A searchspace“cartography”forguidinggraphcoloringheuristics

We presentasearchspaceanalysisanditsapplicationinimprovinglocalsearchalgorithmsforthegraph coloring problem.Usingaclassicaldistancemeasurebetweencolorings,weintroducethefollowing clustering hypothesis: thehighqualitysolutionsare not randomly scatteredinthesearchspace,but rather groupedinclusterswithinspheresofspecificdiameter.Wefirstprovideintuitiveevidenceforthis hypothesis bypresentingaprojectionofalargesetoflocalminimainthe3Dspace.Anexperimental confirmation isalsopresented:weintroducetwoalgorithmsthatexploitthehypothesisbyguidingan underlying TabuSearch(TS)process.Thefirstalgorithm(TS-Div)usesalearningprocesstoguidethe basic TSprocesstowardas-yet-unvisited spheres. Thesecondalgorithm(TS-Int)makesdeepinvestigations within aboundedregionbyorganizingitasatree-likestructureofconnectedspheres.Weexperimentally demonstrate thatifsucharegioncontainsaglobaloptimum,TS-Intdoesnotfailineventuallyfindingit. This pairofalgorithmssignificantlyoutperformstheunderlyingbasicTSalgorithm;itcanevenimprove some ofthebest-knownsolutionseverreportedintheliterature(e.g.for dsjc1000.9).