 threads exist
2 run concurrently

SOLVER_CUTOFFVAL (real): solver will exit if optimal solution is worse than this

If the optimal objective value of the LP being solved is shown to be worse than this (e.g., if the dual simplex method is being used), then the solver will exit without finding a feasible solution. This is a way of saving computer time if there is no sufficiently attractive solution. SOLVER_USECUTOFFVAL needs to be set to 1 to activate this value.

Default: 0

SOLVER_FEASTOL (real): feasibility tolerance

This is the feasibility tolerance. A constraint is considered violated if the artificial, slack, or surplus variable associated with the constraint violates its lower or upper bounds by the feasibility tolerance.

Default: 1e-7

SOLVER_IPMSOL (integer): basis crossover flag for barrier solver

This flag controls whether a basis crossover will be performed when solving LPs with the barrier solver. A value of 0 indicates that a crossover to a basic solution will be performed. If the value is 1, then the barrier solution will be left intact. For example, if alternate optima exist, the barrier method will return a solution that is, loosely speaking, the average of all alternate optima.

Default: 0

value meaning
0 Perform crossover to basis solution
1 Leave barrier solution intact

SOLVER_IUSOL (integer): flag for computing basic solution for infeasible model

This is a flag that, when set to 1, will force the solver to compute a basic solution to an infeasible model that minimizes the sum of infeasibilities and a basic feasible solution to an unbounded problem from which an extreme direction originates. When set to the default of 0, the solver will return with an appopriate status flag as soon as infeasibility or unboundedness is detected. If infeasibility or unboundedness is declared with presolver's determination, no solution will be computed.

Default: 0

value meaning
0 Return appropriate status if infeasibility is encountered
1 Force the solver to compute a basic solution to an infeasible model

SOLVER_METHOD (integer): specifies the method to use when generic solver is invoked

Default: 0

value meaning
0 FREE
1 PSIMPLEX
2 DSIMPLEX
3 BARRIER
4 NLP
5 MIP
6 MULTIS
7 GOP
8 IIS
9 IUS
10 SBD
11 SPRINT
12 GA

SOLVER_MODE (integer): controls some of the advanced strategies when solving LPs

Default: 1

value meaning
+1 Add distinct basic solutions to the pool of alternate optimal solutions
+2 Add edge/nonbasic solutions to the pool of alternate optimal solutions
+4 Favor basic solutions with integer values when choosing solutions to add to the pool of alternate optimal solutions
+32 Export each lex-model
+64 Export failed lex-model when numerical issues are encountered
+128 Resolve failed lex-model with presolver off
+256 Eliminate all dependent variables from the formulation by substitution

SOLVER_OPTTOL (real): dual feasibility tolerance

This is the optimality tolerance. It is also referred to as the dual feasibility tolerance. A dual slack (reduced cost) is considered violated if it violates its lower bound by the optimality tolerance.

Default: 1e-7

SOLVER_PRE_ELIM_FILL (integer): fill-in introduced by the eliminations during pre-solve

This is a nonnegative value that controls the fill-in introduced by the eliminations during pre-solve. Smaller values could help when the total nonzeros in the presolved model is significantly more than the original model.

Default: 1000

SOLVER_RESTART (integer): starting basis flag

This is the starting basis flag. 1 means LINDO API will perform warm starts using any basis currently in memory. 0 means LINDO API will perform cold starts discarding any basis in memory and starting from scratch.

Default: 0

value meaning
0 Perform cold start
1 Perform warm start

SOLVER_TIMLMT (integer): time limit in seconds for continous solver

This is a time limit in seconds for the LP solver. The default value of -1 imposes no time limit.

Range: {-1, ..., ∞}

Default: GAMS ResLim

SOLVER_USECUTOFFVAL (integer): flag for using cutoff value

This is a flag for the parameter SOLVER_CUTOFFVAL

Default: 0

value meaning
0 Do not use cutoff value
1 Use cutoff value

SPLEX_DPRICING (integer): pricing option for dual simplex method

This is the pricing option to be used by the dual simplex method.

Default: -1

value meaning
-1 Solver decides the dual pricing method
0 Partial pricing
1 Steepest edge

SPLEX_DUAL_PHASE (integer): controls the dual simplex strategy

This controls the dual simplex strategy, single-phase versus two-phase.

Default: 0

value meaning
0 Solver decides
1 Single-phase
2 Two-phase

SPLEX_PPRICING (integer): pricing option for primal simplex method

This is the pricing option to be used by the primal simplex method.

Default: -1

value meaning
-1 Solver decides the primal pricing method
0 Partial pricing
1 Devex

SPLEX_REFACFRQ (integer): number of simplex iterations between two consecutive basis re-factorizations

This is a positive integer scalar referring to the simplex iterations between two consecutive basis re-factorizations. For numerically unstable models, setting this parameter to smaller values may help.

Default: 100

STOC_ABSOPTTOL (real): absolute optimality tolerance (w.r.t lower and upper bounds on the true objective) to stop the solver

Absolute optimality tolerance (w.r.t lower and upper bounds on the true objective) to stop the solver. . Possible values are reals in (0,1) interval.

Default: GAMS OptCA

Flag to use add-instructions mode when building deteq.

Default: 0

STOC_ALD_DUAL_FEASTOL (real): dual feasibility tolerance for ALD

Dual feasibility tolerance for ALD.

Default: 1e-4

STOC_ALD_DUAL_STEPLEN (real): dual step length for ALD

Dual step length for ALD.

Default: 0.9

STOC_ALD_INNER_ITER_LIM (integer): inner loop iteration limit for ALD

Inner loop iteration limit for ALD.

Default: 1000

STOC_ALD_OUTER_ITER_LIM (integer): outer loop iteration limit for ALD

Outer loop iteration limit for ALD.

Default: 200

STOC_ALD_PRIMAL_FEASTOL (real): primal feasibility tolerance for ALD

Primal feasibility tolerance for ALD.

Default: 1e-4

STOC_ALD_PRIMAL_STEPLEN (real): primal step length for ALD

Primal step length for ALD.

Default: 0.5

STOC_AUTOAGGR (integer): flag to enable or disable autoaggregation

Flag to enable or disable autoaggregation.

Default: 1

STOC_BENCHMARK_SCEN (integer): benchmark scenario to compare EVPI and EVMU against

Benchmark scenario to compare EVPI and EVMU against.

Range: {-2, ..., ∞}

Default: -2

STOC_BIGM (real): big-M value for linearization and penalty functions

Big-M value for linearization and penalty functions.

Default: 1e7

STOC_BUCKET_SIZE (integer): bucket size in Benders decomposition

Bucket size in Benders decomposition. Possible values are positive integers or (-1) for solver decides.

Range: {-1, ..., ∞}

Default: -1

STOC_CALC_EVPI (integer): flag to enable or disable calculation of EVPI

Flag to enable/disable calculation of lower bounds on EVPI.

Default: 1

value meaning
0 disable
1 enable

STOC_CORRELATION_TYPE (integer): correlation type associated with correlation matrix

Correlation type associated with the correlation matrix.

Default: 0

value meaning
-1 Target correlation
0 Pearson correlation
1 Kendall correlation
2 Spearman correlation

STOC_DEQOPT (integer): method to solve the DETEQ problem

This specifies the method to use when solving the deterministic equivalent.

Default: 0

value meaning
0 Solver decides
10 Use simple Benders Decomposition

STOC_DETEQ_TYPE (integer): type of deterministic equivalent

Type of deterministic equivalent to be used by the solver. Implicit determinisitc equivalent is valid for linear and integer models only.

Default: -1

value meaning
-1 Solver decides
0 Implicit determinisitc equivalent
1 Explicit determinisitc equivalent

STOC_DS_SUBFORM (integer): subproblem formulation to use in DirectSearch

This parameter specifies the type of subproblem formulation to be used in heuristic search.

Default: -1

value meaning
-1 Solver decides
0 Perform heuristic search in the original solution space
1 Perform heuristic search in the space of discrete variables coupled with optimizations in the linear space

STOC_ELIM_FXVAR (integer): flag to enable elimination of fixed variables from deteq MPI

Flag to enable elimination of fixed variables from deteq MPI.

Default: 1

STOC_INFBND (real): value to truncate infinite bounds at non-leaf nodes

Value to truncate infinite bounds at nonleaf nodes.

Default: 1e9

STOC_ITER_LIM (integer): iteration limit for stochastic solver

Iteration limit for stochastic solver. Possible values are positive integers or (-1) no limit.

Range: {-1, ..., ∞}

Default: infinity

STOC_MAP_MPI2LP (integer): flag to specify whether stochastic parameters in MPI will be mapped as LP matrix elements

Flag to specify whether stochastic parameters in MPI will be mapped as LP matrix elements.

Default: 0

STOC_MAX_NUMSCENS (integer): maximum number of scenarios before forcing automatic sampling

Maximum number of scenarios before forcing automatic sampling. Possible values are positive integers.

Default: 40000

STOC_METHOD (integer): stochastic optimization method to solve the model

Stochastic optimization method to solve the model.

Default: -1

value meaning
-1 Solve with the method chosen by the solver
0 Solve the deterministic equivalent (DETEQ)
1 Solve with the Nested Benders Decomposition (NBD) method

STOC_NAMEDATA_LEVEL (integer): name data level

Name data level.

Default: 1

STOC_NODELP_PRELEVEL (integer): presolve level solving node-models

Presolve level solving node-models.

Default: 0

value meaning
+2 Simple pre-solving
+4 Probing
+8 Coefficient reduction
+16 Elimination
+32 Dual reductions
+64 Use dual information
+512 Maximum pass

STOC_NSAMPLE_PER_STAGE (string): list of sample sizes per stage (starting at stage 2)

Comma separated list of sample sizes per stage. The sample size of stage 1 is assumed to be 1 so that this list starts with stage stage 2.

STOC_NSAMPLE_SPAR (integer): common sample size per stochastic parameter

Common sample size per stochastic parameter. Possible values are positive integers.

Range: {-1, ..., ∞}

Default: -1

STOC_NSAMPLE_STAGE (integer): common sample size per stage

Common sample size per stage.

Range: {-1, ..., ∞}

Default: -1

This value specifies the number of parallel threads to be used when solving a stochastic programming model.

Default: 1

STOC_RELOPTTOL (real): relative optimality tolerance (w.r.t lower and upper bounds on the true objective) to stop the solver

Relative optimality tolerance (w.r.t lower and upper bounds on the true objective) to stop the solver. Possible values are reals in (0,1) interval.

Default: GAMS OptCR

STOC_REL_DSTEPTOL (real): dual-step tolerance

This value specifies the dual-step tolerance in decomposition based algorithms.

Default: 1e-7

STOC_REL_PSTEPTOL (real): primal-step tolerance

This value specifies the primal-step tolerance in decomposition based algorithms.

Default: 1e-8

STOC_REOPT (integer): reoptimization method to solve the node-models

Reoptimization method to solve the node-models.

Default: 0

value meaning
0 Solver decides
1 Use primal method
2 Use dual simplex
3 Use barrier solver
4 Use NLP solver

STOC_RG_SEED (integer): seed to initialize the random number generator

Seed to initialize the random number generator. Possible values are positive integers.

Default: 1031

STOC_SAMP_CONT_ONLY (integer): flag to restrict sampling to continuous stochastic parameters only or not

Flag to restrict sampling to continuous stochastic parameters only or not.

Default: 1

value meaning
0 disable
1 enable

STOC_SBD_MAXCUTS (integer): max cuts to generate for master problem

Max cuts to generate for master problem.

Range: {-1, ..., ∞}

Default: -1

STOC_SBD_NUMCANDID (integer): maximum number of candidate solutions to generate at SBD root

Maximum number of candidate solutions to generate at SBD root.

Range: {-1, ..., ∞}

Default: -1

STOC_SBD_OBJCUTFLAG (integer): flag to enable objective cut in SBD master problem

Flag to enable objective cut in SBD master problem.

Default: 1

STOC_SBD_OBJCUTVAL (real): RHS value of objective cut in SBD master problem

RHS value of objective cut in SBD master problem.

Default: 1e-30

STOC_SHARE_BEGSTAGE (integer): stage beyond which node-models are shared

Stage beyond which node-models share the same model structure. Possible values are positive integers less than or equal to number of stages in the model or (-1) for solver decides.

Range: {-1, ..., ∞}

Default: -1

STOC_TIME_LIM (real): time limit for stochastic solver

Time limit for stochastic solver. Possible values are nonnegative real numbers or -1 for solver decides.

Range: [-1, ∞]

Default: GAMS ResLim

STOC_TOPOPT (integer): optimization method to solve the root problem

Optimization method to solve the root problem.

Default: 0

value meaning
0 Solver decides
1 Use primal method
2 Use dual simplex
3 Use barrier solver
4 Use NLP solver
6 Use multi-start solver
7 Use global solver

STOC_VARCONTROL_METHOD (integer): sampling method for variance reduction

Sampling method for variance reduction.

Default: 1

value meaning
0 Montecarlo sampling
1 Latinsquare sampling
2 Antithetic sampling

STOC_WSBAS (integer): warm start basis for wait-see model

Warm start basis for wait-see model .

Range: {-1, ..., ∞}

Default: -1

SVR_LS_ANTITHETIC (string): Sample variance reduction map to Lindo Antithetic algorithm

SVR_LS_LATINSQUARE (string): Sample variance reduction map to Lindo Latin Square algorithm

SVR_LS_MONTECARLO (string): Sample variance reduction map to Lindo Montecarlo algorithm

TUNER_PRINT_LEVEL (integer): specifies the amount of print to do during parameter tuning

Default: 1

value meaning
0 Do not print anything default
>0 Print more information

USEGOP (integer): use global optimization

This value determines whether the global optimization will be used.

Default: 1

value meaning
0 Do not use global optimization
1 Use global optimization

WRITEDEMPI (string): write deterministic equivalent in MPI format

WRITEDEMPS (string): write deterministic equivalent in MPS format

WRITEMPI (string): write (S)MPI file of processed model

If this option is set, Lindo write an MPI file of processed model. If set, the value of this option defines the name of the MPI file.

WRITEMPS (string): write (S)MPS file of processed model

# Stochastic Programming (SP) in GAMS/Lindo

GAMS/Lindo can also solve stochastic programming models. The syntax to set up an SP problem in GAMS is explained in the chapter Stochastic Programming (SP) with EMP. The options to control LINDOs stochastic solver are described in the subsection SP Options.

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