1. Presenter: Tsung-Yu Ho 2011.09.22

2. What is Niching ? Signing Baseball Players After regular season, every team’s manager is worried about signing Free Agent (FA). ABILITY SALARY(Demand) High Low Good Bad A. Pujols P. Fielder R. Cano J. Reyes H. Bell J. Francis H. Kuroda 王建民 Matsui B. Webs[SALARY] High Low 2012 FAs Reduce to one axis Strategy?

3. Boston Red Sox CEO Larry Lucchino says Yankees is the “ evil empire” 2012 FAs 2011 FAs 2010 FAs 2009 FAs 2008 FAs High Low Evil Empire

4. A movie “Moneyball” shows different strategy by using Implicit Function to find suitable player. High Low Free Agents Choose local windows Use Implicit Function Moneyball Team

5. Baseball management is a complicated game that hardly knows the optimal strategy. Here are two points that we should consider.  Keep current optima not always lead to find global optima.  Allow some local solutions may improve the performance.  The estimated metric is important  For example, play’s salary is not a good judgment.  There are many different metrics to make different result.

6. Optimization without Niching Optimization with Niching Hierarchical

7. SGA selection Cross over Model-based GA + Model-Building SXO Model Building RTR CPF Solve Exponential (hBOA) Polynomial (CGA, ECGA) Reason Results Show 1 2 3 4 5 RTR Weakness Assumption Binomial RTR Modification 6 + EDAs, result again CPF

8. Trap Functions, k=5 u(x)0 5 1 2 34 Fitness 11111 10111 1001110010 00010 1 0.8 00000 11111 xxxxx xxxxxx 00000 xxxxx xxxxxx Number XO 11000 00111 11111 xxxxx xxxxxx 00000 xxxxx xxxxxx 0.5N N 0 Increase 00000

9. Avoid disruption by XO 11111 00000 11111 1 1 1 1 1 0 0 0 0 0 00000 00000 11111 1 1 1 1 1 Pair-wise Linkage Learning after selection 0 0 0 0 0 ‘11’ = ‘1’ ‘00’ = ‘0’ 11111 00000 11111 00000 00000 11111 1 0 1 0 0 1

10. RTR keeps 000 and 111 in Hierarchical Problem 000 111 0 1 1 1 F 1 (000 111 111) F 2 (011) > F 2 (111) 111

12. 少林寺招收新血, 舉辦比武大會  希望提升整體實力, 並維持等比例的武藝.(A, B, C, D, E 表示武力等級 ) BABC EDDCDDA DEB ( 少林寺 ) ( 參賽者 ) Random C B A C

13. 少林寺招收新血, 舉辦比武大會  希望提升整體實力, 並維持等比例的武藝.(A, B, C, D, E 表示武力等級 ) BAB EDD C DDA DEB ( 少林寺 ) ( 參賽者 ) Random DDD C B

14. 少林寺招收新血, 舉辦比武大會  希望提升整體實力, 並維持等比例的武藝.(A, B, C, D, E 表示武力等級 ) B B ED C E ( 少林寺 ) ( 參賽者 ) A D BABC EDD NEW Original

15. Model-Building according to some distribution Probability Fitness PDF Probability Fitness PDF Before selection and RTR After selection and RTR Lead to different model building

16. Concatenated parity function  Single BB, where F(u even ) =2 and F(u odd ) = 0. 0 0 0 0 0 1 0 1 0 1 0 0 0 1 1 1 0 1 1 1 0 1 1 1 After Selection (s=2) 0 0 0 0 1 1 1 1 0 1 0 1 P(00) = P(11) = P(10) = P(01) = 0.25 No dependency between the pair

17. EDAs with pairwise linkage learning can not detect any k>1 linkage on CPF. 0 0 0 0 1 1 1 1 0 1 0 1 0 0 0 0 0 1 0 1 0 1 0 0 0 1 1 1 0 1 1 1 0 1 1 1 After RTR Parent Population Offspring Population Window size = 4 0 0 0 0 1 1 1 1 0 0 1 1 1 0 1 1 1 0 1 1 1 Dependency increase

18. Spurious Linkage  Add linkage on the independent pair. RTR produce spurious linkage  Preserved local solutions change the expected distribution  Model-building works on inaccuracy distribution  and produces spurious linkage However, selection can decrease the bias on distribution  EDAs with RTR solve most problems in polynomial time Exception for hBOA on CPF  hBOA is a powerful EDA  RTR is hard to understand  It is mysterious?

19. Test EDAs on CPF  CGA, ECGA, and hBOA CGA  No linkage learning, no RTR  Polynomial time ECGA  has linkage learning, no RTR  Polynomial time hBOA  Has linkage learning and RTR  Exponential time

20. EDAs(pairwise) can not learn linkage on CPF  CPF is a difficulty problem ? CGA can solve CPF in polynomial time  The performance of CGA is similar to SGA  CPF is a easy problem ? Summary  What is real linkage for EDAs is unclear.  If EDAs can solve CPF without any linkage structure in polynomial time, CPF is like a one max problem.

22. F(u odd ) > F(u even ) 1 1 1 0 0 1 0 1 0 1 0 0 Probability 0.25 Probability + bias

23. RTR use Hamming distance to detect two similar genes.  It has less relation in linkage-learning. Trap Problem (k=4) Fitness 1.6 0.8 Distance = 2 0 1 0 0 1 1 1 1 0 1 1 1 0 0 0 0 1 1 0 1 0 1 1 1 0.6 1 0.8 0 0 0

24. Binomial distribution supports sequence of n independent elements. If we have n independent bits in the problem, binomial distribution of population can make sure no dependent linkage. In fact, because the bias, it is hard to form the idea distribution. However, niching can approach what we need.

25. Probability = Average Fitness of population Number = Population size Parent + Offspring form binomial population. Fitness

26. RTR is not meaningful for linkage learning Linkage can reduce to a single bit BB. The binomial distribution can be implemented on linkage structure. 1101011 0 1 1101011 0 1 3 BBs 9 BBs

27. RTR use Hamming distance 111…111000…000 Distance(i,j) F High F Low Distance(i,j) > EquDistance(F i,F j ) Modification consider fitness and distance P P P

28. Fitness-based  Fitness => Rank (r 1, r 2, r 3, … r N ) => Rank (0.01, 0.02, …, 0.98, 0.99) Model-building based  Match “most frequency shema” => +1  Because we don’t what is optima 0 0 0 0 0 1 1 1 0 1 1 1 (0 0 0) (0 0 0) (1 1 0) (1 1 1) +1 Most Frequency Shema ith population r i =

29. Parent (i) Population 1 5 10 14 1 Offspring(j) Population

30. RTR is well-used for most EDAs because of its well performance. RTR has some weakness  Poor on allelic pairwise independent functions (CPF)  Hard to understand the relation between with RTR  Do not consider solution quality BRTR has some advantage  Similar as RTR  Use binomial distribution to keep solution  Consider both fitness and similarity.