Priority Location and Enhancement in the p-Median Problem: A Modified Hybrid Binary PSO Approach

The p-median problem has been extensively investigated, resulting in numerous variant models and corresponding algorithms. The aim of this problem is to find the optimal location of sites and their allocation. However, current research lacks exploration into factors encompassing facility reinforcement decisions, intricate cost considerations, prioritized establishment of critical facilities, and reinforcement principles. To address this gap, this paper introduces the p-median problem with priority location and enhancement (PLE-pM problem). Additionally, we propose the modified hybrid binary particle swarm optimization algorithm (MHBPSO), built upon the hybrid binary particle swarm optimization (HBPSO) algorithm framework. The proposed algorithm combines the efficient features of multiple heuristic algorithms. Based on the characteristics of the PLE-pM problem, high-quality initial positions are specially generated, and the components of the original algorithm are redesigned, including: position updating rule based on previous optima, tabu based mutation operator for diversification, and greedy solution repair and local search for position improving. Computational experiments validate the effectiveness of the algorithm, demonstrating that MHBPSO efficiently finds high-quality solutions for solving the PLE-pM problem.