On the estimation of pareto front and dimensional similarity in many-objective evolutionary algorithm

• Published in: Information sciences Vol. 563; pp. 375 - 400
• Main Authors: Li, Li, Yen, Gary G., Sahoo, Avimanyu, Chang, Liang, Gu, Tianlong
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.07.2021
• Subjects: Achievement scalarizing function; Angle-based selection; Decomposition; Evolutionary algorithm; Many-objective optimization; Pareto front curvature; Reference vector; Similarity; Similarity; Reference vector; Evolutionary algorithm; Achievement scalarizing function; Decomposition; Many-objective optimization; Pareto front curvature; Angle-based selection
• ISSN: 0020-0255; 1872-6291
• DOI: 10.1016/j.ins.2021.03.008

•We propose an on-line Pareto front shape estimation strategy for adaptive selection. We use achievement scalarizing function to locate the pivotal point, which can best characterize the curvature of Pareto front. Then the curvature of Pareto front can be approximately obtained according to the ratio of distances.•An adaptive scalarizing function based fitness evaluation, which can guarantee the Pareto optimality, is presented. According to the estimated curvature of Pareto front, we select a proper indicator to maximize the convergence.•A new similarity measure named dimensionality margin distance for diversity is proposed which can eliminate the abnormality and improve the discrimination of MaOPs. Compared to the existing methods, the proposed approach shows a better consistency especially in high-dimensional and those with abnormal values. Evolutionary algorithms have been proven to be effective in solving multi-objective optimization problems. However, their performance deteriorates progressively in handling many-objective optimization problems due to the sensitivity upon the curvature of Pareto front, as well as the implicit evaluation on similarity in high dimensionality. This paper proposes an on-line Pareto front curvature estimator for an adaptive selection, in which the achievement scalarizing function is used to identify the pivotal solution to extrapolate the geometric information. Then an adaptive scalarizing function based fitness assessment, which guarantees the Pareto optimality, is presented. The diversity of the Pareto optimal solutions is also ensured by introducing a novel similarity metric. Finally, an extensive experimental analysis is presented to corroborate the analytical result by evaluating problems with various types of Pareto fronts. The experimental results substantiate the efficacy of the results with competitive performance.