Dynamic Objective Sampling in Many-objective Optimization

Given the poor convergence of multi-objective evolutionary algorithms (MOEAs) demonstrated in several studies that address many-objective optimization, we propose a simple objective sampling scheme that can be incorporated in any MOEA in order to enhance its convergence towards the Pareto front. An unsupervised clustering algorithm is applied in the space of objectives at various moments during the search process performed by the MOEA, and only representative objectives are used to guide the optimizer towards the Pareto front during next iterations. The effectiveness of the approach is experimentally demonstrated in the context of the NSGA-II optimizer. The redundant objectives are eliminated during search when the number of clusters (representative objectives) is automatically selected by an unsupervised standard procedure, popular in the field of unsupervised machine learning. Furthermore, if after eliminating all the redundant objectives the number of conflicting objectives is still high, continuing to eliminate objectives by imposing a lower number of clusters speeds-up the convergence towards the Pareto front.