Abstract
The p-center location problem is concerned with determining the location of p centers in a plane/space to serve n demand points having fixed locations. The continuous absolute p-center location problem attempts to locate facilities anywhere in a space/plane with Euclidean distance. The continuous Euclidean p-center location problem seeks to locate p facilities so that the maximum Euclidean distance to a set of n demand points is minimized. A particle swarm optimization (PSO) algorithm previously advised for the solution of the absolute p-center problem on a network has been extended to solve the absolute p-center problem on space/plan with Euclidean distance. In this paper we develop a PSO algorithm for the continuous absolute p-center location problem to minimize the maximum Euclidean distance from each customer to his/her nearest facility, called “PSO-ED”. This problem is proven to be NP-hard. We tested the proposed algorithm “PSO-ED” on a set of 2D and 3D problems and compared the results with a branch and bound algorithm. The numerical experiments show that PSO-ED algorithm can solve optimally location problems with Euclidean distance including up to 1,904,711 points.
Highlights
The p-center location problem is a major class of location problems
Continuous location problem with Euclidean distance is a main variant of the p-center location which is concerned with determining the location of p centers in a plane/space to serve n demand points having fixed locations
This paper extended that algorithm to solve the absolute p-center location problem on space/plan with Euclidean distance
Summary
The p-center location problem ( called minimax facility location problem) is a major class of location problems. Our main objective is to locate new p centers/facilities in the space/plane in such a way that the maximum distance between demand points and their nearest facility becomes minimum. It is assumed that all the facilities are identical and provide the same service to the customers, and there is no limit for the number of customers who can get service from the centers [2]. This kind of location problem is suggested by Hakimi [3, 4], and some of its applications are used to locate fire stations, hospital emergency services, data file location, police stations, and so on. Megiddo and Supowit [5] have shown that the continuous Euclidean p-center location problem in the plane is NP-hard, and, such problems are difficult to solve
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