Improving multiobjective particle swarm optimization method

Abstract

An improved multiobjective particle swarm optimization algorithm is developed to get and compare Pareto fronts for constrained and unconstrained optimization test problems, with two objective functions and with a variable number of decision variables, available in literature. A new Minimum Angular Distance Information technique, to assign the best local guide for each particle within the swarm to get the Pareto front in the polar coordinate system, is adopted and verified. An external repository (archive) is used to store the nondominated particles at the end of each iteration, and a crowding distance technique is followed to maintain the archive size and the front diversity for each test problem. A self-adaptive penalty function technique is used to handle the constraint functions through transforming the original objective functions into new penalized functions based on their amount of constraint violation at each iteration. The developed algorithm is coded by Matlab formulas and verified via thirteen well-known test problems. Test results, represented in the regular Pareto fronts and the values of three comparative metrics (GD, S, and ER) calculated to verify the proposed algorithm, show more efficient and realistic agreements compared with that gained from previous studies and algorithms. Applying different engineering design problems to the developed algorithm is suggested as a future work.