Anytime Behavior of Inexact TSP Solvers and Perspectives for Automated Algorithm Selection
This work addresses the problem of optimizing solver selection for NP-hard TSP instances, offering incremental improvements in understanding solver behavior for researchers and practitioners in combinatorial optimization.
The study analyzed the anytime behavior of inexact TSP solvers like LKH and EAX using empirical runtime distributions, revealing that solver performance rankings depend heavily on the targeted approximation quality, with insights enabling better hybrid solvers and improved automated algorithm selection models.
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.