An enhanced decomposition-based multi-objective evolutionary algorithm with a self-organizing collaborative scheme

The multi-objective evolutionary algorithm based on decomposition (MOEA/D) decomposes a multi-objective optimization problem (MOP) into multiple single-objective subproblems using an aggregation function and optimizes them together using a collaborative approach. MOEA/D exhibits extraordinary optimization ability in solving MOPs. However, the algorithm's performance is hampered by the single evolutionary operator, fixed control parameters, and fixed neighborhood architecture used in primal MOEA/D. To obtain the balance between convergence and diversity, a self-organizing collaborative scheme (SCS) is designed to achieve the best combination of differential evolution (DE) operator, control parameters, and neighborhood size in this paper. The SCS is integrated into MOEA/D to form the MOEA/D-SCS. In MOEA/D-SCS, firstly, the evolutionary process is separated into three stages: early, middle, and late, and different indicators are utilized to screen elite and inferior solutions for the early and late stages. Secondly, different evolutionary strategies are developed for the three stages and the various types of solutions to help boost the algorithm's efficiency. Then, to enhance convergence and diversity in different evolutionary stages, a neighborhood reconstruction strategy is proposed to assign different neighborhood sizes according to the neighborhood information. Finally, the capability of MOEA/ D-SCS was tested using three standard test suites, ZDT, DTLZ, and UF, and a MOP of sewage treatment. The simulation results demonstrate that the proposed MOEA/D-SCS can achieve better optimization results and show stronger optimization ability in most cases compared to state-of-the-art evolutionary algorithms, such as MOEA/ D-DE, MOEA/D-STM, MOEA/D-FRRMAB, MOEA/D-DRA, NSGA-II, and dMOPSO, especially in problems with multiple peaks, complex Pareto fronts, and practical engineering optimization problems.