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Genetic and Evolutionary Computation — GECCO 2004

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

Produktform: E-Buch Text Elektronisches Buch in proprietärem

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.weiterlesen

Dieser Artikel gehört zu den folgenden Serien

Elektronisches Format: PDF

Sprache(n): Englisch

ISBN: 978-3-540-24855-2 / 978-3540248552 / 9783540248552

Verlag: Springer Berlin

Erscheinungsdatum: 01.06.2004

Seiten: 1448

Herausgegeben von Dipankar Dasgupta, Kalyanmoy Deb, Dario Floreano, Wolfgang Banzhaf, Edmund Burke, Andrea G. B. Tettamanzi, Hans-Georg Beyer, James A. Foster, Mark Harman, Riccardo Poli, James Foster, Lee Spector, Pier Luca Lanzi, Andy Tyrrell, Andrea Tettamanzi, Paul Darwen, Owen Holland, Dirk Thierens

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