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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Terence soule and pavankumarreddy komireddy

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

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

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

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

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

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 rate1

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

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 evolution1

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

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

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

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

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

Results


Island histograms 3 members

Island Histograms (3 Members)


Team histograms 3 members

Team Histograms (3 members)


Oet histograms 3 members

OET Histograms (3 Members)


Inter twined spirals

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 – Best Teams


Results error rate

Results – Error Rate


Results teams and members

Results – teams and members


Conclusions

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

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 you questions

Thank YouQuestions?


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