Pareto Set

find the pareto set from n points with k objectives

Description

It is motivated by Gianluca Dorini's isParetoSetMember program. The new m-file version is much faster than the C version because of the more elegant algorithm. The efficiency is significantly improved in version 3. By implementing a new sorting scheme and recoding to reduce overhead, the code is even faster than the mex version, paretomember, where sorting is not adopted. However, it puzzles me that the performance of mex code does not affected by sorting. Follow the links bellow to download these two codes for comparison.

A more efficient version available in
http://www.mathworks.com/matlabcentral/fileexchange/loadFile.do?objectId=17251&objectType=File

Acknowledgements

The author wishes to acknowledge the following in the creation of this submission:
Performing Pareto set membership tester for sets of points in K-dimensions
This submission has inspired the following:
Pareto Front

• MATLAB release: MATLAB 7.5 (R2007b)

[wang chenxu]

Why I can't find isParetoSetMember function?

[Yi Cao]

isParetosetMember function can be obtained from http://www.mathworks.com/matlabcentral/fileexchange/loadFile.do?objectId=15172&objectType=FILE

[liudaohai liudaohai]

error:
example,if X=[3 1;1 2;2 1],and membership=paretoset(X),then membership
=[1 1 1].elseif X=[1 2;2 1;3 1],then
membership=[1 1 0].

[Yi Cao]

Thanks for pointing out the bug. The bug now has been corrected and performance has been slightly improved (for some problems).

[liudaohai liudaohai]

beddug:
example : if X=[3 1;3 2;3 1],and membership=paretoset(X)...
Warning: Divide by zero
In paretoset at 22

[Yi Cao]

The bug has been fixed. It should be avialble for download in a few days. Thanks for pointing out this.

Yi Cao

[liudaohai liudaohai]

beddug:
example : if X=[3 1;3 1;3 1],and membership=paretoset(X)...
Warning: Divide by zero.
In paretoset at 23

[Yi Cao]

Should be ok now.

[V. Poor]