Abstract
Hypervolume indicator is a commonly accepted quality measure for comparing Pareto approximation set generated by multi-objective optimizers. The best known algorithm to calculate it for n points in d-dimensional space has a run time of O(n d/2) with special data structures. This paper presents a recursive, vertex-splitting algorithm for calculating the hypervolume indicator of a set of n non-comparable points in dā>ā2 dimensions. It splits out multiple children hyper-cuboids which can not be dominated by a splitting reference point. In special, the splitting reference point is carefully chosen to minimize the number of vertices of the child hyper-cuboid. The complexity analysis shows that the proposed algorithm achieves \(O((\frac{d}{2})^n)\) time and O(dn 2) space complexity in the worst case.
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Yang, Q., Ding, S. (2007). Novel Algorithm to Calculate Hypervolume Indicator of Pareto Approximation Set. In: Huang, DS., Heutte, L., Loog, M. (eds) Advanced Intelligent Computing Theories and Applications. With Aspects of Contemporary Intelligent Computing Techniques. ICIC 2007. Communications in Computer and Information Science, vol 2. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74282-1_27
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DOI: https://doi.org/10.1007/978-3-540-74282-1_27
Publisher Name: Springer, Berlin, Heidelberg
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