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### Highlights from Performing Pareto set membership tester for sets of points in K-dimensions

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# Performing Pareto set membership tester for sets of points in K-dimensions

### Gianluca Dorini (view profile)

01 Jun 2007 (Updated )

This fast function takes as input a sets of points, and determines which ones are Pareto optimal

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Description

isParetoSetMember returns the logical Pareto membership of a set of N points in K dimensions. It takes as input a N-by-N matrix and return a N-binary-array, denoting for each of the N points, whether it is Pareto (1) o not (0).

The concept of Pareto dominance considered herein is the standard multiobjective minimization problem.

The help containst three meaningful examples.

The c coding (mex file) allows effective performances. For this reason, this function may be a useful tool to be incorporated into multi-objective optimization algorithms implementation.

Acknowledgements

This file inspired Pareto Front.

MATLAB release MATLAB 6.5 (R13)
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Comments and Ratings (7)
11 Nov 2009 Matteo

### Matteo (view profile)

29 Jul 2008 liudaohai liudaohai

inconsistent:
if X=[3 1;3 1;3 1];and membership=paretofront(X),then membership=[1 0 0]';
membership=isparetosetMember(X);membership=[1 1 1]'.

Comment only
29 Jul 2008 liudaohai liudaohai

error:
if X=[3 1;3 1;3 1];then membership = isparetosetMember(X);
membership = [1 1 1]'.

Comment only
01 May 2008 simarpreet kaur

hi

Comment only
22 Sep 2007 liudaohai liudaohai

Thank you very much,but I do not how to use it

07 Sep 2007 Guillaume Jacquenot

Simple and efficient, all you ask from an algorithm. C implementation allows fast evaluation.

07 Sep 2007 Guillaume Jacquenot