A novel nondominated sorting simplified swarm optimization for multi-stage capacitated facility location problems with multiple quantitative and qualitative objectives

Capacitated facility location problems (CFLPs) arise in the practical application of many supply chain networks that select a set of suppliers, plants, distribution centers, and customers. In general, the goal of CFLPs is to consider multiple critical performances that involve quantitative and qualitative factors, such as cost, transportation time, inventory, profit, and customer satisfaction, to obtain various perspectives from decision makers in most real-world applications. CFLP becomes increasingly complex and challenging when decision makers simultaneously consider both factors; however, offering comprehensive decisions is important. In this study, a novel solution based on simplified swarm optimization (SSO) and a nondominated sorting technique is proposed to provide Pareto-optimal solutions for enhancing search efficiency and solution quality. To yield feasible solutions, three repairer mechanisms, namely, random repair, cost-based, and utility-based mechanisms, are proposed to enhance the search efficiency and diversity of each population. A fuzzy analytic hierarchy process is used to calculate the weight of qualitative objectives. To evaluate the efficiency and effectiveness of the proposed algorithm, extensive experiments are conducted on benchmark and newly generated instances of the four stages of CFLPs. Then, results are compared with those of the nondominated sorting genetic algorithm-II, multi-objective SSO, and multi-objective particle swarm optimization reported from the literature. The computational results demonstrate that the proposed algorithm is highly competitive and performs well in terms of solution quality and computational time. The Pareto set in the investigated type of facility location problems leads to solutions that may better support decision-making.