Lignes directrices. Constraint Programming. Software to solve CSPs

Transcription

1 Lignes directrices Constraint Programming Lab 1. Introduction to OPL Ruslan Sadykov INRIA Bordeaux Sud-Ouest 6 March / 18 2 / 18 Software to solve CSPs Commercial IBM ILOG CP Optimizer (free for academic use), interfaces : C++, Java, IBM ILOG CPLEX Optimization Studio (OPL). Artelys Kalis, interfaces : C++, Java, Xpress-Mosel. Microsoft Solver Foundation, interfaces : CLS-compliant languages (C++, IronPython,...) Add-in Designer for Excel Free MiniZinc (modeling language), interface : MiniZincIDE. Choco Solver, interface : Java. Gecode, interface : C++. Others are mentioned on Wikipedia (article «Constraint Programming»). Example : frequency assignment Variables : F i frequency assigned to transmitter i. Additional variables : S i = 0 if low frequency 1 if high frequency. Constraints : Fi F j d ij, (i, j) ; all-different(f 1,..., F 5 ). Additional constraints : element(si, {0, 0, 0, 1, 1, 1, 1, F i ), i. gcc({si i, {0, 1, 2, 3, 2, 3). T 1 3 T 5 T 2 T 4 T / 18 4 / 18

2 Lignes directrices IBM ILOG CPLEX Optimization Studio Trial version (community edition) : http ://www-01.ibm.com/software/integration/ optimization/cplex-cp-optimizer/ (Windows, Linux, Mac OS,...) 5 / 18 6 / 18 Data and variables declaration Data file /********************************************* * OPL Model * File : frequencies.mod *********************************************/ using CP ; //!!!!! int nbfreqs =... ; int nbtrans =... ; range Freqs = 1..nbFreqs ; range Trans = 1..nbTrans ; int Diffs[Trans,Trans] =... ; int BasseHaute[Freqs] =... ; dvar int F[Trans] in Freqs ; dvar int S[Trans] in 0..1 ; /********************************************* * OPL Data * File : frequencies.dat *********************************************/ nbfreqs = 7 ; nbtrans = 5 ; Diffs = [[ ] [ ] [ ] [ ] [ ]] ; BasseHaute = [ ] ; 7 / 18 8 / 18

3 Objective and constraints declaration Find all solutions minimize max(t in Trans) F[t] ; subject to { forall (ordered t1, t2 in Trans : Diffs[t1,t2] > 0) abs( F[t1] - F[t2] ) >= Diffs[t1,t2] ; alldifferent(f) ; forall (t in Trans) S[t] == element(bassehaute,f[t]) ; count(s,0) == 2 ; count(s,1) == 3 ; for (var t=1 ; t<=nbtrans ; t++) writeln("f["+t+"]="+f[t]) ; main { thisoplmodel.generate() ; cp.startnewsearch() ; var n=0 ; while (cp.next()) { n = n+1 ; write("solution -> ") ; writeln(n) ; for (var t=1 ; t<=thisoplmodel.nbtrans ; t++) writeln("\t F["+t+"]="+thisOplModel.F[t]) ; cp.endsearch() ; 9 / / 18 Some constraints available in OPL Declaration of heuristics Arithmétiques (on peut utilisez min, max, count, abs, element). Logiques (&&,,!, =>,!=, ==). Explicites (allowedassignments, forbiddenassignments). Pour l ordonnancement (endbeforestart, endatstart, nooverlap,...) Specialisées (alldifferent, allmindistance, inverse, lex, pack) var fc = cp.factory ; var phase1 = fc.searchphase(f, fc.selectsmallest(fc.varindex(f)), fc.selectlargest(fc.value())) ; cp.setsearchphases(phase1) ; Variable evaluations : varindex(dvar int[]) domainsize() domainmin() regretonmin() successrate() impact()... Value evaluations : value() valueimpact() valuesuccessrate() explicitvalueeval(int[],int[]) valueindex(int[]) 11 / / 18

4 Solver parameters Using OPL in CREMI var p = cp.param ; p.logperiod = ; p.searchtype = "DepthFirst" ; p.timelimit = 600 ; Options : AllDiffInterenceLevel CountInferenceLevel ElementInferenceLevel BranchLimit TimeLimit LogVerbosity PropagationLog SearchType <number> <number>(in seconds) Quiet, Terse, Normal, Verbose Quiet, Terse, Normal, Verbose depthfirst, Restart, MultiPoint 1. Download and unarchive the model for frequency assignment problem : teaching/mse3315c/tp/frequencies.zip 2. Open Terminal and connect to server : ssh mcgonagall ou ssh trelawney 3. Execute the following command (or put in ~/.bashrc) export LD_LIBRARY_PATH=$LD_LIBRARY_PATH:/ opt/local/cplex_studio/opl/bin/ x86-64_sles10_ Go to the frequency assignment model repository and execute : oplrun frequencies.mod frequencies.dat 13 / / 18 Using OPL in CREMI (2) Documentation is available or search for in the Internet. /opt/local/cplex_studio/doc/html/ en-us/documentation.html «IBM ILOG CPLEX Optimization Studio V documentation» Accessing OPL from exterior of CREMI Lignes directrices 1. Connect ot the access server of CREMI by ssh : ssh <login>@jaguar.emi.u-bordeaux1.fr 2. Connect to one of the servers : ssh mcgonagall ou ssh trelawney 15 / / 18

5 Problem description Practical information A steel mill has an inventory of steel slabs of different sizes. From these steel slabs, we need to manufacture different types of steel coils. Every steel coil type requires a different production process encoded by a color. Every order is characterized by the weight and color of the steel coil. Every steel slab can be used for production of steel coils of at most two different colors. The total weight of steel coils produced from the same steel slab cannot exceed its capacity (or size). The objective is to minimize to total loss (unused capacity of steel slabs). Necessary files are available at Help teaching/mse3315c/tp/stillmill.zip or : IDE and OPL > OPL > OPL keywords > or dexpr : IDE and OPL > OPL > OPL keywords > dexpr pack : IDE and OPL > OPL > OPL functions > pack 17 / / 18