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Open AccessFeature PaperArticle

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

by Oliver Cuate 1,* and Oliver Schütze 2,*
1
Computer Science Department, Cinvestav-IPN, Mexico City 07360, Mexico
2
Dr. Rodolfo Quintero Ramirez Chair, UAM Cuajimalpa, Mexico City 05370, Mexico
*
Authors to whom correspondence should be addressed.
This paper is an extended version of our paper published in the 10th International Conference on Evolutionary Multi-Criterion Optimization (EMO 2019), East Lansing, MI, USA, in 10–13 March 2019.
Math. Comput. Appl. 2019, 24(3), 82; https://doi.org/10.3390/mca24030082
Received: 30 July 2019 / Revised: 10 September 2019 / Accepted: 11 September 2019 / Published: 13 September 2019
(This article belongs to the Special Issue Numerical and Evolutionary Optimization)
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. View Full-Text
Keywords: evolutionary computation; multi-objective optimization; decision space diversity evolutionary computation; multi-objective optimization; decision space diversity
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Cuate, O.; Schütze, O. Variation Rate to Maintain Diversity in Decision Space within Multi-Objective Evolutionary Algorithms. Math. Comput. Appl. 2019, 24, 82.

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