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Mathematics 2019, 7(2), 129; https://doi.org/10.3390/math7020129

Search Acceleration of Evolutionary Multi-Objective Optimization Using an Estimated Convergence Point

1
Computer Science Division, University of Aizu, Aizuwakamatsu 965-8580, Japan
2
Graduate School of Design, Kyushu University, Fukuoka 815-8540, Japan
3
Faculty of Design, Kyushu University, Fukuoka 815-8540, Japan
*
Author to whom correspondence should be addressed.
Received: 21 November 2018 / Revised: 23 January 2019 / Accepted: 23 January 2019 / Published: 28 January 2019
(This article belongs to the Special Issue Evolutionary Computation)
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Abstract

We propose a method to accelerate evolutionary multi-objective optimization (EMO) search using an estimated convergence point. Pareto improvement from the last generation to the current generation supports information of promising Pareto solution areas in both an objective space and a parameter space. We use this information to construct a set of moving vectors and estimate a non-dominated Pareto point from these moving vectors. In this work, we attempt to use different methods for constructing moving vectors, and use the convergence point estimated by using the moving vectors to accelerate EMO search. From our evaluation results, we found that the landscape of Pareto improvement has a uni-modal distribution characteristic in an objective space, and has a multi-modal distribution characteristic in a parameter space. Our proposed method can enhance EMO search when the landscape of Pareto improvement has a uni-modal distribution characteristic in a parameter space, and by chance also does that when landscape of Pareto improvement has a multi-modal distribution characteristic in a parameter space. The proposed methods can not only obtain more Pareto solutions compared with the conventional non-dominant sorting genetic algorithm (NSGA)-II algorithm, but can also increase the diversity of Pareto solutions. This indicates that our proposed method can enhance the search capability of EMO in both Pareto dominance and solution diversity. We also found that the method of constructing moving vectors is a primary issue for the success of our proposed method. We analyze and discuss this method with several evaluation metrics and statistical tests. The proposed method has potential to enhance EMO embedding deterministic learning methods in stochastic optimization algorithms. View Full-Text
Keywords: evolutionary multi-objective optimization; convergence point; acceleration search; evolutionary computation; optimization evolutionary multi-objective optimization; convergence point; acceleration search; evolutionary computation; optimization
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Pei, Y.; Yu, J.; Takagi, H. Search Acceleration of Evolutionary Multi-Objective Optimization Using an Estimated Convergence Point. Mathematics 2019, 7, 129.

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