New Mathematical Formulations and an Efficient Genetic Algorithm for Finding a Stable Set in a Competitive Location Problem

경쟁적 입지선정 문제의 안정집합을 찾기 위한 수리적 모형과 유전 알고리즘

Companies often have to locate their facilities considering competitors' response to their locational decision. One model available in the literature is due to Dobson and Karmarkar, in which a firm has to decide locations so as to prevent competitors from entering the market after the firm's entry. In this paper, we provide new compact binary integer program formulations for their competitive location model and also present an efficient Genetic Algorithm(GA) for finding a (near-)optimal stable set. The GA we propose utilizes a penalty function to handle the feasibility of the problem and modified elitism for better performance of the algorithm. Computational comparisons indicate the superior performance of the GA over the Dobson and Karmarkar's branch and fathom algorithm.