RETRACTED: A Novel Cooperation Multi-Objective Optimization Approach: Multi-Swarm Multi-Objective Evolutionary Algorithm Based on Decomposition (MSMOEA/D)

Abstract

In order to achieve good adaptability, medical bone implants for clinical applications need to have porous characteristics. From a biological and mechanical point of view, the design of porous structures requires both suitable porosities to facilitate cell ingrowth and suitable strength to avoid implant damage. To handle the multiobjective optimization problems of porous structure design, this work introduced an improved multi-objective optimization algorithm, which is called a multi-swarm multi-objective evolutionary algorithm based on decomposition (MSMOEA/D), and the main idea is a multi-swarm strategy. After a predetermined algebraic evolution, the whole swarm was evenly divided into several parts, and the elite non-dominated sorting mechanism was used to select the individuals with excellent performance and poor performance in the sub-swarms to exchange information between the sub-swarms. The performance of the MSMOEA/D algorithm was verified and validated on 12 constraint two-objective and three-objective benchmark functions and compared with MOEA/D, MOEADM2M, and MOEADDRA algorithms in terms of generational distance indicators. The solutions obtained by the proposed MSMOEA/D algorithm were accurate. Finally, the proposed MSMOEA/D algorithm was applied to optimize the constructed RS porous structure, and the porous optimized models with porosities of 50%, 60% and 70% were obtained.