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An Iterated Local Search Approach for Finding Provably Good Solutions for Very Large TSP Instances

  • Peter Merz
  • Jutta Huhse
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5199)

Abstract

Meta-heuristics usually lack any kind of performance guarantee and therefore one cannot be certain whether the resulting solutions are (near) optimum solutions or not without relying on additional algorithms for providing lower bounds (in case of minimization).

In this paper, we present a highly effective hybrid evolutionary local search algorithm based on the iterated Lin-Kernighan heuristic combined with a lower bound heuristic utilizing 1-trees. Since both upper and lower bounds are improved over time, the gap between the two bounds is minimized by means of effective heuristics. In experiments, we show that the proposed approach is capable of finding short tours with a gap of 0.8% or less for TSP instances up to 10 million cities. Hence, to the best of our knowledge, we present the first evolutionary algorithm and meta-heuristic in general that delivers provably good solutions and is highly scalable with the problem size. We show that our approach outperforms all existing heuristics for very large TSP instances.

Keywords

Local Search Problem Size Travel Salesman Problem Travel Salesman Problem Memetic Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Peter Merz
    • 1
  • Jutta Huhse
    • 2
  1. 1.Department of Computer ScienceUniversity of KaiserslauternGermany
  2. 2.IBFI Schloss DagstuhlWadernGermany

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