Optimization of multiple traveling salesmen problem by a novel representation based genetic algorithm

András Király, János Abonyi

Research output: Chapter in Book/Report/Conference proceedingChapter

27 Citations (Scopus)

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.

Original languageEnglish
Title of host publicationIntelligent Computational Optimization in Engineering
Subtitle of host publicationTechniques and Applications
EditorsMario Koppen, Gerald Schaefer, Ajith Abraham
Pages241-269
Number of pages29
DOIs
Publication statusPublished - Sep 7 2011

Publication series

NameStudies in Computational Intelligence
Volume366
ISSN (Print)1860-949X

ASJC Scopus subject areas

  • Artificial Intelligence

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  • Cite this

    Király, A., & Abonyi, J. (2011). Optimization of multiple traveling salesmen problem by a novel representation based genetic algorithm. In M. Koppen, G. Schaefer, & A. Abraham (Eds.), Intelligent Computational Optimization in Engineering: Techniques and Applications (pp. 241-269). (Studies in Computational Intelligence; Vol. 366). https://doi.org/10.1007/978-3-642-21705-0_9