Symposium “New Directions in Evolutionary Computation”

Dr. Daniel TauritzDirector, Natural Computation Laboratory

Associate Professor, Department of Computer ScienceResearch Investigator, Intelligent Systems Center

Collaborator, Energy Research & Development Center

New Directions in ParameterlessEvolutionary Algorithms

Vision

EAfitness function

representation

EA operators

EA parameters

solution(good solution if operators and parameters are suitably configured)

NOW GOAL

problem instance

Parameter-lessEA

fitness function

representation

problem instance

good solution

EA Operators

• Parent selection, mate pairing

• Recombination

• Mutation

• Survival selection

EA Parameters

• Population size• Initialization related parameters• Parent selection parameters• Number of offspring• Recombination parameters• Mutation parameters• Survivor selection parameters• Termination related parameters

Motivation for Parameterless EAs

• Parameterless EAs do not require parameters to be specified a priori

• A priori parameter tuning is computationally expensive

• Facilitate use by non-experts

Static vs. dynamic parameters

• Static parameters remain constant during evolution, dynamic can change

• The optimal value of a parameter can change during evolution

• Parameterless EAs w/ static parameters need a fully automated tuning mechanism (still computationally expensive & suboptimal)

• Therefore desired:Parameterless EA w/ dynamic parameters

Parameter Control

• While dynamic parameters can benefit from tuning, they can be much less sensitive to initial values (versus static)

• Controls dynamic parameters

• Three main parameter control classes:– Blind– Adaptive– Self-Adaptive

Prior (Semi-)Parameterless EAs

1994 Genetic Algorithm with Varying Population Size (GAVaPS)

2000 Genetic Algorithm with Adaptive Population Size (APGA)

– dynamic population size as emergent behavior of individual survival tied to age

– both introduce two new parameters: MinLT and MaxLT; furthermore, population size converges to 0.5 * offspring size * (MinLT + MaxLT)

Prior (Semi-)Parameterless EAs

1995 (1,λ)-ES with dynamic offspring size employing adaptive control

– adjusts λ based on the second best individual created

– goal is to maximize local serial progress-rate, i.e., expected fitness gain per fitness evaluation

– maximizes convergence rate, which often leads to premature convergence on complex fitness landscapes

Prior (Semi-)Parameterless EAs1999 Parameter-less GA– runs multiple fixed size populations in parallel– the sizes are powers of 2, starting with 4 and

doubling the size of the largest population to produce the next largest population

– smaller populations are preferred by allotting them more generations

– a population is deleted if a) its average fitness is exceeded by the average fitness of a larger population, or b) the population has converged

– no limit on number of parallel populations

Prior (Semi-)Parameterless EAs

2003 self-adaptive selection of reproduction operators

– each individual contains a vector of probabilities of using each reproduction operator defined for the problem

– probability vectors updated every generation– in the case of a multi-ary reproduction

operator, another individual is selected which prefers the same reproduction operator

Prior (Semi-)Parameterless EAs

2004 Population Resizing on Fitness Improvement GA (PRoFIGA)

– dynamically balances exploration versus exploitation by tying population size to magnitude of fitness increases with a special mechanism to escape local optima

– introduces several new parameters

Prior (Semi-)Parameterless EAs2005 (1+λ)-ES with dynamic offspring size

employing adaptive control– adjusts λ based on the number of offspring fitter

than their parent: if none fitter, than double λ; otherwise divide λ by number that are fitter

– idea is to quickly increase λ when it appears to be too small, otherwise to decrease it based on the current success rate

– has problems with complex fitness landscapes that require a large λ to ensure that successful offspring lie on the path to the global optimum

Prior (Semi-)Parameterless EAs

2006 self-adaptation of population size and selective pressure

– employs “voting system” by encoding individual’s contribution to population size in its genotype

– population size is determined by summing up all the individual “votes”

– adds new parameters pmin and pmax that determine an individual’s vote value range

NC-LAB Vision for a New Direction in Parameterless EAs:

Autonomous EAs (AutoEAs)

Motivation

• Selection operators are not commonly used in an adaptive manner

• Most selection pressure mechanisms are based on Boltzmann selection

• Framework for creating Parameterless EAs

• Centralized population size control, parent selection, mate pairing, offspring size control, and survival selection are highly unnatural!

Approach

Remove unnatural centralized control by:

• Letting individuals select their own mates

• Letting couples decide how many offspring to have

• Giving each individual its own survival chance

Autonomous EAs (AutoEAs)

• An AutoEA is an EA where all the operators work at the individual level (as opposed to traditional EAs where parent selection and survival selection work at the population level in a decidedly unnatural centralized manner)

• Population & offspring size become dynamic derived variables determined by the emergent behavior of the system

Self-Adaptive Semi-Autonomous Parent Selection (SASAPAS)

• Each individual has an evolving mate selection function

• Two ways to pair individuals:– Democratic approach– Dictatorial approach

Democratic Approach

Democratic Approach

Dictatorial Approach

Self-Adaptive Semi-Autonomous Dictatorial Parent Selection

(SASADIPS)• Each individual has an evolving mate

selection function

• First parent selected in a traditional manner

• Second parent selected by first parent –the dictator – using its mate selection function

Mate selection function representation

• Expression tree as in GP

• Set of primitives – pre-built selection methods

Mate selection function evolution• Let F be a fitness function defined on a

candidate solution. Letimprovement(x) = F(x) – max{F(p1),F(p2)}

• Max fitness plot; slope at generation i is s(gi)

Mate selection function evolution

• IF improvement(offspring)>s(gi-1)

– Copy first parent’s mate selection function (single parent inheritance)

• Otherwise– Recombine the two parents’ mate selection

functions using standard GP crossover(multi-parent inheritance)

– Apply a mutation chance to the offspring’s mate selection function

Experiments• Counting ones

• 4-bit deceptive trap– If 4 ones => fitness = 8– If 3 ones => fitness = 0– If 2ones => fitness = 1– If 1 one => fitness = 2– If 0 ones => fitness = 3

• SAT

Counting ones results

Highly evolved mate selection function

SAT results

4-bit deceptive trap results

SASADIPS shortcomings

• Steep fitness increase in the early generations may lead to premature convergence to suboptimal solutions

• Good mate selection functions hard to find

• Provided mate selection primitives may be insufficient to build a good mate selection function

• New parameters were introduced

• Only semi-autonomous

Greedy Population Sizing(GPS)

|P1| = 2|P0| …

|Pi+1| = 2|Pi|

The parameter-less GA

P0 P1 P2

Evolve an unbounded number of populations in parallel

Smaller populations are given more fitness evaluations

Fitn

ess

eval

s

Terminate smaller pop. whose avg. fitness is exceeded by a larger pop.

Greedy Population Sizing

P0 P1 P2 P3 P4 P5

F1

F2

F3

F4

Evolve exactly two populations in parallel

Equal number of fitness evals. per population

Fitness evals

GPS-EA vs. parameter-less GA

F1

F2

F3

F4

NN

F1

2F1

F2

2F2

F3

2F3

F4

2F4

2F1 + 2F2 + … + 2Fk + 3N

N

2N

F1 + F2 + … + Fk + 2N

N

Parameter-less GA

GPS-EA

GPS-EA vs. the parameter-less GA, OPS-EA and TGA

80

85

90

95

100

100 500 1000

problem size

MB

F%

of m

axim

um fi

tnes

s

OPS-EA GPS-EA

TGA parameter-less GA

80

85

90

95

100

100 500 1000

problem size

best

sol

utio

n fo

und

% o

f max

imum

fitn

ess

OPS-EA GPS-EATGA parameter-less GA

• GPS-EA < parameter-less GA• TGA < GPS-EA < OPS-EA

GPS-EA finds overall bettersolutions than parameter-less GA

Deceptive Problem

Limiting Cases

0

20

40

60

80

1 2 3 4 5 6 7 8 9 10 11

Fitness Evals

Avg

. P

op

. F

itn

ess

P3 P4

0

20

40

60

80

100

100 500 1000

problem size

% o

f ru

ns

limiting cases non-limiting cases

• Favg(Pi+1)<Favg(Pi)• No larger populations are created• No fitness improvements until termination

• Approx. 30% - limiting cases• Large std. dev., but lower MBF• Automatic detection of the limiting cases is needed

GPS-EA Summary

• Advantages– Automated population size control– Finds high quality solutions

• Problems– Limiting cases– Restart of evolution each time

Estimated Learning Offspring Optimizing

Mate Selection(ELOOMS)

Traditional Mate Selection

25 3 8 2 4 5

MATES

5 8

5 4

• t – tournament selection• t is user-specified

ELOOMS

NOYES YES MATESYES

NOYES

YES

Mate Acceptance Chance (MAC)

j How much do I like ?

k

b1 b2 b3 … bL

(1 )

1

(1 ) ( 1)( , )

i

Lb

i ii

b dMAC j k

L

d1 d2 d3 … dL

Desired Features

j

d1 d2 d3 … dL

# times past mates’ bi = 1 was used to produce fit offspring

# times past mates’ bi was used to produce offspring

b1 b2 b3 … bL

• Build a model of desired potential mate• Update the model for each encountered mate• Similar to Estimation of Distribution Algorithms

ELOOMS vs. TGA

L=500With Mutation

L=1000With Mutation

Easy Problem

ELOOMS vs. TGA

Without Mutation With Mutation

Deceptive ProblemL=100

Why ELOOMS works on Deceptive Problem

• More likely to preserve optimal structure

• 1111 0000 will equally like:– 1111 1000– 1111 1100– 1111 1110

• But will dislike individuals not of the form:– 1111 xxxx

Why ELOOMS does not work as well on Easy Problem

• High fitness – short distance to optimal

• Mating with high fitness individuals – closer to optimal offspring

• Fitness – good measure of good mate

• ELOOMS – approximate measure of good mate

ELOOMS computational overhead

• L – solution length

• μ – population size

• T – avg # mates evaluated per individual

• Update stage:– 6L additions

• Mate selection stage:– 2L*T* μ additions

ELOOMS Summary

• Advantages– Autonomous mate pairing– Improved performance (some cases)– Natural termination condition

• Disadvantages– Relies on competition selection pressure– Computational overhead can be significant

GPS-EA + ELOOMS Hybrid

Expiration of population Pi

• If Favg(Pi+1) > Favg(Pi)

– Limiting cases possible

• If no mate pairs in Pi (ELOOMS)

– Detection of the limiting cases

0

20

40

60

80

100

100 500 1000

problem size

% o

f ru

ns

limiting cases non-limiting cases

0

20

40

60

80

1 2 3 4 5 6 7 8 9 10 11

Fitness Evals

Avg

. P

op

. F

itn

ess

P3 P4

Comparing the Algorithms

Without Mutation With Mutation

Deceptive ProblemL=100

GPS-EA + ELOOMS vs. parameter-less GA and TGA

Without Mutation With MutationDeceptive Problem

L=100

GPS-EA + ELOOMS vs. parameter-less GA and TGA

Without Mutation With MutationEasy Problem

L=500

GPS-EA + ELOOMS Summary

• Advantages– No population size tuning– No parent selection pressure tuning– No limiting cases– Superior performance on deceptive problem

• Disadvantages– Reduced performance on easy problem– Relies on competition selection pressure

NC-LAB’s current AutoEA research• Make λ a dynamic derived variable by self-

adapting each individual’s desired offspring size• Promote “birth control” by penalizing fitness

based on “child support” and use fitness based survival selection

• Make μ a dynamic derived variable by giving each individual its own survival chance

• Make individuals mortal by having them age and making an individual’s survival chance dependent on its age as well as its fitness