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

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

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 submission has inspired the following:; Pareto Set, Pareto Front
• MATLAB release: MATLAB 6.5 (R13)

[Guillaume Jacquenot]

 

[Guillaume Jacquenot]

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

[liudaohai liudaohai]

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

[simarpreet kaur]

hi

[liudaohai liudaohai]

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

[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]'.

[Matteo]