Terence Soule and Pavankumarreddy Komireddy

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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
• 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.