A Constrained multi-objective particle swarm optimization algorithm based on adaptive penalty and normalized non-dominated sorting

In order to deal with constrained multi-objective optimization problems (CMOPs), a novel constrained multi-objective particle swarm optimization (CMOPSO) algorithm is proposed based on an adaptive penalty technique and a normalized non-dominated sorting technique. The former technique is utilized to optimize constrained individuals in each generation to obtain new objective functions, while the latter technique ranks individuals along with the new objective functions obtaine d from the adaptive penalty technique. Additionally, the external archive maintenanc e has been improved by external population size decrease, and selection of individuals with better ranks which are operated by Pareto constrained-dominance. Based on the concept of crowding distance, the global best solution is obtained and the individuals of the next generation are provided by the basic PSO algorithm. The results of the simulation tests indicate precise convergence and diverse distribution of the non-dominant solutions on true Pareto front, which demonstrates that the proposed algorithm possesses outstanding performance metrics for generational distance and spacing. Finally, the trajectory optimization problem for hypersonic reentry glide vehicles (HRGVs) applied further verifies the effectiveness and efficiency of the proposed CMOPSO algorithm, which shows a goo d application prospect of the proposed algorithm as well.