Hybrid QPSO-NNIA2 Algorithm for Multi-Objective Optimization Problem

Abstract

To improve the convergence and distribution of a multi-objective optimization algorithm, a hybrid multi-objective optimization algorithm, based on the quantum particle swarm optimization (QPSO) algorithm and adaptive ranks clone and neighbor list-based immune algorithm (NNIA2), is proposed. The contribution of this work is threefold. First, the vicinity distance was used instead of the crowding distance to update the archived optimal solutions in the QPSO algorithm. The archived optimal solutions are updated and maintained by using the dynamic vicinity distance based m-nearest neighbor list in the QPSO algorithm. Secondly, an adaptive dynamic threshold of unfitness function for constraint handling is introduced in the process. It is related to the evolution algebra and the feasible solution. Thirdly, a new metric called the distribution metric is proposed to depict the diversity and distribution of the Pareto optimal. In order to verify the validity and feasibility of the QPSO-NNIA2 algorithm, we compare it with the QPSO, NNIA2, NSGA-II, MOEA/D, and SPEA2 algorithms in solving unconstrained and constrained multi-objective problems. The simulation results show that the QPSO-NNIA2 algorithm achieves superior convergence and superior performance by three metrics compared to other algorithms.