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

TL;DR

This paper investigates the anytime performance of inexact TSP solvers, analyzing empirical runtime distributions to improve understanding of solver behavior, problem hardness, and to enhance automated algorithm selection.

Contribution

It extends benchmarking studies by analyzing anytime behavior, introduces instance features for performance prediction, and explores hybrid solver construction based on performance intersections.

Findings

Performance ranking depends on approximation quality.

Intersection points of solver performances enable hybridization.

Instance features improve automated algorithm selection.

Abstract

The Traveling-Salesperson-Problem (TSP) is arguably one of the best-known NP-hard combinatorial optimization problems. The two sophisticated heuristic solvers LKH and EAX and respective (restart) variants manage to calculate close-to optimal or even optimal solutions, also for large instances with several thousand nodes in reasonable time. In this work we extend existing benchmarking studies by addressing anytime behaviour of inexact TSP solvers based on empirical runtime distributions leading to an increased understanding of solver behaviour and the respective relation to problem hardness. It turns out that performance ranking of solvers is highly dependent on the focused approximation quality. Insights on intersection points of performances offer huge potential for the construction of hybridized solvers depending on instance features. Moreover, instance features tailored to anytime performance and corresponding performance indicators will highly improve automated algorithm selection models by including comprehensive information on solver quality.