An Efficient Hybrid CS and K-Means Algorithm for the Capacitated PMedian Problem

a School of Railway Engineering, Iran University of Science and Technology, 1684613114 Narmak,Tehran, Iran; b Department of Industrial Engineering, Amir Kabir University, Tafresh, Iran; c Master Student in Complex Adaptive Systems, Department of Physics, University of Göteborg, 41296 Göteborg, Sweden. Capacitated p-median problem (CPMP) is an important variation of facility location problem in which p capacitated medians are economically selected to serve a set of demand vertices so that the total assigned demand to each of the candidate medians must not exceed its capacity. This paper surveys and analyses the combination of Cuckoo Search and K-Means algorithms to solve the CPMP. In order to check for quality and validity of the suggestive method, we compared the final solution produced over the two test problems of Osman and Christofides, each of which including 10 sample tests. According to the results, the suggested meta-heuristic algorithm shows superiority over the rest known algorithms in this field as all the best known solutions in the first problem set, and several sample sets in the second problem set have been improved within reasonable periods of time.