An Exploration of Evolutionary Algorithms for a Bi-Objective Competitive Facility Location Problem in Congested Systems

This paper presents a bi-objective competitive facility location model for congested systems in which the entering facilities compete with the competitors’ facilities for capturing the market share. In the proposed model, customers can choose which facility to patronize based on the gravity function that depends on both the quality of service provider and the travel time to facilities. The proposed model attempts to simultaneously maximize the captured demand from each facility and minimize the total waiting time in the system. Two multi-objective evolutionary algorithms, involving a multi-objective harmony search algorithm (MOHS) and a non-dominated sorting genetic algorithm-II (NSGA-II), are designed to solve the proposed model. The performance of solution procedures are compared on the basis of different performance metrics including generational distance, spacing metric, diversification metric, and number of non-dominated solution. The computational results based on different test problems show that in general MOHS outperforms NSGA-II.