dicegrid.gms : MIP Decomposition and Parallel Grid Submission - DICE Example


Keywords: mixed integer linear programming, dice designment, mathematics,
          nontransitive dice, decomposition, GAMS grid facility


  • Gardner, M, The Colossal Book of Mathematics. WV Norton, New York, NY, 2001.
  • Bosch, R A, Mindsharpener. Optima MP 70 (2003), 8-9.
  • Bosch, R A, Monochromatic Squares. Optima MP 71 (2004), 6-7.

Large Model of Type : MIP

Category : GAMS Model library

Main file : dicegrid.gms

$title MIP Decomposition and Parallel Grid Submission - DICE Example (DICEGRID,SEQ=330)

Keywords: mixed integer linear programming, dice designment, mathematics,
          nontransitive dice, decomposition, GAMS grid facility

$eolCom //
$ifE %system.gamsversion%<231 $abort Version too old! Need 231 or higher

$if not set mipmodel $set mipmodel dice

* Retrieve the model '%mipmodel%' from the GAMS Model library and include the model source
$call gamslib -q %mipmodel%
$set nosolve yes       // Instruct the dice model source to skip the solve statement
$include %mipmodel%

* Set some model spefic parameters for the generic decompostion and
* solution procedure.  This requires knowledge about naming in the
* dice model:
$if not set objvar $set objvar wnx
$if not set module $set module xdice
$if not set minmax $set minmax max
$if not set gdxvar $set gdxvar comp
$if not set solvar $set solvar fval.l,%objvar%.l,%gdxvar%.l

* Configuration parameters for Decomposition
$if not set nsub     $set nsub 4  // 2 to 3 times the number of machines available
$if not set submit   $set submit parsubmit

* Some macro definition to keep the remain source readable
$set solve solve %module% using mip %minmax% %objvar%
$set test '>' $set cutoff 'cutlo' $set incumbent -INF
$ifI %minmax% == min
$set test '<' $set cutoff 'cutup' $set incumbent +INF

File and container names
 GAMS Sub-Programs
   writeincb.gms  GAMS program called by GAMS/Cplex whenever a new incumbent
                  is found by the Cplex workers
   checkincb.gms  GAMS program frequently called by the master to see if a
                  better overall incumbent has been found by the Cplex workers.
                  In case of a new incumbent, this program communicates the
                  incumbent value as a cutoff to all Cplex workers.

 GAMS/Cplex Option files
   cplex.opt      Includes 'dumptree' option to produce decomposition
   cplex.op2      worker option file in case of sequential submit
   cplex.op3      incumbent as cutoff option (written by checkincb.gms, read by workers)
   cplex.XXX      XXX=100+userjobid (UJI) option file for worker with userjobid

 Text files
   t%UJI%.trg     trigger names that instruct the GAMS/Cplex work to read cplex.op3
   incb%UJD%.txt  current worker incumbent values
   allincb.txt    temp file to collect work incumbent values used by checkincb.gms

 GDX files
   bnd%UJI%.gdx   decomposition bound files created by 'dumptree' option
   incb.gdx       container name for incumbent value and solution values
   bchout_i%UJI%.gdx  worker incumbent solution processed by writeincb.gms

* Remove files so we start clean
$call rm -f bnd*.gdx bch*.gdx t*.trg incb.gdx incb*.txt allincb.txt GMSbch*.*

$onEcho > cplex.opt
dumptree %nsub%  // stop after having nsub open nodes and export these
mipInterval 1    // just for display

* All remaining options focus on improving the bound to generate
* subproblems of equal but reduced level of difficulty
nodeSel 1        // best bound selection
preSlvNd 2       // node presolve
repeatPresolve 3 // second presolve after cut generation
mipEmphasis 3    // focus on improving the best bound
varSel 3         // strong branching

   rep       'report of times and solution'
   incumbent 'best solution so far' / %incumbent% /;

   s_grid   'subproblems from GAMS/Cplex dumpopt' / 1*%nsub% /;

   flog 'file handle to write to the log'   / '' /
   fopt 'file handle to write option files' / 'cplex.opt' /;

* Create decomposition with up to nsub GDX containers with bounds on discrete variables
option optCr = 0, optCa = 0, solPrint = off, mip = cplex, limRow=0, limCol = 0;
%module%.optFile = 1; %solve%;

execute_unload 'incb.gdx', incumbent; // Create GDX container for incumbent

* Save possible integer feasible solution of this run, it could be the optimum
if(%module%.modelStat = %modelStat.optimal% or %module%.modelStat = %modelStat.integerSolution%,
   incumbent = %objvar%.l;
   execute_unload 'incb.gdx', incumbent, %solvar%;

$goto %submit%

$label  seqsubmit
$sTitle Sequential Submit and Solve of the Subproblems
$echo mipEmphasis 3 > cplex.op2
*  Load the bounds corresponding to the subproblem and solve the subproblem
   put_utility 'gdxin' / 'bnd' s_grid.tl;
   execute_load %gdxvar%;
   if(not execerror,
      %module%.cutoff = incumbent;
      %module%.optFile = 2; %solve%;
      rep(s_grid,'elapsed') = timeelapsed;
      rep(s_grid,'time')    = %module%.resUsd;
      rep(s_grid,'mstat' )  = %module%.modelStat;
      rep(s_grid,'sstat')   = %module%.solveStat;
      if(%module%.modelStat = %modelStat.optimal% or %module%.modelStat = %modelStat.integerSolution%,
         rep(s_grid,'obj')  = %module%.objVal;
         if(%objvar%.l %test% incumbent,
            incumbent       = %module%.objVal;
            execute_unload 'incb.gdx', incumbent, %solvar%;
         rep(s_grid,'obj') = na;
      rep(s_grid,'mstat') = 99;
      rep(s_grid,'sstat') = 99;
      execerror = 0;

if(not mapval(incumbent), // not INF or -INF
   execute_load 'incb.gdx', %solvar%;
   display %solvar%;
   put flog '*** Optimal solution found: ' incumbent /;
   put flog '*** Problem infeasible' /;

display rep;

$label parsubmit
$sTitle Parallel Submit and Solve in parallel
$eval nsubp1 %nsub%+1

Create a Cplex option file for each job. This option file instructs
the GAMS/Cplex worker to call out to the GAMS program writeincb.gms
(userincbicall) to save the incumbents found by the workers. It also
tells the GAMS/Cplex jobs to look for a trigger file (iatriggerfile).
If the file exists, GAMS/Cplex will remove the trigger file and read
an option file (iafile). The time GAMS/Cplex looks for a trigger file
(iatriggertime) is set to 1 second, which is quiet small and should be
significantly increased for more difficult problems.

Because of name conflicts every communication file is postfixed with
the userjobid and postfixed with the GAMS working directory. This is
necessary if this run on a real grid system with shared file system.

The nsub problems created by the 'dumptree' decomposition are solved
with an emphasis on moving the best bound. The nsub+1 job will run on
the original problem and focus on finding good feasible solutions.

Scalar cnt;
for(cnt = 1 to %nsubp1%,
   put_utility fopt 'ren' / 'cplex.' (100+cnt):0:0;
*  put   'userincbicall ""%gams.workdir%writeincb.gms"" lo=0'
   put   'userincbicall writeincb.gms lo=0'
       / 'userjobid ' cnt:0:0 / 'usergdxprefix %gams.workdir%'
       / 'interactive 1' / 'iafile "%gams.workdir%cplex.op3"' / 'iatriggertime 1'
       / 'iatriggerfile "%gams.workdir%t' cnt:0:0 '.trg"'
       / 'mipemphasis 3';
   put$(cnt=%nsubp1%) / 'mipemphasis 1';
putclose fopt;

* Save the overall incumbent in file incb0.txt. This file gets updated
* by checkincb.gms if we find an imporved incumbent
put_utility fopt 'ren' / 'incb0.txt';
putclose    fopt '0 ' incumbent:18:8;

%module%.solveLink = %solveLink.AsyncGrid%; // use the GAMS grid submission

    h(s_grid)     'job handle'
    jobssubmitted 'actual number of submitted jobs';

* s_grid is a superset for the decomposition bound sets, execerror will signal the end
loop(s_grid$(not execerror),
*  Load the bounds on the discrete variables
   put_utility 'gdxin' / 'bnd' s_grid.tl:0;
   execute_load %gdxvar%;
   if(not execerror,
      %module%.optFile = 100 + ord(s_grid);
      h(s_grid) = %module%.handle;
execerror     = 0;
jobssubmitted = card(h);

* Submit job with emphasis on finding good feasible solutions.  We do
* not wait for this job to be complete, we just use its incumbent to
* have good cutoff values early. After GAMS is completed we should
* kill the job. Unfortunately, killing a job is extremely system
* dependent (especially if this runs on a real grid).

Scalar feashandle;
%module%.optFile = 100+%nsubp1%; %solve%; feashandle = %module%.handle;

* Collect
rep(s_grid,'mstat')$h(s_grid) = na;
rep(s_grid,'sstat')$h(s_grid) = na;

Scalar bestcompleted 'the best solution of all completed jobs';
bestcompleted = incumbent;

   loop(s_grid$handlecollect(h(s_grid)), // collect if job is completed
      rep(s_grid,'time')  = %module%.resUsd;
      rep(s_grid,'mstat') = %module%.modelStat;
      rep(s_grid,'sstat') = %module%.solveStat;
      rep(s_grid,'obj')   = %module%.objVal;
         if((%module%.modelStat = %modelStat.optimal% or %module%.modelStat = %modelStat.integerSolution%) and %objvar%.l %test% bestcompleted,
            bestcompleted  = %module%.objVal;
            execute_unload 'incb.gdx', bestcompleted, %solvar%;
      display$handledelete(h(s_grid)) 'trouble deleting handles';
      h(s_grid) = 0;
*  see if any of the completed and outstanding jobs has an improved incumbent
   execute$card(h) 'gams checkincb lo=2 --jobs=%nsubp1%';
   display$sleep(card(h)*0.2) 'was sleeping for some time';
until card(h) = 0 or timeelapsed > 150;

Scalar optimal 'optimality indicator';
optimal = sum(s_grid$(rep(s_grid,'sstat')=1),1) = jobssubmitted;

* Load incumbent of job with emphasis on feasibility which might be the optimal solution
execute_load 'bchout_i%nsubp1%.gdx', %solvar%;
if(not execerror and %objvar%.l %test% bestcompleted,
   bestcompleted = %module%.objVal;
   execute_unload 'incb.gdx', bestcompleted, %solvar%;
execerror = 0;

put flog;
put$(card(h)>0)      '*** We have ' card(h):0:0 ' outstanding jobs.' /;
put$(not optimal)    '*** Some jobs returned with solver status <> 1. Optimality not guaranteed' /;
if(not mapval(bestcompleted), // not INF or -INF
   execute_load 'incb.gdx', %solvar%;
   display optimal, %solvar%;
   put$optimal       '*** Optimal solution found: '  bestcompleted /;
   put$(not optimal) '*** Best collected solution: ' bestcompleted /;
   put$optimal       '*** Problem infeasible' /;
   put$(not optimal) '*** No solution found' /;

display rep;

if(not handlecollect(feashandle), display$sleep(5) 'sleeping';);
display$handledelete(feashandle) 'trying now to delete';

$escape =
$onEcho > writeincb.gms
$title Code for worker %userjobid% to update/publish its Incumbent
This uses the existing BCH facility. GAMS/Cplex exports the complete
incumbent in a GDX container called bchout_i%=userjobid%=.gdx. We only
need the objective variable. We create a text file with the userjobid
and the incumbent value. This will be merged with the incumbents from
other workers by the checkincb.gms call. The BCH facility adds the
--ncalls parameter with a sequence number to the call. We do not use
this in this program, but need to list it in the setDDlist.

* Checks for unreferenced double dashes parameters
$setDDlist userjobid ncalls
$set gdxincb %gams.workdir%bchout_i%=userjobid%=.gdx
$set txtincb %gams.workdir%incb%=userjobid%=.txt

Variable %objvar%;
$gdxIn '%gdxincb%' $load %objvar%
File     fx / '%txtincb%' /;
putClose fx '%=userjobid%= ' %objvar%.l:18:8;
$escape %

$escape =
$onEcho > checkincb.gms
$title Collect Incumbents of all worker Jobs.
In case of an improved incumbent update GAMS/Cplex option file
cplex.op3 with a new cutoff value and create the trigger files for the
workers to read the new cutoff value.

This program is frequently executed by the master process.

* Checks for unreferenced double dashes parameters
$setDDlist jobs

* Collect all incumbents from active worker jobs
$call cat incb*.txt > allincb.txt 2> %system.nullfile%
$if not exist allincb.txt $exit

File fx 'filehandle for text files';
Set  s  'jobs submitted' / 0*%=jobs%= /;

   incumbent 'previously found'
   newincb   'new incumbent'
   incb(s)   'incumbent values reported' /
$             onEmpty onEps
$             include allincb.txt

incumbent = incb('0');
newincb   = s%minmax%(s$incb(s), incb(s));

if(newincb %test% incumbent,
   put_utility fx 'ren' / 'cplex.op3';
   put '%cutoff% ' newincb:18:8;
   put_utility fx 'ren' / 'incb0.txt';
   put '0 ' newincb:18:8;
*  tell everyone that we have a new incumbent by posting the trigger file
      put_utility fx 'ren' / 't' s.tl:0 '.trg';
      put 'trigger';
$escape %