A Particle Swarm Optimization (PSO) algorithm is proposed for the solution of large-scale continuous p-median location problems in plane. A PSO algorithm previously developed for the solution of the continuous p-center has been extended to solve the p-median location problem. The p-median location problem seeks to locate p facilities in plane so that the sum of Euclidean distances from p medians to a set of n demand points is minimized. The p-median problem is proven to be NP hard.In this paper, we introduce a new PSO algorithm for large scale p-median location problems. Computational results show that the proposed PSO algorithm is able to find good feasible solutions for instances from TSP library with demand points up to 9,976 and medians (P) up to 75. Our proposed PSO algorithm outperformed one of the most recent aggregation methods, which has been developed to solve large-scale p-median.
In this paper, a new hybridization of a Myopic and Neighborhood approaches is proposed to solve large-size vertex p-median location problems. The effectiveness and efficiency of our approach are demonstrated empirically through an intensive computational experiment on large-size instances taken from TSPLib and BIRCH datasets, with the number of nodes varying from 734 to 9,976 for the former and from 9,600 to 20,000 nodes for the latter. The results show that the new approach, though relatively simple, yields better solutions compared to the ones in the literature. This demonstrates that a simpler approach that takes into account the advantages of other methods can lead to promising outcome and has the potential of being adopted in other combinatorial optimization problems.
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