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Local search algorithms for multiple-depot vehicle routing and for multiple traveling salesman problems with proved performance guarantees

Author

Listed:
  • Asaf Levin

    (Technion–Israel Institute of Technology)

  • Uri Yovel

    (Technion–Israel Institute of Technology)

Abstract

We consider two related problems: the multiple-depot vehicle routing problem (MDVRP) and the Multiple traveling salesman problem (mTSP). In both of them, given is the complete graph on n vertices $$G = (V,E)$$ with nonnegative edge lengths that form a metric on V. Also given is a positive integer k. In typical applications, V represents locations of customers and k represents the number of available vehicles. In MDVPR, we are also given a set of k depots $$\{O_1,\ldots ,O_k\} \subseteq V$$ , and the goal is to find a minimum-length cycle cover of G of size k, that is, a collection of k (possibly empty) cycles such that each $$v \in V$$ is in exactly one cycle, and each cycle in the cover contains exactly one depot. In mTSP, no depots are given, so the goal is to find (any) minimum-length cycle cover of G of size k. We present local search algorithms for both problems, and we prove that their approximation ratio is 2.

Suggested Citation

  • Asaf Levin & Uri Yovel, 2014. "Local search algorithms for multiple-depot vehicle routing and for multiple traveling salesman problems with proved performance guarantees," Journal of Combinatorial Optimization, Springer, vol. 28(4), pages 726-747, November.
    • Handle: RePEc:spr:jcomop:v:28:y:2014:i:4:d:10.1007_s10878-012-9580-x
    DOI: 10.1007/s10878-012-9580-x
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    References listed on IDEAS

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    1. Orlin, James & Punnen, Abraham & Schulz, Andreas, 2004. "Approximate Local Search in Combinatorial Optimization," Working papers 4325-03, Massachusetts Institute of Technology (MIT), Sloan School of Management.
    2. Bektas, Tolga, 2006. "The multiple traveling salesman problem: an overview of formulations and solution procedures," Omega, Elsevier, vol. 34(3), pages 209-219, June.
    3. Chung-Lun Li & David Simchi-Levi, 1990. "Worst-Case Analysis of Heuristics for Multidepot Capacitated Vehicle Routing Problems," INFORMS Journal on Computing, INFORMS, vol. 2(1), pages 64-73, February.
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