Objective reduction for visualising many-objective solution sets

Liangli ZHEN, Miqing LI, Dezhong PENG, Xin YAO

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

11 Citations (Scopus)


Visualising a solution set is of high importance in many-objective optimisation. It can help algorithm designers understand the performance of search algorithms and decision makers select their preferred solution(s). In this paper, an objective reduction-based visualisation method (ORV) is proposed to view many-objective solution sets. ORV attempts to map a solution set from a high-dimensional objective space into a low-dimensional space while preserving the distribution and the Pareto dominance relation between solutions in the set. Specifically, ORV sequentially decomposes objective vectors which can be linearly represented by their positively correlated objective vectors until the expected number of preserved objective vectors is reached. ORV formulates the objective reduction as a solvable convex problem. Extensive experiments on both synthetic and real-world problems have verified the effectiveness of the proposed method. © 2019
Original languageEnglish
Pages (from-to)278-294
Number of pages17
JournalInformation Sciences
Early online date8 Apr 2019
Publication statusPublished - Feb 2020
Externally publishedYes

Bibliographical note

The authors would like to thank Prof. Robert M. Hierons and Dr. Sergio Segura for discussions on the SPL product selection problem. This work was supported by the National Natural Science Foundation of China under grants 61432012 and 61329302 , the Engineering and Physical Sciences Research Council (EPSRC) of U.K. under grants EP/J017515/1 and EP/P005578/1 , the Program for Guangdong Introducing Innovative and Entrepreneurial Teams (Grant no. 2017ZT07X386), Shenzhen Peacock Plan (Grant no. KQTD2016112514355- 531 ), the Science and Technology Innovation Committee Foundation of Shenzhen (Grant no. ZDSYS-201703031748284), the Program for University Key Laboratory of Guangdong Province (Grant no. 2017KSYS008), and the Sichuan Science and Technology Planning Projects (Grants nso. 2019YFH0075 and 2018- GZDZX0030).


  • Evolutionary algorithms
  • Many-objective optimisation
  • Objective reduction
  • Visualisation


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