symposium “new directions in evolutionary computation” dr. daniel tauritz director, natural...
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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
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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
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EA Operators
• Parent selection, mate pairing
• Recombination
• Mutation
• Survival selection
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EA Parameters
• Population size• Initialization related parameters• Parent selection parameters• Number of offspring• Recombination parameters• Mutation parameters• Survivor selection parameters• Termination related parameters
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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
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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
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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
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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)
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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
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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
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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
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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
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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
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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
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NC-LAB Vision for a New Direction in Parameterless EAs:
Autonomous EAs (AutoEAs)
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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!
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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
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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
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Self-Adaptive Semi-Autonomous Parent Selection (SASAPAS)
• Each individual has an evolving mate selection function
• Two ways to pair individuals:– Democratic approach– Dictatorial approach
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Democratic Approach
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Democratic Approach
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Dictatorial Approach
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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
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Mate selection function representation
• Expression tree as in GP
• Set of primitives – pre-built selection methods
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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)
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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
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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
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Counting ones results
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Highly evolved mate selection function
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SAT results
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4-bit deceptive trap results
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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
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Greedy Population Sizing(GPS)
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|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.
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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
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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
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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
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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
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GPS-EA Summary
• Advantages– Automated population size control– Finds high quality solutions
• Problems– Limiting cases– Restart of evolution each time
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Estimated Learning Offspring Optimizing
Mate Selection(ELOOMS)
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Traditional Mate Selection
25 3 8 2 4 5
MATES
5 8
5 4
• t – tournament selection• t is user-specified
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ELOOMS
NOYES YES MATESYES
NOYES
YES
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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
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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
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ELOOMS vs. TGA
L=500With Mutation
L=1000With Mutation
Easy Problem
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ELOOMS vs. TGA
Without Mutation With Mutation
Deceptive ProblemL=100
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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
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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
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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
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ELOOMS Summary
• Advantages– Autonomous mate pairing– Improved performance (some cases)– Natural termination condition
• Disadvantages– Relies on competition selection pressure– Computational overhead can be significant
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GPS-EA + ELOOMS Hybrid
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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
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Comparing the Algorithms
Without Mutation With Mutation
Deceptive ProblemL=100
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GPS-EA + ELOOMS vs. parameter-less GA and TGA
Without Mutation With MutationDeceptive Problem
L=100
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GPS-EA + ELOOMS vs. parameter-less GA and TGA
Without Mutation With MutationEasy Problem
L=500
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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
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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