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A Simple Real-Coded ECGA

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A Simple Real-Coded ECGA Luca Fossati, Pier Luca Lanzi, Kumara Sastry, David E. Goldberg, Osvaldo Gomez Politecnico di Milano, Italy Illinois Genetic Algorithms Laboratory, University of Illinois at Urbana Champaign, USA CEC 2007, Singapore, September 25th, 2007
Real-coded EDAs are complex and difficult to analyze What is our goal? The simplest real-coded EDA possible Elementary discretization + χECGA
ECGA Population MPM Model Selection New Population
Simple Real Coded ECGA Real-Valued Population Selection X-ary Population χECGA … New X-ary Population New Real-Valued Population Intervals I i,j Restrict Tournament Replacement (RTR)
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Simple Real Coded ECGA k = # of intervals rp = real population dp = discrete population I i,j is the j-th interval for gene i
Additively separable problem ,[object Object]
Bisection Procedure ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
K=5
Number of Evaluations for k=5
Population Size for k=5
K=10
Number of Evaluations for k=10
Population Size for k=10
Ks
Number of Evaluations as Function of k
Population Size as Function of k
Class of additively separable problems The population size scales sub-quadratically with problem size The number of function evaluations scales sub-cubically with problem size Simple, amenable for further empirical and theoretical analysis First step towards a systematic analysis of real-coded ECGA
What next? More experiments Scalability analysis Relation between discretization and performance … virtual alphabets?
Virtual Alphabets (Goldberg, 1991) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Virtual Alphabets
Blocking x 1
Simple Real-Coded ECGA Explicitly builds the alphabet Virtual alphabets & RECGA? Blocking & Model Building?
Any Question? Thank you!

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