Improving the efficiency of Helsgaun's Lin-Kernighan Heuristic for the symmetric TSP

Authors:
Dirk Richter;Boris Goldengorin;Gerold Jäger;Paul Molitor
Affiliations:
Computer Science Institute, University of Halle-Wittenberg, Halle, Saale, Germany;Faculty of Economic Sciences, University of Groningen, Groningen, The Netherlands and University of Economics and Business, Khmelnitsky, Ukraine and Department of Applied Mathematics, Khmelnitsky ...;Department of Computer Science, Washington University, St. Louis, Missouri;Computer Science Institute, University of Halle-Wittenberg, Halle, Saale, Germany
Venue:
CAAN'07 Proceedings of the 4th conference on Combinatorial and algorithmic aspects of networking
Year:
2007

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Abstract

Helsgaun has introduced and implemented the lower tolerances (α-values) for an approximation of Held-Karp's 1-tree with the purpose to improve the Lin-Kernighan Heuristic (LKH) for the Symmetric TSP (STSP). The LKH appears to exceed the performance of all STSP heuristic algorithms proposed to date. In this paper we improve Helsgaun's LKH based on an approximation of Zhang and Looks' backbones and an extension of double bridges further combined with implementation details by all of which we guide the search process instead of Helsgaun's α-values. Our computational results are competitive and lead to improved solutions for some of the VLSI instances announced at the TSP homepage.