Orthogonal Evolution of Teams:
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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


Results


Island Histograms (3 Members)


Team Histograms (3 members)


OET Histograms (3 Members)


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


Results – Best Teams


Results – Error Rate


Results – teams and members


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.


Thank YouQuestions?


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