Genetic and Evolutionary Computation — Gecco 2004: Genetic and Evolutionary Computation Conference, Seattle, Wa, USA, June 26–30, 2004 Proceedings, Part II - Couverture souple

Couverture souple

ISBN 10 : 3540223436 ISBN 13 : 9783540223436

Editeur : Springer-Verlag Berlin and Heidelberg GmbH & Co. K, 2004

Synopsis

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.

Détails de l'édition

• Éditeur: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
• Date d'édition: 2004
• Langue: anglais
• ISBN 10: 3540223436
• ISBN 13: 9783540223436
• Reliure: Broché
• Nombre de pages: 1548
• Éditeur: Deb Kalyanmoy, Poli Riccardo, Banzhaf Wolfgang, Beyer Hans-Georg, Burke Edmund, Darwen Paul, Dasgupta Dipankar, Floreano Dario, Foster James A., Harman Mark, Holland Owen, Lanzi Pier Luca, Spector Lee, Tettamanzi Andrea, Thierens Dirk, Tyrrell Andy
• Coordonnées du fabricant: ProductSafety@springernature.com; ProductSafety@springernature.com; ; Poststr. 9; Darmstadt; 64293; Allemagne