Approximating Hypervolume and Hypervolume Contributions Using Polar Coordinate

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Jingda Deng, Qingfu Zhang

Published: 2019, Last Modified: 07 May 2024IEEE Trans. Evol. Comput. 2019EveryoneRevisionsBibTeXCC BY-SA 4.0
Abstract: The hypervolume and hypervolume contributions are widely used in multiobjective evolutionary optimization. However, their exact calculation is NP-hard. By definition, hypervolume is an m-D integral (where m is the number of objectives). Using polar coordinate, this paper transforms the hypervolume into an (m - 1)-D integral, and then proposes two approximation methods for computing the hypervolume and hypervolume contributions. Numerical experiments have been conducted to investigate the performance of our proposed methods.