Distribution search on evolutionary many-objective optimization: Selection mappings and recombination rate

Abstract

This work studies distribution search in the context of evolutionary many-objective optimization where, in addition to good convergence towards the optimal Pareto front, it is required to find a set of trade-off solutions spread according to a given distribution. We particularly focus on the effectiveness of Adaptive ε-Ranking, which reclassifies sets of non-dominated solutions using iteratively a randomized sampling procedure that applies ε-dominance with a mapping function f(x)↦ϵf′(x) to bias selection towards the distribution of solutions implicit in the mapping. We analyze the effectiveness of Adaptive ε-Ranking with three linear mapping functions for ε-dominance and study the importance of recombination to properly guide the algorithm towards the distribution we aim to find. As test problems, we use functions of the DTLZ family with M = 6 objectives, varying the number of variables N from 10 to 50.