Ensemble of Pareto-based Selections for Many-objective optimization

Performance of Pareto Dominance-based Multi-objective Evolutionary Algorithms (PDMOEAs) degrades in many-objective optimization problems (MaOPs), where the number of objectives is greater than three. The degradation in the performance of PDMOEs arises due to the inability of Pareto dominance relationships that are decided using conventional nondominated sorting (CNDS) to differentiate between the population members during environmental selection. Therefore, the selection of individuals depends entirely on the secondary criterion that enforces diversity. In literature, the idea of modifying the definition of Pareto dominance to improve the converging ability of PDMOEAs has been investigated. Recently, an approximate effective nondominated sorting (AENS) was proposed, that utilizes only three objective comparisons to determine the dominance relation between the individuals. PDMOEAs based on the approximation of Pareto dominance improves the convergence, but fails to enforce the diversity; whereas the use of conventional Pareto dominance enforces the necessary diversity but fail to achieve the convergence. In this paper, we propose an ensemble of Pareto-based selections (EPS) to improve the performance of PDMOEAs on many-objective optimization problems. The ensemble includes - a) environmental and mating selections of any existing PDMOEA based on CNDS and respective density estimation; and b) environmental and mating selections based on AENS and shift-based density estimation. Experiments are performed on 16 different test problems with two different PDMOEA frameworks to analyze the performance of proposed ensemble of Pareto-based selections (EPS).