# Genetic and Evolutionary Computation – GECCO 2004 [electronic resource] :Genetic and Evolutionary Computation Conference, Seattle, WA, USA, June 26-30, 2004. Proceedings, Part II /

##### Contributor(s): Deb, Kalyanmoy [editor.] | SpringerLink (Online service).

Material type: BookSeries: Lecture Notes in Computer Science: 3103Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2004.Description: C, 1448 p. 660 illus. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9783540248552.Subject(s): Computer science | Microprocessors | Computers | Algorithms | Computer science -- Mathematics | Artificial intelligence | Computer Science | Artificial Intelligence (incl. Robotics) | Computer Science, general | Computation by Abstract Devices | Algorithm Analysis and Problem Complexity | Processor Architectures | Discrete Mathematics in Computer ScienceOnline resources: Click here to access onlineGenetic Algorithms (Continued) -- Genetic Algorithms – Posters -- Genetic Programming -- Genetic Programming – Posters -- Learning Classifier Systems -- Learning Classifier Systems – Poster -- Real World Applications -- Real World Applications – Posters -- Search-Based Software Engineering -- Search-Based Software Engineering – Posters.

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.

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