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

Asaf Levin () and Uri Yovel ()
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Asaf Levin: Technion–Israel Institute of Technology
Uri Yovel: Technion–Israel Institute of Technology

Journal of Combinatorial Optimization, 2014, vol. 28, issue 4, No 2, 726-747

Abstract: 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.

Keywords: Traveling salesman; Vehicle routing; Local search; Approximation algorithms (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/s10878-012-9580-x

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