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Optimization of Multiple Traveling Salesmen Problem by a Novel Representation Based Genetic Algorithm

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Intelligent Computational Optimization in Engineering

Part of the book series: Studies in Computational Intelligence ((SCI,volume 366))

Abstract

The Vehicle Routing Problem (VRP) is a complex combinatorial optimization problem that can be described as follows: given a fleet of vehicles with uniform capacity, a common depot, and several requests by the customers, find a route plan for the vehicles with overall minimum route cost (eg. distance traveled by vehicles), which service all the demands. It is well known that multiple Traveling Salesman Problem (mTSP) based algorithms can also be utilized in several VRPs by incorporating some additional constraints, it can be considered as a relaxation of the VRP, with the capacity restrictions removed. The mTSP is a generalization of the well known traveling salesman problem (TSP), where more than one salesman is allowed to be used in the solution. Because of the fact that TSP is already a complex, namely an NP-hard problem, heuristic optimization algorithms, like genetic algorithms (GAs) need to be taken into account. The extension of classical GA tools for mTSP is not a trivial problem, it requires special, interpretable encoding and genetic operators to ensure efficiency. The aim of this chapter is to review how genetic algorithms can be applied to solve these problems, and propose a novel, easily interpretable and problem-oriented representation and operators, that can easily handle constraints on the tour lengths, and the number of salesmen can vary during the evolution. The elaborated heuristic algorithm is demonstrated by a complete realistic example.

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Authors and Affiliations

  1. Department of Process Engineering, University of Pannonia, P.O. Box 158, Veszprém, H-8200, Hungary

    András Király & János Abonyi

Authors
  1. András Király
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  2. János Abonyi
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Editors and Affiliations

  1. Dept. Artificial Intelligence, Kyushu Institute of Technology, 680-4 Kawazu, 820-8502, Izuka-Shi, Fukuoka, Japan

    Mario Köppen

  2. School of Engineering and Applied Science, Aston University, Aston Triangle, B4 7ET, Birmingham, U.K.

    Gerald Schaefer

  3. Machine Intelligence Research Labs (MIR Labs), Scientific Network for Innovation and Research Excellence, P.O. Box 2259, 98071-2259, Auburn, Washington, USA

    Ajith Abraham

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Király, A., Abonyi, J. (2011). Optimization of Multiple Traveling Salesmen Problem by a Novel Representation Based Genetic Algorithm. In: Köppen, M., Schaefer, G., Abraham, A. (eds) Intelligent Computational Optimization in Engineering. Studies in Computational Intelligence, vol 366. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21705-0_9

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  • DOI: https://doi.org/10.1007/978-3-642-21705-0_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-21704-3

  • Online ISBN: 978-3-642-21705-0

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