Inthisarticle,thenewcrossover operatorBBXfor Evolutionary Algorithms (EAs) for traveling salesmanproblems(TSPs)isintroduced.Itusesbranch-and-boundtofindtheoptimalcombination ofthe(directed)edgespresentintheparentsolutions.Theoffspringsolutionscreatedareatleastas goodastheirparentsandareonlycomposedofparentalbuildingblocks.Theoperatorisclosertothe idealconceptofcrossoverinEAsthanexistingoperators.Thisarticleprovidesthemostextensive studyoncrossoveroperatorsontheTSP,comparingBBXtotenotheroperatorsonthe110instances oftheTSPLibbenchmarksetinEAswithfourdifferentpopulationsizes.BBX,withitsbetterability toreuseandcombinebuildingblocks,surprisinglydoesnotgenerallyoutperformtheotheroperators. However,itperformswellincertainscenarios.Besidespresentinganovelapproachtocrossoveron theTSP,thestudysignificantlyextendsandrefinesthebodyofknowledgeonthefieldwithnew conclusionsandcomparisonresults.