1. Convergence Analysis of Canonical Genetic Algorithm 2010.10.14 ChungHsiang, Hsueh

2. Agenda Introduction Markov chain analysis of CGA Discussion with respect to the schema theorem Conclusion

3. Agenda Introduction Markov chain analysis of CGA Discussion with respect to the schema theorem Conclusion

4. Introduction: Gunter Rudolph Computational Intelligence Research Group Chair of Algorithm Engineering (LS XI) Department of Computer Science TU Dortmund University Associate editor of the IEEE Transactions on EC. Editorial board member of the Journal on EC

5. Introduction: Markov Chain

7. Agenda Introduction Markov chain analysis of CGA Discussion with respect to the schema theorem Conclusion

8. Describing CGA as A Markov Chain n l

9. Theorem 3 C:The crossover operator can be regarded as a random total function whose domain and range are S -> each state of S is mapped probabilistically to another state -> C is stochastic

10. Theorem 4: CGA does not converge to the global optimum

11. Theorem6 & Theorem7

12. Adaption of Markov Chain Description ->upgrade matrix

13. Adaption of Markov Chain Description(cont.)

14. Theorem 6-Proof

15. Theorem 7-Proof

16. Agenda Introduction Markov chain analysis of CGA Discussion with respect to the schema theorem Conclusion

17. Schema Theorem V.S. Convergence

18. Lemma 2

19. Agenda Introduction Markov chain analysis of CGA Discussion with respect to the schema theorem Conclusion

20. Convergence to the global optimum is not an inherent property of the CGA but rather as a consequence of the algorithmic trick of keeping track of the best solution found over time. Introducing time varying mutation and selection probabilities may make the Markov process inhomogeneous and reach the global optimum. #Introducing time varying mutation alone does not help. ->Selection operator is the key problem of the CGA.

21. Reference [1]Gunter Rudolph, Convergence Analysis of Canonical Genetic Algorithms,2002