Terence Soule and Pavankumarreddy Komireddy

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 I1,1 I2,1 I3,1 IN,1 I1,2 I2,2 I3,2 I1,3 I1,i IN,P I1,P

4. Team Model 1 population – each individual is a team, best ‘individual’ is the best team I1,1 I2,1 I3,1 IN,1 fitness1 I1,2 I2,2 I3,2 fitness2 I1,3 I1,P IN,P fitnessp

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 • fmeasured = f : member errors are independent/uncorrelated • fmeasured > f : member errors are correlated (island) • fmeasured < f : member errors are inversely correlated (team)

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

8. Orthogonal Evolution fitness1,1 I1,1 I2,1 I3,1 IN,1 fitness1 I1,2 I2,2 I3,2 fitness2 I1,3 I1,P IN,P fitnessp Alternately treat as islands and as teams

9. Orthogonal Evolution Select and copy 2 highly fit members from each island I1,1 I2,1 I3,1 IN,1 I1,2 I2,2 I3,2 I1,x I2,y … IN,z I1,a I2,b … IN,c Crossover and mutation I1,x I2,y … IN,z I1,a I2,b …IN,c Replace two poorly fit teams I1,3 I1,P IN,P Fit members are selected, poor teams are replaced.

10. 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.

11. Illustrative Problem Individual: Individual = | V1 | … | V70 | 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

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

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

14. Results

15. Island Histograms (3 Members)

16. Team Histograms (3 members)

17. OET Histograms (3 Members)

18. 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

19. Results – Best Teams

20. Results – Error Rate

21. Results – teams and members

22. 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 ???

23. 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.

24. Thank YouQuestions?