A study on multi-objective particle swarm optimization with weighted scalarizing functions

In literature, multi-objective particle swarm optimization (PSO) algorithms are shown to have great potential in solving simulation optimization problems with real number decision variables and objectives. This paper develops a multi-objective PSO algorithm based on weighted scalarization (MPSOws) in which objectives are scalarized by different sets of weights at individual particles while evaluation results are shared among the swarm. Various scalarizing functions, such as simple weighted aggregation (SWA), weighted compromise programming (WCP), and penalized boundary intersection (PBI) can be applied in the algorithm. To improve the diversity and uniformity of the Pareto set, a hybrid external archiving technique consisting of both KNN and ε-dominance methods is proposed. Numerical experiments on noise-free problems are conducted to show that MPSOws outperforms the benchmark algorithm and WCP is the most preferable strategy for the scalarization. In addition, simulation allocation rules (SARs) can be further applied with MPSOws when evaluation error is considered.