Hypervolume Indicator

A tool to estimate the hypervolume indicator

Description

In Evolutionary Multiobjective Optimization (EMO), an algorithm produces a set of points in the performance space as an estimation of the Pareto front. A quantitive measure is desired to estimate the closeness of the estimated data points to the true Pareto front.

One of such measures is the hypervolume indicator, which gives the hypervolume between the estimated Pareto front (P) and a reference point (R). However, to rigorously calcuate the indicator is time-consuming. This tool uses a Monte Carlo approach to estimate the hypervolume by calculating the percentage of a set of random points in the performance space to be dominated by the Pareto front.

The code was developed in response to a request made by Timo Aittokoski, who used the Pareto Front code developed by the Author.

Acknowledgements

The author wishes to acknowledge the following in the creation of this submission:
Pareto Front

• MATLAB release: MATLAB 7.6 (R2008a)

[liudaohai liudaohai]

??? Undefined command/function 'bsxfun'.

Error in ==> hypervolume at 45
fcheck=all(bsxfun(@gt, C, lB),2);

[Yi Cao]

As I indicated, the code is developed in R2008a. bsxfun was introduced since R2007a. If you use earlier version, you have change these two lines (45 and 49) to some other approaches, such as repmat or, for example, change line 45 to,

fcheck=all(C>lB(ones(N,1),:),2);

and change line 49 to

f=all(C(fcheck,:)>P(k(ones(sum(fcheck),1)),:),2);

HTH.

[V. Poor]

 

[Matteo]

Thank you, it's perfect!

[Ninh Duong]

thank you very much