A Many-Objective Evolutionary Algorithm with Local Shifted Density Estimation Based on Dynamic Decomposition

Abstract

Pareto dominance-based many-objective evolutionary algorithms (PDMaOEAs) are challenging in dealing with many-objective problems (MaOPs) encountering many incomparable nondominated solutions. Recently, convergence-related metrics have been incorporated into PDMaOEAs to enhance the selection pressure approaching the true Pareto front and furtherly improve the balance of diversity and convergence, however these approaches still have limitations. To address the drawbacks of the previous approaches, a many objective evolutionary algorithm with local shifted density estimation based on dynamic decomposition (MaOEA/LSD-DD) is proposed in this paper. The proposed MaOEA/LSD-DD maintains the convergence and diversity of populations through the dynamic synergy of dynamic decomposition and shifted density estimation. First, identifying potential regions through dynamic decomposition can reduce redundant evaluation to save computational resources and maintain good distribution. Then, shifted density estimation is executed in potential regions to selected the individuals with good diversity and convergence into next generation population. Finally, this process is repeated until the population size is satisfied. The performance of the MaOEA/LSD-DD is investigated extensively on 28 test problem from three popular benchmark problem suites and a practical problem of water resource planning problem by comparing them with seven excellent MaOEAs. The experimental results show the effectiveness of the proposed MaOEA/LSD-DD in keeping a good tradeoff between diversity and convergence over other MaOEAs when solving most of these MaOPs.