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Open AccessArticle

A New Hybrid Evolutionary Algorithm for the Treatment of Equality Constrained MOPs

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Department of Computer Science, Cinvestav-IPN, Mexico City 07360, Mexico
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Metropolitan Autonomous University, Azcapotzalco Unit, Av. San Pablo No. 180, Col. Reynosa Tamaulipas, Azcapotzalco 02200, Mexico
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Instituto Politécnico Nacional, Mexico City 07738, Mexico
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Department of Applied Mathematics and Systems, Metropolitan Autonomous University, Cuajimalpa Unit (UAM-C), Vasco de Quiroga 4871, Santa Fe Cuajimalpa 05370, Mexico
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Dr. Rodolfo Quintero Ramirez Chair, Metropolitan Autonomous University, Cuajimalpa Unit (UAM-C), Vasco de Quiroga 4871, Santa Fe Cuajimalpa 05370, Mexico
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(1), 7; https://doi.org/10.3390/math8010007
Received: 27 November 2019 / Revised: 5 December 2019 / Accepted: 5 December 2019 / Published: 18 December 2019
(This article belongs to the Special Issue Recent Trends in Multiobjective Optimization and Optimal Control)
Multi-objective evolutionary algorithms are widely used by researchers and practitioners to solve multi-objective optimization problems (MOPs), since they require minimal assumptions and are capable of computing a finite size approximation of the entire solution set in one run of the algorithm. So far, however, the adequate treatment of equality constraints has played a minor role. Equality constraints are particular since they typically reduce the dimension of the search space, which causes problems for stochastic search algorithms such as evolutionary strategies. In this paper, we show that multi-objective evolutionary algorithms hybridized with continuation-like techniques lead to fast and reliable numerical solvers. For this, we first propose three new problems with different characteristics that are indeed hard to solve by evolutionary algorithms. Next, we develop a variant of NSGA-II with a continuation method. We present numerical results on several equality-constrained MOPs to show that the resulting method is highly competitive to state-of-the-art evolutionary algorithms. View Full-Text
Keywords: multi-objective optimization; equality constraints; evolutionary algorithm; continuation method multi-objective optimization; equality constraints; evolutionary algorithm; continuation method
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Cuate, O.; Ponsich, A.; Uribe, L.; Zapotecas-Martínez, S.; Lara, A.; Schütze, O. A New Hybrid Evolutionary Algorithm for the Treatment of Equality Constrained MOPs. Mathematics 2020, 8, 7.

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