Abstract: The competitive location problem is one of the key problems for the research areas of spatial economy, regional development, combinatorial optimization and system engineering. Generally speaking, competitive location problems tend to maximize the market share as the final goal without considering the sustainable operation capability, which leads to the deviation of the actual operating results from the original intention of decision. To tackle this problem, the ability of continuing operations is considered, the constraints of the probability of sustainable operation probability are given and a nonlinear integer programming model for competitive location is established. In this paper, an effective Real Coded Genetic Algorithm (RCGA) is presented for the competitive location problem to maximize the market share with the constraints of the sustainable operation probability. Genetic algorithm is a widely used random search algorithm and has very good performance in solving nonlinear programming and combinational optimization problems. First, it is assumed that the operating costs are the function of the size of the competitive facility and the constraints of the sustainable operation probability are formulated. Then a nonlinear mixed integer programming model for the facility location-design problem is built based on the gravity attractive model. Second, a RCGA is presented regarding the value types of the location variables and the scale variables. The numerical results show that RCGA can get high quality solutions in very short time, and the gap between feasible and optimal solutions is less than 0.5%. Related issues are also discussed by comparison to other algorithms to further demonstrate the success and practicability of the proposed approach, which provides an alternative way and an effective algorithm for the competitive location problem.

Key words: location, competitive facility, chance constraint, genetic algorithm, real coded