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Format
Språk
Engelska
Antal sidor
1448
Utgivningsdatum
2004-10-01
Upplaga
2004 ed.
Förlag
Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Medarbetare
Deb, Kalyanmoy (ed.), Poli, Riccardo (ed.), Banzhaf, Wolfgang (ed.)
Illustrationer
660 Illustrations, black and white; C, 1448 p. 660 illus. In 2 volumes, not available separately.
Volymtitel
Part II
Antal komponenter
2
Komponenter
2 Paperbacks
ISBN
9783540223436

# Genetic and Evolutionary Computation - GECCO 2004

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

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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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