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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. Teams/Ensembles. Multiple solutions that ‘cooperate’ to generate a solution
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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
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
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
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
Previous Results(?) • Island Model – • Good individuals (=evolved individuals) • Poor teams (worse than ‘expected’) • Team Model – • Poor individuals (<< evolved individuals) • Good teams (> evolved individuals)
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)
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
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
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.
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.
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
Biased Version • Initial values are in the range 1-80, not 1-100. • Values 81-100 can only be found through mutation – harder cases.
Parameters • Population size = 500 • Mutation rate = 0.014 • Iterations = 500 • One point crossover • 3 member tournament selection • Team size = 3, 5, 7 • 100 Trials
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
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 ???
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.
