1. Orthogonal Evolution of Teams: A Class of Algorithms for Evolving Teams with Inversely Correlated Errors Terence Soule and Pavankumarreddy Komireddy This work is supported by NSF Grant #0535130

2. Teams/Ensembles Multiple solutions that ‘cooperate’ to generate a solution Cooperation mechanisms: Majority vote Weighted vote Team leader Multiple agents/distributed workload Some problems are too hard to reasonably expect a monolithic solution

3. Island Model P populations – best from each to make a team I 1,1 I 1,2 I 3,2 I N,1 I 3,1 I 2,2 I 2,1 I 1,P I 1,i I 1,3 I N,P

4. Team Model 1 population – each individual is a team, best ‘individual’ is the best team I 1,1 I 1,2 I 3,2 I N,1 I 3,1 I 2,2 I 2,1 I 1,P I 1,3 I N,P fitness 1 fitness 2 fitness p

5. Previous Results(?) Island Model – Good individuals (=evolved individuals) Poor teams (worse than ‘expected’) Team Model – Poor individuals (<< evolved individuals) Good teams (> evolved individuals)

6. Expected Failure Rate f = expected failure rate of the team P = probability of a member failing N = team size M = minimum number of member failures to create a team failure f measured = f : member errors are independent/uncorrelated f measured > f : member errors are correlated (island) f measured < f : member errors are inversely correlated (team)

7. Expected Failure Rate f measured = f : member errors are independent/uncorrelated f measured > f : member errors are correlated (island) –Limited cooperation/specialization f measured < f : member errors are inversely correlated (team) –High cooperation/specialization

8. Orthogonal Evolution I 1,1 I 1,2 I 3,2 I N,1 I 3,1 I 2,2 I 2,1 I 1,P I 1,3 I N,P fitness 1 fitness 2 fitness p fitness 1,1 Alternately treat as islands and as teams

9. Orthogonal Evolution Generate a population of teams Repeat for X iterations{ Repeat for each of the N islands{ Select two highly fit team members } Apply crossover and mutation Select two low fitness teams to delete Insert the two offspring teams }

10. Orthogonal Evolution I 1,1 I 1,2 I 3,2 I N,1 I 3,1 I 2,2 I 2,1 I 1,P I 1,3 I N,P Select and copy 2 highly fit members from each island I 1,x I 2,y … I N,z I 1,a I 2,b … I N,c Crossover and mutation I 1,x I 2,y … I N,z I 1,a I 2,b … I N,c Replace two poorly fit teams Fit members are selected, poor teams are replaced.

11. Hypotheses OET members > team model members. OET produces teams whose errors are inversely correlated. OET teams > evolved individuals. OET teams > team model teams. OET teams > island model teams.

12. Illustrative Problem Individual: Individual = | V 1 | … | V 70 | V  {1,100} Fitness = number of unique values (max = 70) Team: N individuals Fitness = number of unique values in majority of individuals 5 | 6 | 3 | 13 | 7 | 5 | 3 8 | 2 | 9 | 14 | 2 | 3 | 2 3 | 8 | 6 | 11 | 8 | 4 | 1 3, 6, and 8 NOT 5 or 2

13. Biased Version Initial values are in the range 1-80, not 1-100. Values 81-100 can only be found through mutation – harder cases.

14. Parameters Population size = 500 Mutation rate = 0.014 Iterations = 500 One point crossover 3 member tournament selection Team size = 3, 5, 7 100 Trials

15. Results UnbiasedBiased Size expected Alg.TeamMemberTeamMember 3 (78.4) Island78.3169.6477.1369.53 Team98.0867.0197.3966.79 OET99.9669.8999.9569.84 5 (83.7) Island83.5169.6877.5469.76 Team97.5764.5092.8563.11 OET10069.5610069.48 7 (87.4) Island89.9369.5685.4769.62 Team93.4562.5987.3560.35 OET10069.2599.9769.24

16. Island Histograms (3 Members)

17. Team Histograms (3 members)

18. OET Histograms (3 Members)

19. Inter-twined Spirals Population size = 400 Mutation rate = 0.01 Iterations = 200,000 (600,000 for non-team) 90/10 crossover 3 member tournament selection Team size = 3 Ramped half and half initialization 40 Trials

20. Results – Best Teams

21. Results – Error Rate Alg. Average Member Expected Team Average Team Best Member Expected Team Best Team Indivi dual 0.116- 0.096- Island0.1582--0.13750.05150.0492 Team0.32420.24710.116--0.0813 OET0.18060.08610.0654--0.0439

22. Results – teams and members

23. Conclusions Evolving ensembles helps OET produces better team members than the team approach. OET produces teams whose errors are inversely correlated. OET teams > island model teams ???

24. Discussion Expected fault tolerance model is useful for measuring cooperation/specialization Is it necessary to measure team members’ fitness? Team model – no Island, OET – yes Could use team fitness for, e.g., lead member’s fitness.

25. Thank You Questions?