Lecture Notes in Computer Science

# Genetic and Evolutionary Computation — GECCO 2004

## Genetic and Evolutionary Computation Conference Seattle, WA, USA, June 26–30, 2004 Proceedings, Part I

Editors: Deb, K., Poli, R., Banzhaf, W., Beyer, H.-G., Burke, E., Darwen, P., Dasgupta, D., Floreano, D., Foster, J., Harman, M., Holland, O., Lanzi, P.L., Spector, L., Tettamanzi, A.G.B., Thierens, D., Tyrrell, A. (Eds.)

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MostMOEAsuseadistancemetricorothercrowdingmethodinobjectivespaceinorder to maintain diversity for the non-dominated solutions on the Pareto optimal front. By ensuring diversity among the non-dominated solutions, it is possible to choose from a variety of solutions when attempting to solve a speci?c problem at hand. Supposewehavetwoobjectivefunctionsf (x)andf (x).Inthiscasewecande?ne 1 2 thedistancemetricastheEuclideandistanceinobjectivespacebetweentwoneighboring individuals and we thus obtain a distance given by 2 2 2 d (x ,x )=[f (x )?f (x )] +[f (x )?f (x )] . (1) 1 2 1 1 1 2 2 1 2 2 f wherex andx are two distinct individuals that are neighboring in objective space. If 1 2 2 2 the functions are badly scaled, e.g.[?f (x)] [?f (x)] , the distance metric can be 1 2 approximated to 2 2 d (x ,x )? [f (x )?f (x )] . (2) 1 2 1 1 1 2 f Insomecasesthisapproximationwillresultinanacceptablespreadofsolutionsalong the Pareto front, especially for small gradual slope changes as shown in the illustrated example in Fig. 1. 1.0 0.8 0.6 0.4 0.2 0 0 20 40 60 80 100 f 1 Fig.1.Forfrontswithsmallgradualslopechangesanacceptabledistributioncanbeobtainedeven if one of the objectives (in this casef ) is neglected from the distance calculations. 2 As can be seen in the ?gure, the distances marked by the arrows are not equal, but the solutions can still be seen to cover the front relatively well.

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## Bibliographic Information

Bibliographic Information
Book Title
Genetic and Evolutionary Computation — GECCO 2004
Book Subtitle
Genetic and Evolutionary Computation Conference Seattle, WA, USA, June 26–30, 2004 Proceedings, Part I
Editors
• Kalyanmoy Deb
• Riccardo Poli
• Wolfgang Banzhaf
• Hans-Georg Beyer
• Edmund Burke
• Paul Darwen
• Dipankar Dasgupta
• Dario Floreano
• James Foster
• Mark Harman
• Owen Holland
• Pier Luca Lanzi
• Lee Spector
• Andrea G. B. Tettamanzi
• Dirk Thierens
• Andy Tyrrell
Series Title
Lecture Notes in Computer Science
Series Volume
3103
2004
Publisher
Springer-Verlag Berlin Heidelberg
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-24855-2
DOI
10.1007/b98645
Softcover ISBN
978-3-540-22343-6
Series ISSN
0302-9743
Edition Number
1
Number of Pages
C, 1448
Number of Illustrations and Tables
660 b/w illustrations
Topics