Approximation techniques for variations of the p-median problem

In this paper we investigate the genetic algorithm (GA) as a heuristic technique for obtaining near optimal solutions to location problems that are variations of the p-median problem. The results have applications in a variety of contexts including telecommunications network design. The p-median problem is to find an optimal set of K vertices from a connected, undirected graph with N vertices (KcN). Each of the K selected vertices is a service center for other nearby vertices. An optimal selection is one that minimizes the sum, over all vertices, of the path length from a vertex to the nearest service center. The p-median problem, also known as the min-sum multicenter problem, is a classical NPcomplete network design problem. A more general location problem involves service centers that are not vertices and various strategies for their placement. One variation investigated by this research allows for the service centers to be located at arbitrary points in the Cartesian plane. A second variation allows other terms, including the cost of service centers and the cost of interconnecting service centers, to contribute to the function being optimized, Techniques for locating a service center corresponding to a subset of vertices include a centroid strategy and a bounding circle strategy.

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