Objective reduction based on nonlinear correlation information entropy

• Published in: Soft computing (Berlin, Germany) Vol. 20; no. 6; pp. 2393 - 2407
• Main Authors: Wang, Handing, Yao, Xin
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2016; Springer Nature B.V
• Subjects: Artificial Intelligence; Computational Intelligence; Control; Correlation; Engineering; Entropy (Information theory); Evolutionary algorithms; Genetic algorithms; Impact analysis; Machine learning; Mathematical analysis; Mathematical Logic and Foundations; Mechatronics; Methodologies and Application; Multiple objective analysis; Objectives; Optimization; Performance enhancement; Reduction; Redundancy; Robotics; Nonlinear correlation information entropy; Dimension reduction; Multi-objective optimization; Objective reduction; Multi-objective evolutionary algorithm
• ISSN: 1432-7643; 1433-7479
• DOI: 10.1007/s00500-015-1648-y

It is hard to obtain the entire solution set of a many-objective optimization problem (MaOP) by multi-objective evolutionary algorithms (MOEAs) because of the difficulties brought by the large number of objectives. However, the redundancy of objectives exists in some problems with correlated objectives (linearly or nonlinearly). Objective reduction can be used to decrease the difficulties of some MaOPs. In this paper, we propose a novel objective reduction approach based on nonlinear correlation information entropy (NCIE). It uses the NCIE matrix to measure the linear and nonlinear correlation between objectives and a simple method to select the most conflicting objectives during the execution of MOEAs. We embed our approach into both Pareto-based and indicator-based MOEAs to analyze the impact of our reduction method on the performance of these algorithms. The results show that our approach significantly improves the performance of Pareto-based MOEAs on both reducible and irreducible MaOPs, but does not much help the performance of indicator-based MOEAs.