Abstract: This paper addresses the multi-center location problem, in which a set of p centers to be located to minimize the maximum distance between a center p and its nearest demand point. The problem is NP-hard. Therefore, polynomial time-bounded algorithms are unlikely to yield an optimal solution. Particle swarm optimization (PSO) is a metaheuristic algorithm that has been shown to be effective in solving such hard and complex optimization problems.
This paper presented a new PSO for the multi-center location problem on small networks. Three objectives are considered as follows: (1) developing a new PSO algorithm to solve the problem, (2) applying the developed algorithm to a set of well-known benchmark location problems, and comparing the results. (3) verifying the stability of the algorithm. The result is a simple but effective algorithm for solving multi-center problems on networks. The new proposed PSO algorithm solved multi-center location problems, when all candidate solutions can be investigated. PSO was found to be stable and the average time of runs increases linearly as the number of centers increases. The advantage of this algorithm is that, it calculates the optimal solution for each candidate solutions.