Genetic and Evolutionary Computation - GECCO 2004: Genetic and Evolutionary Computation Conference Seattle, WA, USA, June 26-30, 2004 Proceedings, Part I (Lecture Notes in Computer Science)

Deb, Kalyanmoy [Editor]; Poli, Riccardo [Editor]; Banzhaf, Wolfgang [Editor]; Beyer, Hans-Georg [Editor]; Burke, Edmund [Editor]; Darwen, Paul [Editor]; Dasgupta, Dipankar [Editor]; Floreano, Dario [Editor]; Foster, James [Editor]; Harman, Mark [Editor]; Holland, Owen [Editor]; Lanzi, Pier Luca [Editor]; Spector, Lee [Editor]; Tettamanzi, Andrea [Editor]; Thierens, Dirk [Editor]; Tyrrell, Andy [Editor];

ISBN 10: 3540223436 / ISBN 13: 9783540223436

Edité par Springer, 2004

A propos de cet article

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Détails bibliographiques

• Titre: Genetic and Evolutionary Computation - GECCO 2004: Genetic and Evolutionary Computation Conference Seattle, WA, USA, June 26-30, 2004 Proceedings, Part I (Lecture Notes in Computer Science)
• Éditeur: Springer
• Date de parution: 2004
• Langue: anglais
• ISBN à 10 chiffres: 3540223436
• ISBN à 13 chiffres: 9783540223436
• Reliure: Paperback
• État de l'article: Very Good
• Poids: 56 onces

A propos de ce titre

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.