Non-dominated Solution Sampling Using Environmental Selection in EMO algorithms

Abstract

This work focuses on the environmental selection methods incorporated in several evolutionary multi-objective optimization (EMO) algorithms for sampling representative nondominated solutions from a large non-dominated solution set. Evolutionary multi- and many-objective optimization generally provides a large set of non-dominated solutions. They are useful for precisely approximating the Pareto front but harm decision making when selecting one solution among them. Sampling and presenting a representative set of solutions is a promising method for addressing this issue. The selection of a subset of solutions from a large set of solutions is a type of combinatorial optimization problem. Its difficulty is increased by increasing the size of the non-dominated solution set, because the number of selection combinations of the solutions increases exponentially. This work focuses on environmental selection as a reasonable method to sample a solution subset from a large set. We compare 17 environmental selection methods incorporated in EMO algorithms and show that the one-by-one selection or deletion approach is suitable for sampling a representative nondominated set.