An efficient solution method for Weber problems with barriers based on genetic algorithms

An efficient solution method for Weber problems with barriers based on genetic algorithms

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Article ID: iaor20084286
Country: Netherlands
Volume: 177
Issue: 1
Start Page Number: 22
End Page Number: 41
Publication Date: Feb 2007
Journal: European Journal of Operational Research
Authors: ,
Keywords: heuristics: genetic algorithms
Abstract:

In this paper we consider the problem of locating one new facility with respect to a given set of existing facilities in the plane and in the presence of convex polyhedral barriers. It is assumed that a barrier is a region where neither facility location nor travelling are permitted. The resulting non-convex optimization problem can be reduced to a finite series of convex subproblems, which can be solved by the Weiszfeld algorithm in case of the Weber objective function and Euclidean distances. A solution method is presented that, by iteratively executing a genetic algorithm for the selection of subproblems, quickly finds a solution of the global problem. Visibility arguments are used to reduce the number of subproblems that need to be considered, and numerical examples are presented.

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