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Binomial RTR with Linkage learning

Binomial RTR with Linkage learning . Presenter: Tsung -Yu Ho 2011.09.22. A story about Niching . Signing Baseball Players. What is Niching ?. After regular season, every team’s manager is worried about signing Free Agent (FA). . [SALARY]. High. A. Pujols. P. Fielder. High.

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Binomial RTR with Linkage learning

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  1. Binomial RTR with Linkage learning Presenter: Tsung-Yu Ho 2011.09.22

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

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

  4. Strategy for Preserving Local • A movie “Moneyball” shows different strategy by using Implicit Functionto find suitable player. Choose local windows High Moneyball Team Low Use Implicit Function Free Agents

  5. Discussion of Strategy • 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. Niching on Optimization • Optimization without Niching • Optimization with Niching Hierarchical

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

  8. Model-Building(1) • Trap Functions, k=5 XO Fitness Number Fitness 1 11111 xxxxxxxxxxx 0.5N 0.8 00000 xxxxxxxxxxx 0.5N 11000 Increase00000 00111 11111 xxxxxxxxxxx 0 N 00000 xxxxxxxxxxx 5 u(x) 0 2 1 3 4 00000 00010 10111 10010 10011 11111

  9. Model-Building(2) • Avoid disruption by XO 11111 00000 11111 00000 00000 11111 • Pair-wise Linkage Learning after selection 1 1 1 1 1 11111 00000 11111 0 0 0 0 0 ‘11’ = ‘1’ 00000 00000 11111 1 1 1 1 1 ‘00’ = ‘0’ 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 1 1 0 0 1

  10. Model-Building with RTR • RTR keeps 000 and 111 in Hierarchical Problem 1 1 1 0 F2(011) > F2(111) 111 F1(000 111 111) 000 111 111

  11. RTR Algorithm

  12. Example • 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) (少林寺) (參賽者) B A B C D E D C D D A B D E Random A B C C

  13. Example • 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) (少林寺) (參賽者) B A B C D E D D D A B D E Random B C D D D

  14. Example • 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) (少林寺) (參賽者) D E E D C A B B NEW B A B C D E D Original

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

  16. CPF(1) • Concatenated parity function • Single BB, where F(ueven) =2 and F(uodd) = 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 0 0 0 0 0 0 0 1 1 0 1 1 11 0 1 1 0 1 0 1 1 0 1 After Selection (s=2) P(00) = P(11) = P(10) = P(01) = 0.25 No dependency between the pair

  17. CPF(2) • EDAs with pairwise linkage learning can not detect any k>1 linkage on CPF. 0 0 0 0 0 1 0 1 0 1 0 0 0 1 1 1 0 1 1 1 0 1 1 1 0 0 0 0 0 0 0 1 1 0 1 1 1 1 0 1 1 0 1 0 1 1 0 1 0 0 0 0 0 0 0 1 1 1 1 0 0 1 1 1 0 1 1 1 0 1 1 1 After RTR Window size = 4 Parent Population Offspring Population Dependency increase

  18. Spurious Linkage • 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. Experiment Results • 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. The difficulty of CPF • 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.

  21. Converge of CGA on CPF(1) • Too many Global Optima • A (CPF problem • Drift • 00 and 11 are global optima • One of Shemata with bias will converge.

  22. Converge of CGA on CPF(2) • F(uodd) > F(ueven) Probability Probability + bias 1 11 0 0 1 0 1 0 1 0 0 0.25 0.25 0.25 0.25

  23. Unclear of RTR • 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 0.6 1 0 0 10 0 1 1 1 1 0 1 1 1 0 0 0 0 1 1 0 1 0 1 1 1 0 0 0.8 Distance = 2

  24. Idea Distribution • Binomial distribution supports sequence of nindependent 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. Binomial Distribution • Probability = Average Fitness of population • Number = Population size • Parent + Offspring form binomial population. Fitness

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

  27. Modification of RTR • RTR use Hamming distance Distance(i,j) 111…111 000…000 • Modification consider fitness and distance P FHigh FLow P P Distance(i,j) > EquDistance(Fi,Fj)

  28. Binomial RTR(1) • Fitness-based • Fitness => Rank (r1, r2, r3, … rN) => 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 0) (1 1 0) (1 1 1) Most Frequency Shema ithpopulation 0 0 0 0 0 1 1 1 0 1 1 1 ri = +1 +1 +1

  29. Binomial RTR(2) 1 1 Offspring(j) Population Parent (i) Population 5 10 14

  30. Conclusion • 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.

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