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A Fast and Deterministic Approach to a Near Optimal Solution for the p-Median Problem

A Fast and Deterministic Approach to a Near Optimal Solution for the p-Median Problem

Xiang Li, Christophe Claramunt, Xihui Zhang, Yingping Huang
Copyright: © 2012 |Volume: 3 |Issue: 3 |Pages: 14
ISSN: 1947-9328|EISSN: 1947-9336|EISBN13: 9781466613836|DOI: 10.4018/joris.2012070101
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MLA

Li, Xiang, et al. "A Fast and Deterministic Approach to a Near Optimal Solution for the p-Median Problem." IJORIS vol.3, no.3 2012: pp.1-14. http://doi.org/10.4018/joris.2012070101

APA

Li, X., Claramunt, C., Zhang, X., & Huang, Y. (2012). A Fast and Deterministic Approach to a Near Optimal Solution for the p-Median Problem. International Journal of Operations Research and Information Systems (IJORIS), 3(3), 1-14. http://doi.org/10.4018/joris.2012070101

Chicago

Li, Xiang, et al. "A Fast and Deterministic Approach to a Near Optimal Solution for the p-Median Problem," International Journal of Operations Research and Information Systems (IJORIS) 3, no.3: 1-14. http://doi.org/10.4018/joris.2012070101

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Abstract

Finding solutions for the p-median problem is one of the primary research issues in the field of location theory. Since the p-median problem has proved to be a NP-hard problem, several heuristic and approximation methods have been proposed to find near optimal solutions with acceptable computational time. This study introduces a computationally efficient and deterministic algorithm whose objective is to return a near optimal solution for the p-median problem. The merit of the proposed approach, called Relocation Median (RLM), lies in solving the p-median problem in superior computational time with a tiny percentage deviation from the optimal solution. This approach is especially relevant when the problem is enormous where, even when a heuristic method is applied, the computational time is quite high. RLM consists of two parts: The first part uses a greedy search method to find an initial solution; the second part sequentially substitutes medians in the initial solution with additional vertices to reduce the total travel cost. Experiments show that to solve the same p-median problem, the RLM approach can significantly shorten the computational time needed by a genetic algorithm based approach to obtain solutions with similar quality.

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