Variation Rate to Maintain Diversity in Decision Space within Multi-Objective Evolutionary Algorithms

Abstract

The performance of a multi-objective evolutionary algorithm (MOEA) is in most cases measured in terms of the populations’ approximation quality in objective space. As a consequence, most MOEAs focus on such approximations while neglecting the distribution of the individuals of their populations in decision space. This, however, represents a potential shortcoming in certain applications as in many cases one can obtain the same or very similar qualities (measured in objective space) in several ways (measured in decision space). Hence, a high diversity in decision space may represent valuable information for the decision maker for the realization of a given project. In this paper, we propose the Variation Rate, a heuristic selection strategy that aims to maintain diversity both in decision and objective space. The core of this strategy is the proper combination of the averaged distance applied in variable space together with the diversity mechanism in objective space that is used within a chosen MOEA. To show the applicability of the method, we propose the resulting selection strategies for some of the most representative state-of-the-art MOEAs and show numerical results on several benchmark problems. The results demonstrate that the consideration of the Variation Rate can greatly enhance the diversity in decision space for all considered algorithms and problems without a significant loss in the approximation qualities in objective space.

VSD-MOEA: A Dominance-Based Multiobjective Evolutionary Algorithm with Explicit Variable Space Diversity Management

“…Then, a ranking that considers both the original objectives and the diversity objective is used to sort individuals. More complex ways of integrating the information on both kinds of diversity to alter the selection mechanisms have been devised (Deb and Tiwari, 2005;Shir et al, 2009;Cuate and Sch ütze, 2019). Another related method involves modifying the hypervolume to integrate the decision variable space diversity into a single metric (Ulrich et al, 2010).…”

A Set Based Newton Method for the Averaged Hausdorff Distance for Multi-Objective Reference Set Problems

“…Examples for the latter are subdivision [34][35][36] and cell mapping techniques [37][38][39]. Another class of set based methods is given by multi-objective evolutionary algorithms (MOEAs) that have proven to be very effective for the treatment of MOPs [14,16,[40][41][42][43]. Some reasons for this include that are very robust, do not require hard assumptions on the model, and allow to compute a reasonable finite size representation of the solution set already in a single run.…”