On algorithmsforthetricriteriashortestpathproblemwithtwobottleneck objective functions

This paperaddressesatricriteriapathprobleminvolvingtwobottleneckobjectivefunctionsandacost. It presentsanenhancedmethodthatcomputesshortestpathsinsubnetworks,obtainedbyrestricting the setofarcsaccordingtothebottleneckvaluesinordertofindtheminimalcompletesetofPareto- optimalsolutions,andtakingintoaccounttheobjectivevaluesofthedeterminedshortestpathsto reduce thenumberofconsideredsubnetworks,andthusthenumberofsolvedshortestpathproblems. A labelingprocedurefortheproblemisalsodeveloped.Thealgorithmsarecomparedwiththeprevious literature.Moreoveravariantofthefirstmethodispresented.Itsaimistochoosethesolutionswiththe best bottleneckvaluewhenthecostisthesame.Resultsforrandominstancesrevealthattheenhanced method isthefastest,andthat,inaverage,itrunsinlessthan20sfornetworkswith30000nodes,an averagedegreeof20and1000distinctbottleneckvalues.Itsvariantthatavoidstiesimprovedthe formerversionupto15%forcostsin ½1; 10 .