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A Fast Dimension-Sweep Algorithm for the Hypervolume Indicator in Four Dimensions
| Content Provider | CiteSeerX |
|---|---|
| Abstract | The Hypervolume Indicator is one of the most widely used quality indicators in Evolutionary Multiobjective Optimization. Its computation is a special case of Klee’s Measure Problem (KMP) where the upper end of all rectangular ranges coincides with a given reference point (assuming minimization, without loss of general-ity). Although the time complexity of the hypervolume indicator in two and three dimensions is known to be Θ(n log n), improving upon the O(nd/2 log n) complex-ity of Overmars and Yap’s algorithm for the general KMP in higher dimensions has been a challenge. In this paper, a new dimension-sweep algorithm to com-pute the hypervolume indicator in four dimensions is proposed, and its complexity is shown to be O(n2). 1 |
| File Format | |
| Access Restriction | Open |
| Subject Keyword | Hypervolume Indicator Fast Dimension-sweep Algorithm Evolutionary Multiobjective Optimization Used Quality Indicator Upper End Klee Measure Problem Rectangular Range Coincides General Kmp Reference Point Special Case Time Complexity New Dimension-sweep Algorithm |
| Content Type | Text |