A test problem for visual investigation of high-dimensional multi-objective search

Research output: Chapter in Book/Report/Conference proceedingConference contribution


Colleges, School and Institutes

External organisations

  • Brunel University
  • De Montfort University


An inherent problem in multiobjective optimization is that the visual observation of solution vectors with four or more objectives is infeasible, which brings major difficulties for algorithmic design, examination, and development. This paper presents a test problem, called the Rectangle problem, to aid the visual investigation of high-dimensional multiobjective search. Key features of the Rectangle problem are that the Pareto optimal solutions 1) lie in a rectangle in the two-variable decision space and 2) are similar (in the sense of Euclidean geometry) to their images in the four-dimensional objective space. In this case, it is easy to examine the behavior of objective vectors in terms of both convergence and diversity, by observing their proximity to the optimal rectangle and their distribution in the rectangle, respectively, in the decision space. Fifteen algorithms are investigated. Underperformance of Pareto-based algorithms as well as most state-of-the-art many-objective algorithms indicates that the proposed problem not only is a good tool to help visually understand the behavior of multiobjective search in a high-dimensional objective space but also can be used as a challenging benchmark function to test algorithms' ability in balancing the convergence and diversity of solutions.


Original languageEnglish
Title of host publicationProceedings of the 2014 IEEE Congress on Evolutionary Computation, CEC 2014
Publication statusPublished - 16 Sep 2014
Event2014 IEEE Congress on Evolutionary Computation, CEC 2014 - Beijing, China
Duration: 6 Jul 201411 Jul 2014


Conference2014 IEEE Congress on Evolutionary Computation, CEC 2014