Quantum binary particle swarm optimization-based algorithm for solving a class of bi-level competitive facility location problems

This paper deals with a special class of competitive facility location problems, in which two non-cooperative firms compete to capture the most of a given market, in order to maximize their profit. This paper intends to present a simple and effective nested strategy based on the quantum binary particle swarm optimization (QBPSO) method for solving the bi-level mathematical model of the problem. In solution approach, an improvement procedure is embedded into QBPSO to increase the convergence speed and generate more accurate solutions. Taguchi's method is employed to systematically determine the optimal values of QBPSO parameters. Finally, computational results on large-scale instances with up to 300 locations and 350 clients (more than 100,000 variables and 300,000 constraints at each level) confirmed the method efficiency in terms of solution quality and time.