Objective reduction based on nonlinear correlation information entropy

Handing WANG, Xin YAO

Research output: Journal PublicationsJournal Article (refereed)peer-review

60 Citations (Scopus)


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. © 2015, Springer-Verlag Berlin Heidelberg.
Original languageEnglish
Pages (from-to)2393-2407
Number of pages15
JournalSoft Computing
Issue number6
Early online date16 Mar 2015
Publication statusPublished - Jun 2016
Externally publishedYes

Bibliographical note

This work was supported by the National Basic Research Program (973 Program) of China (No. 2013CB329402), an EU FP7 IRSES Grant (No. 247619) on "Nature Inspired Computation and its Applications (NICaiA)", an EPSRC grant (No. EP/J017515/1) on "DAASE: Dynamic Adaptive Automated Software Engineering", the Program for Cheung Kong Scholars and Innovative Research Team in University (No. IRT1170), the National Natural Science Foundation of China (No. 61329302), National Science Foundation of China under Grant (No.91438103 and 91438201), and the Fund for Foreign Scholars in University Research and Teaching Programs (the 111 Project) (No. B07048). Xin Yao was supported by a Royal Society Wolfson Research Merit Award.


  • Dimension reduction
  • Multi-objective evolutionary algorithm
  • Multi-objective optimization
  • Nonlinear correlation information entropy
  • Objective reduction


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