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Title: A test problem for visual investigation of high-dimensional multi-objective search
Authors: Li, M
Yang, S
Liu, X
Keywords: Rectangle problem;multiobjective optimization;visual observation;Pareto optimization;Convergence;Search problems;Visualization
Issue Date: 2014
Publisher: IEEE
Citation: Proceedings of the 2014 IEEE Congress on Evolutionary Computation, CEC 2014, 2140 - 2147, Beijing, (6-11 July 2014)
Abstract: 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.
ISBN: 9781479914883
Appears in Collections:Dept of Computer Science Research Papers

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