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/EnsemblesMultiple solutions that ‘cooperate’ to generate a solutionCooperation mechanisms:

Majority voteWeighted voteTeam leaderMultiple agents/distributed workload

Some problems are too hard to reasonably expect a monolithic solution

Island ModelP populations – best from each to make a team

I1,1

I1,2 I3,2

IN,1I3,1

I2,2

I2,1

I1,P

I1,i

I1,3

IN,P

Team Model1 population – each individual is a team, best

‘individual’ is the best team

I1,1

I1,2 I3,2

IN,1I3,1

I2,2

I2,1

I1,P

I1,3

IN,P

fitness1

fitness2

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

kkN ppN

MKK

Nf )(1

f = expected failure rate of the team P = probability of a member failingN = team sizeM = 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

I1,1

I1,2 I3,2

IN,1I3,1

I2,2

I2,1

I1,P

I1,3

IN,P

fitness1

fitness2

fitnessp

fitness1,1

Alternately treat as islands and as teams

Orthogonal Evolution

I1,1

I1,2 I3,2

IN,1I3,1

I2,2

I2,1

I1,P

I1,3

IN,P

Select and copy 2 highly fit members from each island

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 teamsFit 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 ProblemIndividual:

Individual = | V1 | … | V70 |V {1,100}Fitness = number of unique values (max = 70)

Team: N individualsFitness = number of unique values in majority of individuals

5 | 6 | 3 | 13 | 7 | 5 | 38 | 2 | 9 | 14 | 2 | 3 | 23 | 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 = 500Mutation rate = 0.014

Iterations = 500One point crossover3 member tournament selectionTeam size = 3, 5, 7100 Trials

ResultsUnbiased Biased

Sizeexpecte

d

Alg. Team Member Team Member

3(78.4)

Island 78.31 69.64 77.13 69.53

Team 98.08 67.01 97.39 66.79

OET 99.96 69.89 99.95 69.84

5(83.7)

Island 83.51 69.68 77.54 69.76

Team 97.57 64.50 92.85 63.11

OET 100 69.56 100 69.48

7(87.4)

Island 89.93 69.56 85.47 69.62

Team 93.45 62.59 87.35 60.35

OET 100 69.25 99.97 69.24

Island Histograms (3 Members)

Team Histograms (3 members)

OET Histograms (3 Members)

Inter-twined SpiralsPopulation size = 400Mutation rate = 0.01 Iterations = 200,000 (600,000 for non-team)90/10 crossover3 member tournament selectionTeam size = 3Ramped half and half initialization40 Trials

Results – Best Teams

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0 100 200 300 400 500

Err

or

rate

Iterations/pop. size

Individual x3 iterationsTeamIsland

OET

Results – Error RateAlg. Averag

e Member

Expected Team

Average Team

Best Member

ExpectedTeam

Best Team

Individual

0.116 - 0.116 0.096 - 0.096

Island

0.1582

- - 0.1375

0.0515

0.0492

Team 0.3242

0.2471

0.116 - - 0.0813

OET 0.1806

0.0861

0.0654

- - 0.0439

Results – teams and members

0

0.1

0.2

0.3

0.4

0.5

0 100 200 300 400 500

Err

or

rate

Iterations/pop. size

Team -TeamTeam - Members

OET - TeamOET - Members

ConclusionsEvolving ensembles helpsOET produces better team members than the team approach.OET produces teams whose errors are inversely correlated. OET teams > island model teams ???

DiscussionExpected fault tolerance model is useful for measuring cooperation/specializationIs it necessary to measure team members’ fitness?

Team model – noIsland, OET – yesCould use team fitness for, e.g., lead member’s fitness.

Thank You

Questions?