Genetic And Evolutionary Computation Gecco 2004 Genetic And Evolutionary Computation Conference Seattle Wa Usa June 2630 2004 Proceedings Part Ii 1st Edition Marco Antonio Pazramos by Marco Antonio Paz-ramos, Jose Torres-jimenez, Enrique Quintero-marmol-marquez (auth.), Kalyanmoy Deb (eds.) 9783540223436, 9783540248552, 3540223436, 3540248552 instant download after payment.

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.