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ImprovedPruningofN-DSBasedonCDforBi.pdf
Improved Pruning of Non-Dominated Solutions Based on
Crowding Distance for Bi-Objective Optimization Problems
Saku Kukkonen and Kalyanmoy Deb
Kanpur Genetic Algorithms Laboratory (KanGAL)
Indian Institute of Technology Kanpur
Kanpur, PIN 208 016, India
saku.kukkonen@lut.fi, {saku, deb}@iitk.ac.in
KanGAL Report Number 2006007
Abstract ever, this is computationally expensive since cluster-
ing algorithms take usually time O MN 2 to prune
In this paper an algorithm for pruning a set of non- a set of size N with M objectives [9]. In NSGA-
dominated solutions is proposed. The algorithm is II the pruning of non-dominated solutions is done in
based on the crowding distance calculation used in time O (MN log N ) based on crowding distance (CD) .
the elitist non-dominated sorting genetic algorithm However, this method often gives non-optimal distribu-
(NSGA-II). The time complexity class of the new al- tion as it is demonstrated later in this paper. Therefore,
gorithm is estimated and in most cases it is the same an improved pruning based on CD is proposed here.
as for the original pruning algorithm. Numerical results Besides NSGA-II, CD has been used as a distribution
also support this estimate. maintenance method in many other MOEAs [1, 10–13,
For used bi-objective test problems, the proposed 16–18, 20, 22]. There also exist studies where the orig-
pruning algorithm is demonstrated to provide better dis- inal CD has been slightly modified to use,
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