Variable neighbourhooddecompositionsearchfor0–1mixed integerprograms

In thispaperweproposeanewhybridheuristicforsolving0–1mixedintegerprogramsbasedonthe principleofvariableneighbourhooddecompositionsearch.Itcombinesvariableneighbourhoodsearch with ageneral-purposeCPLEXMIPsolver.Weperformsystematichardvariablefixing(ordiving) following thevariableneighbourhoodsearchrules.Thevariablestobefixedarechosenaccordingto their distancefromthecorrespondinglinearrelaxationsolutionvalues.Ifthereisanimprovement, variableneighbourhooddescentbranchingisperformedasthelocalsearchinthewholesolutionspace. Numericalexperimentshaveproventhatexploitingboundaryeffectsinthiswayconsiderablyimproves solution quality.Withourapproach,wehavemanagedtoimprovethebestknownpublishedresultsfor 8 outof29instancesfromawell-knownclassofverydifficultMIPproblems.Moreover,computational results showthatourmethodoutperformstheCPLEXMIPsolver,aswellasthreeotherrecentmost successfulMIPsolutionmethods.