Abstract:
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 ...Show MoreMetadata
Abstract:
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 n points in O(n^{[{3}/{2}]}\log n) time. Our algorithm improves the currently best time complexity O(n^{2}) by O({\sqrt {n}}/{\log n}) , 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.
Published in: IEEE Transactions on Evolutionary Computation ( Volume: 28, Issue: 4, August 2024)