Decomposition-based multiobjective evolutionary algorithm with density estimation-based dynamical neighborhood strategy

The multiobjective evolutionary algorithm based on decomposition (MOEA/D) decomposes a multiobjective optimization problem (MOP) into several scalar subproblems and then optimizes them cooperatively in their respective neighborhoods. Since the neighborhood size remains constant during the evolution process, striking a balance between diversity and convergence is a challenging for the conventional MOEA/D. In this study, a density estimation-based dynamical neighborhood (DEDN) strategy is proposed and integrated into MOEA/D to form MOEA/D-DEDN. In the MOEA/D-DEDN, an angle-based evolutionary state evaluation (AESE) scheme is first developed to evaluate the evolutionary state of the algorithm. Second, a distance-based density estimation (DDE) scheme is designed to calculate the population density for all the subproblems. Finally, the neighborhood size and penalty parameters of each subproblem are adjusted based on the AESE scheme and DDE schemes during the evolutionary process to overcome the disadvantages of computational resource waste and premature convergence. The performance of the proposed MOEA/D-DEDN is validated using the ZDT, DTLZ, and UF test suits in terms of IGD, HV, and Spacing metrics. The experimental results show that MOEA/D-DEDN has a significant improvement over the traditional MOEA/D and six state-of-the-art MOEA/D variants. Furthermore, to verify its effectiveness and usefulness, the proposed MOEA/D-DEDN is applied to address MOPs for three engineering applications: trajectory planning for parafoil UAVs, structural optimization for space trusses, and parameters optimization for wastewater treatment processes.