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

• Published in: Mathematics (Basel) Vol. 7; no. 2; p. 129
• Main Authors: Pei, Yan, Yu, Jun, Takagi, Hideyuki
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 28.01.2019
• Subjects: acceleration search; Approximation; Convergence; convergence point; evolutionary computation; evolutionary multi-objective optimization; Genetic algorithms; Linear programming; Machine learning; Mathematics; Methods; Multiple objective analysis; Objectives; optimization; Optimization algorithms; Parameters; Pareto optimization; Pareto optimum; Searching; Sorting algorithms; Statistical tests
• ISSN: 2227-7390; 2227-7390
• DOI: 10.3390/math7020129

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.