Genetic And Evolutionary Computation- GECCO 2004

Genetic And Evolutionary Computation Conference, Seattle, Wa, Usa, June 26-30, 2004, Proceedings

• Author(s): Kalyanmoy Deb,
• Publisher: Springer Science & Business Media
• Pages: 1448
• ISBN_10: 3540223436
  ISBN_13: 9783540223436
  
• Language: en
• Categories: Computers / General , Computers / Artificial Intelligence / General , Computers / Computer Architecture , Computers / Computer Science , Computers / Data Science / General , Computers / Information Technology , Computers / Machine Theory , Computers / Software Development & Engineering / General , Computers / Programming / Algorithms , Computers / User Interfaces , Mathematics / Discrete Mathematics , Science / Life Sciences / Biology , Science / Life Sciences / Genetics & Genomics , Science / Bioinformatics ,

Description:... 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.