Dancing to the State of the Art? How Candidate Lists Influence LKH for Solving the Traveling Salesperson Problem

Research output: Contribution to book/Conference proceedings/Anthology/ReportConference contributionContributedpeer-review

Abstract

Solving the Traveling Salesperson Problem (TSP) remains a persistent challenge, despite its fundamental role in numerous generalized applications in modern contexts. Heuristic solvers address the demand for finding high-quality solutions efficiently. Among these solvers, the Lin-Kernighan-Helsgaun (LKH) heuristic stands out, as it complements the performance of genetic algorithms across a diverse range of problem instances. However, frequent timeouts on challenging instances hinder the practical applicability of the solver. Within this work, we investigate a previously overlooked factor contributing to many timeouts: The use of a fixed candidate set based on a tree structure. Our investigations reveal that candidate sets based on Hamiltonian circuits contain more optimal edges. We thus propose to integrate this promising initialization strategy, in the form of POPMUSIC, within an efficient restart version of LKH. As confirmed by our experimental studies, this refined TSP heuristic is much more efficient – causing fewer timeouts and improving the performance (in terms of penalized average runtime) by an order of magnitude – and thereby challenges the state of the art in TSP solving.

Details

Original languageEnglish
Title of host publicationParallel Problem Solving from Nature – PPSN XVIII
EditorsMichael Affenzeller, Stephan M. Winkler, Anna V. Kononova, Thomas Bäck, Heike Trautmann, Tea Tušar, Penousal Machado
Pages100-115
Number of pages16
ISBN (electronic)978-3-031-70055-2
Publication statusPublished - 7 Sept 2024
Peer-reviewedYes

Publication series

SeriesLecture Notes in Computer Science
Volume15148
ISSN0302-9743

External IDs

Scopus 85204605590
ORCID /0000-0003-3929-7465/work/168718804
ORCID /0000-0003-2862-1418/work/168719591
ORCID /0000-0002-3571-667X/work/168720492

Keywords

Keywords

  • Algorithm Configuration, Benchmarking, Heuristic Search, Problem Hardness, Traveling Salesperson Problem