Hypervolume approximation

Hypervolume indicator of a Pareto frontier.

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Approximates the hypervolume of a Pareto frontier. First, it generates
random samples in the hypercuboid defined by the utopia and antiutopia
points. Second, it counts the number of samples dominated by the front.
The hypervolume is approximated as the ratio 'dominated points / total
points'.
Please notice that the choice of the utopia and antiutopia point is
crucial: using points very far from the frontier will result in similar
hypervolume even for very different frontiers (if the utopia is too far
away, the hypervolume will be always low; if the antiutopia is too far
away, the hypervolume will be always high).
Also, frontier points "beyond" the reference points will not be counted
for the approximation (e.g., if the antiutopia is above the frontier or
the utopia is below, the hypervolume will be 0).
Inputs:
- F : the Pareto front to evaluate
- AU : antiutopia point
- U : utopia point
- N : number of sample for the approximation

Outputs:
- hv : hypervolume

引用格式

Simone (2026). Hypervolume approximation (https://ww2.mathworks.cn/matlabcentral/fileexchange/50517-hypervolume-approximation), MATLAB Central File Exchange. 检索时间: .

致谢

参考作品: Hypervolume Indicator

启发作品: Hypervolume Approximation (MEX)

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版本 已发布 发行说明 Action
1.0.0.0