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: | Klamroth K., Bischoff M. |
Keywords: | heuristics: genetic algorithms |
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.