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A Fast Exact Algorithm for Computing the Hypervolume Contributions in 4-D Space
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DOI：10.1109/TEVC.2023.3271679.png)
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Abstract
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The hypervolume (HV) contribution is widely used in indicator-based multiobjective algorithms. We propose an algorithm to compute exact 4-D HV contributions for a set of O(n([3/2])logn) time. Our algorithm improves the currently best time complexity O(n(2))byO(root n/logn) , and it is the first algorithm of subquadratic time for this problem. Our algorithm is built upon a space partition method in computational geometry and a geometric structure called the anchored gradient. We also propose a new space partition strategy to reduce the practical running time and the space overhead of this algorithm. Experimental results on a variety of test instances show that our proposed algorithm performs better than the existing state-of-the-art algorithm, especially, on point sets with cliff or other irregular properties.
Keywords:
Hypervolume (HV) contribution
Klee's measure problem (KMP)
multiobjective optimization
space partition method
Hypervolume (HV) contribution
Klee's measure problem (KMP)
multiobjective optimization
space partition method
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12
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1.9K
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2.4W
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