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# Gecco2007 Recga

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### Gecco2007 Recga

1. 1. 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 OBUPM GECCO'07, July 7--11, 2007, London, UK.
2. 2. Real-coded EDAs are complex and difficult to analyze What is our goal? The simplest real-coded EDA possible Elementary discretization + χECGA
3. 3. ECGA New Selection Population Population MPM Model
4. 4. Simple Real Coded ECGA Restrict Tournament Replacement (RTR) Real-Valued New Real-Valued Population Selection Population Intervals Ii,j χECGA X-ary New X-ary … Population Population
5. 5. Simple Real Coded ECGA k = # of intervals rp = real population dp = discrete population 1: procedure RECGA(k) Ii,j is the j-th interval for gene i 2: rp ← random(); 3: Generate a random population rp 4: Evaluate the fitness in rp 5: while stop criterion not true do 6: Undergo tournament selection at a rate S 7: Discretize rp into dp using k and generate Ii,j 8: Model dp using a greedy MPM search 9: If the model has converged, stop 10: Generate a new dp+1 using the model 11: Generate a new rp+1 from dp+1 using Ii,j 12: rp ← ApplyRTR(rp+1,rp) 13: Evaluate the fitness in rp 14: end while 15: end procedure
6. 6. Number of Evaluations for k=5
7. 7. Population Size for k=5
8. 8. Number of Evaluations for k=10
9. 9. Population Size for k=10
10. 10. Number of Evaluations as Function of k
11. 11. Population Size as Function of k
12. 12. 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
13. 13. What next? More experiments Scalability analysis Relation between discretization and performance … virtual alphabets?
14. 14. Virtual Alphabets (Goldberg, 1991) Theory of convergence for real-coded GAs Selection Dominates early GA performance Restricts subsequent search to intervals with above average fitness It does it, dimension by dimension Intervals form the characters of a virtual alphabet, searched during recombination
15. 15. Virtual Alphabets
16. 16. Blocking x1
17. 17. Simple Real-Coded ECGA Explicitly builds the alphabet Virtual alphabets & RECGA? Blocking & Model Building?
18. 18. Thank you! Any question?