1. Approaches to Selection and their Effect on Fitness Modelling in an Estimation of Distribution Algorithm A. E. I. Brownlee, J. A. McCall, Q. Zhang and D. F. Brown Presented by Kim, Kwonill 2008.06.26 kikim@bi.snu.ac.kr

2. © 2008, SNU CSE BioIntelligence Lab, http://bi.snu.ac.kr/ At a Glance Selection Ability of EDA Effect ? Yes!! Top Bottom Top&Bottom Fitness function modelling by DEUM (Distribution Estimation Using Markov network) Correlation Under Various Conditions Selection EDA Measure Between Predicted & True Fitnesses 2

3. Contents Selection in EDA DEUM Correlation coefficient Experiment method Result & Conclusion Summary & QnA © 2008, SNU CSE BioIntelligence Lab, http://bi.snu.ac.kr/3

4. Selection in EDA Loss of information from population  Truncation selection Related works Topic of this paper  Let’s analyze the effects of selection on the information about fitness function contained in a population. © 2008, SNU CSE BioIntelligence Lab, http://bi.snu.ac.kr/4

5. Distribution Estimation Using Markov network (DEUM) (1/3) Using Markov network to model fitness as an energy distribution over the solution space Markov Network  Random variable → Node  Interaction → Undirected edge  Only neighborhood interactions  A set of cliques © 2008, SNU CSE BioIntelligence Lab, http://bi.snu.ac.kr/5

6. Joint probability distribution (by Gibbs distribution)  U(x): sum of clique potential function  x : each individual  c, α : parameters, which define the Markov network Markov Fitness Model (MFM)  Maximizing Fitness = Minimizing U(x) © 2008, SNU CSE BioIntelligence Lab, http://bi.snu.ac.kr/6 Distribution Estimation Using Markov network (DEUM) (2/3)

7. Distribution Estimation Using Markov network (DEUM) (3/3) Example: MAXSAT problem  An individual x={0011}, with fitness f(x)=2 Parameter determination  By singular value decomposition (SVD) Fitness prediction © 2008, SNU CSE BioIntelligence Lab, http://bi.snu.ac.kr/7

8. Measure: Correlation Coefficient Product moment correlation coefficient  x: a set of true fitnesses calculated by fitness function  y: a set of predicted fitnesses calculated by model © 2008, SNU CSE BioIntelligence Lab, http://bi.snu.ac.kr/8

9. EXPERIMENTS & RESULTS © 2008, SNU CSE BioIntelligence Lab, http://bi.snu.ac.kr/9

10. Correlation: C m & C r © 2008, SNU CSE BioIntelligence Lab, http://bi.snu.ac.kr/10 1.Generate random initial population 2.Select a subset σ of the population 3.Use σ to build MFM 4.For each member of s, repeat: 4.1 Mutate one bit in the individual 4.2 Use MFM to predict fitness of individual 4.3 Use fitness function to determine true fitness 5.Generate a complete new random population equal in size to the first, 6.For each member of this population: 6.1 Use MFM to predict fitness 6.2 Use fitness function to determine true fitness C m : C r : Ability of the model to predict the fitness of randomly generated individuals. → How closely MFM is modeled to fitness function Ability of MFM to predict fitness of solutions “near to” the current population

11. Selection Strategies © 2008, SNU CSE BioIntelligence Lab, http://bi.snu.ac.kr/11 Population n Selected p*n Population n Selected p*n Population n Selected p*n/2 Top SelectionBottom Selection Top & Bottom Selection

12. Underspecified & Overspecified N > n: Underspecified system N ≤ n: Overspecified system  n: population size  N: # of terms in MFM Ex. Onemax problem © 2008, SNU CSE BioIntelligence Lab, http://bi.snu.ac.kr/12

13. Perfect & Imperfect Perfect model structure  MFM includes all interactions defined by the problem Imperfect model structure  MFM misses some interactions  Realistic situation © 2008, SNU CSE BioIntelligence Lab, http://bi.snu.ac.kr/13

14. Problems Onemax Ising Spin Glass MAXSAT © 2008, SNU CSE BioIntelligence Lab, http://bi.snu.ac.kr/14

15. Perfect + Overspecified © 2008, SNU CSE BioIntelligence Lab, http://bi.snu.ac.kr/15

16. Perfect + Underspecified © 2008, SNU CSE BioIntelligence Lab, http://bi.snu.ac.kr/16

17. Imperfect + Overspecified © 2008, SNU CSE BioIntelligence Lab, http://bi.snu.ac.kr/17

18. Conclusion Selection is particularly important when the fitness model is unlikely to perfectly match the fitness function. © 2008, SNU CSE BioIntelligence Lab, http://bi.snu.ac.kr/18

19. Summary & QnA Selection, information loss & ability of EDA Fitness modelling of DEUM  Markov network Measurement  Correlation Coefficient: C m & C r Experiments  Overspecified & underspecified system  Perfect & imperfect model structure  Top, Bottom, Top&Bottom selection strategies © 2008, SNU CSE BioIntelligence Lab, http://bi.snu.ac.kr/19

20. THANK YOU!! © 2008, SNU CSE BioIntelligence Lab, http://bi.snu.ac.kr/20