Don't be greedy when calculating hypervolume contributions
Proceedings of the tenth ACM SIGEVO workshop on Foundations of genetic algorithms
Approximating the Least Hypervolume Contributor: NP-Hard in General, But Fast in Practice
EMO '09 Proceedings of the 5th International Conference on Evolutionary Multi-Criterion Optimization
The maximum hypervolume set yields near-optimal approximation
Proceedings of the 12th annual conference on Genetic and evolutionary computation
An efficient algorithm for computing hypervolume contributions**
Evolutionary Computation
Approximating the least hypervolume contributor: NP-hard in general, but fast in practice
Theoretical Computer Science
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A fast algorithm, called the contribution of a point to the hypervolume by Slicing Objective (CHSO) algorithm, is presented for computing the contribution of a point to the hypervolume directly. It is based on the same idea as HSO algorithm by processing the objectives in a front one at a time, rather than the points one at a time as in LAHC algorithm. It is shown that CHSO is much faster than LAHC for randomly generated data and benchmark data in three to eight objectives. So CHSO will enable the use of hypervolume as a diversity mechanism with larger population in more objectives.