(2011 M)Optimization of Multiple Traveling Salesmen Problem by a Novel Representation.pdf

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(2011 M)Optimization of Multiple Traveling Salesmen Problem by a Novel Representation.pdf

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(2011 M)Optimization of Multiple Traveling Salesmen Problem by a Novel Representation

Optimization of Multiple Traveling Salesmen Problem by a Novel Representation based Genetic Algorithm András Király, János Abonyi University of Pannonia, Department of Process Engineering, P.O. Box 158. Veszprém H-8200, HUNGARY, e-mail: kandras85@ 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 costumer demands; find the set of routes with overall minimum route cost which service all the demands. The multiple traveling salesman problem (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. It is well-known that mTSP-based algorithms can also be utilized in several VRPs by incorporating some additional site constraints. The aim of this chapter is to review how genetic algorithms can be applied to solve these problems and to propose a novel, interpretable representation based algorithm. The elaborated heuristic algorithm is demonstrated by examples considering different round tour types determination of further tasks for optimal operation of the distribution system for instance the modification of the vehicle capacity, and the effects of change of cost elements and data structure. Keywords: mTSP, VRP, genetic algorithm, multi-chromosome, optimization 1 Introduction The aim of logistics is to get the right materials to the right place at the right time, while optimizing a given performance measure (e.g. minimizing total operating costs) and satisfying a given set of constraints (e.g. time and capacity constraints). In most distribution systems goods are transported from various origins to various destinations. For example, many retail chains manage distribution systems in which goods are transported from a number of suppliers to a number of retail stores. It is often economical to consolidate the s