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The Traveling-Salesperson-Problem (TSP) is arguably one of the best-knownNP-hard combinatorial optimization problems. The two sophisticated heuristicsolvers LKH and EAX and respective (restart) variants manage to calculateclose-to optimal or even optimal solutions, also for large instances withseveral thousand nodes in reasonable time. In this work we extend existingbenchmarking studies by addressing anytime behaviour of inexact TSP solversbased on empirical runtime distributions leading to an increased understandingof solver behaviour and the respective relation to problem hardness. It turnsout that performance ranking of solvers is highly dependent on the focusedapproximation quality. Insights on intersection points of performances offerhuge potential for the construction of hybridized solvers depending on instancefeatures. Moreover, instance features tailored to anytime performance andcorresponding performance indicators will highly improve automated algorithmselection models by including comprehensive information on solver quality.

Anytime Behavior of Inexact TSP Solvers and Perspectives for Automated Algorithm Selection