$title MIP Decomposition and Parallel Grid Submission - DICE Example (DICEGRID,SEQ=330) $onText Keywords: mixed integer linear programming, dice designment, mathematics, nontransitive dice, decomposition, GAMS grid facility $offText $eolCom // * Retrieve the model dice from the GAMS Model library and include the model source $call gamslib -q dice $set nosolve yes // Instruct the dice model source to skip the solve statement $include dice.gms * Some macro definition to make the code somewhat independent of the objective direction $set gt '>' $set cutoff 'cutlo' $set incumbentInit -INF * Use the line below for minimization problems *$set gt '<' $set cutoff 'cutup' $set incumbentInit +INF $onText 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 $offText * Set number of binary variables to decompose the original one (note: 2**nsub jobs) $set nvars 4 $eval nsub power(2,%nvars%) Set s_grid 'subproblems' / 1*%nsub% / nvars 'binary variable for scenarios' / 1*%nvars% / up_down 'up/down of binary variable' / up, down / bndUpdate(s_grid,nvars,up_down) 'Binary variables to fix in subproblem' / system.PowerSetRight /; File flog 'file handle to write to the log' / '' / fopt 'file handle to write option files' / 'cplex.opt' /; $sTitle Parallel Submit and Solve in parallel $onText 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. In previous version the GAMS/Cplex option dumptree could be used to create a decomposition of the search space. With the new generic callbacks in Cplex this is not possible anymore and we need to generate a different decompostion scheme. Here we just select a number of variables and fix them to 0 or 1 in the different scenarios. The nsub+1 job will run on the original problem and focus on finding good feasible solutions. $offText Set selbvar(dice,f,fp) 'selected variable to decompose on' bnvarmap(nvars,dice,f,fp) 'mapping between nvars and selbvar'; Scalars diceOffSet, fOffSet, fpOffSet; * Select randomly some binary variables from the model repeat diceOffSet = uniformInt(0,card(dice)-1); fOffSet = uniformInt(0,card(f)-1); fpOffSet = uniformInt(0,card(fp)-1); loop((dice,f,fp)$(sameas('dice1',dice) and sameas('face1',f) and sameas('face1',fp)), selbvar(dice+diceOffSet,f+fOffSet,fp+fpOffSet) = yes); until card(selbvar)>=%nvars%; option bnvarmap(nvars:selbvar); * Remove files so we start clean $hiddenCall rm -f bch*.gdx t*.trg best_incumbent.gdx GMSbch*.* Scalar cnt; for(cnt = 1 to %nsub%+1, put_utility fopt 'ren' / 'cplex.' (100+cnt):0:0; put 'userincbicall updateincb.gms lo=2 appendLog=1' / 'userjobid ' cnt:0:0 / 'interactive 1' / 'iafile cplex.op3' / 'iatriggertime 1' / 'iatriggerfile t' cnt:0:0 '.trg' / 'mipemphasis 3'; put$(cnt=%nsub%+1) / 'mipemphasis 1'; ); putclose fopt; * generate a unique mutex ID $eval mtxID round(frac(jnow)*24*60*60*1000) $funcLibIn mtxlib mtxcclib Function create / mtxlib.Create / timedLock / mtxlib.TimedLock / unlock / mtxlib.Unlock / delete / mtxlib.Delete /; abort$create(%mtxID%) 'problems creating mutex'; * Initialize the best incumbent GDX file wnx.l = %incumbentInit%; execute_unload 'best_incumbent.gdx', wnx; wnx.l = 0; xdice.solveLink = %solveLink.AsyncGrid%; // use the GAMS grid submission Parameter h(s_grid) 'job handle'; option optCr = 0, optCa = 0, solPrint = silent, mip = cplex, limRow=0, limCol = 0; cnt = 0; * Now submit the nsub jobs with the updated bounds asynchronously loop(s_grid, cnt = cnt + 1; xdice.optFile = 100 + cnt; loop((bndUpdate(s_grid,nvars,'up') ,bnvarmap(nvars,selbvar)), comp.fx(selbvar) = 1); loop((bndUpdate(s_grid,nvars,'down'),bnvarmap(nvars,selbvar)), comp.fx(selbvar) = 0); solve xdice using mip max wnx; h(s_grid) = xdice.handle; comp.lo(selbvar) = 0; comp.up(selbvar) = 1; // restore bounds ); * 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 all sub jobs are back and the * incumbent finding jobs still runs, we trigger the termination in the * same way as we trigger updates to the cuttoff. Scalar feashandle; xdice.optFile = 100+%nsub%+1; solve xdice using mip max wnx; feashandle = xdice.handle; Parameter rep 'report of times and solution'; * Collect rep(s_grid,'mstat') = na; rep(s_grid,'sstat') = na; repeat loop(s_grid$handlecollect(h(s_grid)), // collect if job is completed rep(s_grid,'time') = xdice.resUsd; rep(s_grid,'mstat') = xdice.modelStat; rep(s_grid,'sstat') = xdice.solveStat; rep(s_grid,'obj') = xdice.objVal; display$handledelete(h(s_grid)) 'trouble deleting handles'; h(s_grid) = 0; ); 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) = %nsub%; 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' /; abort$timedLock(%mtxID%,1000) 'error acquiring lock for mutex'; execute_load 'best_incumbent.gdx', wnx; abort$unlock(%mtxID%) 'error unlocking mutex'; if(not mapval(wnx.l), // not INF or -INF put$optimal '*** Optimal solution found: ' wnx.l /; put$(not optimal) '*** Best collected solution: ' wnx.l /; else put$optimal '*** Problem infeasible' /; put$(not optimal) '*** No solution found' /; ); display rep; * terminate job with mipemphasis=1 if(not handlecollect(feashandle), put_utility 'shell' / 'echo tilim 0 > cplex.op3' put_utility 'exec' / 'touch t' (%nsub%+1):0:0 '.trg' display$sleep(3) 'sleeping'; ); display$handledelete(feashandle) 'trying now to delete'; display$delete(%mtxID%) 'problems deleting mutex'; * drop the compile-time variable userjobid (perhaps set by command line) so the creation of the * updateincb.gms has the %userjobid% verbatim and not subsituted. $drop userjobid $onEcho > updateincb.gms $title Code for worker %userjobid% to update best_incumbent.gdx $onText 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. If the incumber is better than the so far best known incumbent, we signal to all other jobs a new cutoff. $offText Variable wnx /L 0/, wnx_bi /L 0/; $gdxIn bchout_i%userjobid%.gdx $loadM wnx $gdxIn $funcLibIn mtxlib mtxcclib Function timedLock / mtxlib.TimedLock / unlock / mtxlib.Unlock /; scalar cnt; abort$timedLock(%mtxID%,1000) 'error acquiring lock for mutex'; execute_load 'best_incumbent.gdx', wnx_bi=wnx; if (wnx.l %gt% wnx_bi.l, put_utility 'log' / 'Job %userjobid% updated objective from ' wnx_bi.l:8:2 ' to ' wnx.l:8:2; put_utility 'exec' / 'mv -f bchout_i%userjobid%.gdx best_incumbent.gdx'; * update GAMS/Cplex option file cplex.op3 with a new cutoff value put_utility 'shell' / 'echo %cutoff% ' wnx.l:18:8 ' > cplex.op3'; * create the trigger files for the workers to read the new cutoff value for (cnt=1 to %nsub%+1, put_utility$(cnt<>%userjobid%) 'exec' / 'touch t' cnt '.trg' ); ) abort$unlock(%mtxID%) 'error unlocking mutex'; $offEcho