An efficient solution method for Weber problems with barriers based on genetic algorithms |
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Authors: | M Bischoff K Klamroth |
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Institution: | Institute of Applied Mathematics, University of Erlangen—Nuremberg, Martensstr. 3, 91058 Erlangen, Germany |
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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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Keywords: | Facility location Barriers Non-convex optimization Genetic algorithm |
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