Post on 12-Jan-2016
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Evolvability Analysis for Evolutionary Robotics
Sung-Bae Cho
Yonsei University, Korea
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Agenda
Motivation Analysis framework of evolution
– Adaptive evolution– Adaptive behaviors– Evolutionary pathways
Evolution of fuzzy logic controller Simulation results Summary
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Motivation
Chances
Innovative
functional
structures
Increased
complexity
Desirable EvolutionEvolutionary Phenomena
Necessity
Random genetic drift
Adaptivity
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Evolutionary Routes
Motivation
AdaptiveEvolution
HighEvolvability
LowEvolvability
Non-AdaptiveEvolution
GoodSolution
BadSolution
DesirableEvolutionary Causes
and Effects
High probability
Low probability
Emergence
AdaptiveBehavior
Can the same results be obtained? Adaptive evolution ( ) What properties are genetically preferred? Adaptive behaviors ( ) How the solutions are formed? Evolutionary pathways to the solutions ( ) Behavioral properties? Emergence ( )
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Analysis Framework of Evolution
EvolutionAnalysis
EvolutionaryActivity
Statistics
EvolutionaryActivity
Statistics
SchemaAnalysis
SchemaAnalysis
ObservationalEmergence
ObservationalEmergence
Analysis ofEvolution
AdaptiveEvolution
AdaptiveBehavior
Emergence
EvolutionaryPathways
BehaviorAnalysis
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Role of Analysis Components
Adaptive evolution– Does the evolving system maintains a good level of
evolvability, especially in a real-world problem?
Adaptive behavior– What properties make certain components more adaptive?
Evolutionary pathways– How the solutions have evolved, i.e., evolutionary pathways?
Application of the analysis framework to a real-world problem
Analysis Framework
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Definitions of Evolvability
The capacity to produce good solutions via evolution
Genome’s ability to produce adaptive variants when acted on by the genetic system (Wagner and Altenberg, 1996)
Capacity to generate heritable phenotypic variation (Kirshner and Gerhart, 1998)
Capacity to create new adaptations, and especially new kinds of adaptations, through the evolutionary process (Bedau and Packard, 1992)
Analysis Framework
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Evolvability Measures
Evolvability as the rate of complexity increase– By Chrystopher L. Nehaniv
– maxcpx gives the largest complexity of any entity at time t– The complexity of an entity is the least number of
hierarchically organized computing levels needed to construct an automata model of a target system
– Krohn-Rhodes algebraic automata theory and finite semigroup theory
Evolutionary activity statistics– By Mark A. Bedau
)()()( tmaxcpx1tmaxcpxtEv
Analysis Framework
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Evolutionary Activity Statistics (1)
Evolutionary activity– A counter, , of the ith component at time t
– Updated as the component persistsInherited with reproductionInitialized when the component changes, e.g. mutationUpdate function should be chosen carefully
according to the problems at hand
tk
ii kta )()(
)(tai
)(ki
Analysis Framework
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Evolutionary Activity Statistics (2)
Mean activity:
– D(t) is the number of component I at time t with ai(t)>0
– Represents continual adaptive success of components
New activity:
– is the number of components I with ai(t)>0
– Represents adaptive innovations flowing into the system
)(
)()(
tD
tatA i
i
cum
1
0
),()(
1)(
a
aanew atC
tDtA
),( atC
Analysis Framework
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Evolutionary Activity Statistics (3)
Need to measure evolvability in two models– Target model– Shadow model
To screen off non adaptive evolutionary forces
Analysis Framework
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Schema Analysis
Definition (Holland, 1968)– A similarity template that designates a set of chromosomes
having same alleles at certain loci Consists of a set of characters and don’t-cares Example
– Character set = {0,1}, don’t care=#– #0000 {10000, 00000}– #111# {01110, 01111, 11110, 11111}
Adaptive schema = the size of the set that this schema describes increases
Analysis Framework
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Observational Emergence
Emergence– “creation of new properties” – Morgan, C.L., Emergent
Evolution, Williams and Norgate, 1923
Observational emergence– Proposed by N.A. Bass, 1992
S : structure (system, organization, organism, machine, …)
P : property observed by observational mechanism, Obs
Analysis Framework
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Fuzzy Logic Controller for Mobile Robot
Evolution of Fuzzy Logic Controller
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FLC Parameters for Khepera Robot
Input variables : 8 proximity sensors of Khepera mobile robot Output variables : 2 motors of Khepera mobile robot
Linguistic values of fuzzy sets
Membership function of fuzzy sets
Evolution of Fuzzy Logic Controller
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Gene Encoding of FLC
• 8 proximity sensors
• 2 motors
8 INPUT 2 OUTPUT 20 RULES
Gene representation
for an individual
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
VF F M C VC
Encoding of a membership function
of a variable
00 40 31 21 0 41
d0 d1 d2 d3 d4 d5 d6 d7 v0 v1
21 01 30 10
1 2
variable toggle flag
rule toggle flag
1 conditional part
2 consequent part
Decoding of a rule
Evolution of Fuzzy Logic Controller
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Experimental Setup
Population size : 50 Maximum generation : 1000 Overlapped population by 50% with elitism Crossover rate : 0.5 Mutation rate : 0.01
Evolutionary activity
Measuring evolvability in two models– Target model– Neutral shadow : no selective pressure
To screen off non adaptive evolutionary forces
otherwise0
tatexistsigenotypeif)()( 0
t
ii
dttnta
Simulation Results
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Adaptive Evolution
0 200 400 600 800 10000
0.5
1
1.5
2
2.5
3
3.5x 10
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Generation
To
tal A
ctiv
ity
Fuzzy Model Neutral Shadow
0 200 400 600 800 10000
0.02
0.04
0.06
0.08
0.1
0.12
Generation
Ne
w A
ctiv
ity
Fuzzy Model Neutral Shadow
Evolutionary activity
Mean activity
New activity
tk
ii kta )()(
)(
)()(
tD
tatA i
i
cum
1
0
),()(
1)(
a
anew atC
tDtA
Simulation Results
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Adaptive Behavior
Salient Rules
0 100 200 300 400 500 600 700 800 900 10000
1000
2000
3000
4000
5000
6000
Generation
Act
ivat
ion
SR1 SR
2
SR3
SR4
SR7
SR6
SR5
SR8
SR9
SR10
SR12
SR
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Simulation Results
With SR2 Without SR2 With SR8 Without SR8 With SR10 Without SR10
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Schema Analysis
0 100 200 300 400 500 600 700 800 900 10000
1000
2000
3000
4000
5000
6000
Generation
Activa
tion
SR1 SR
2
SR3
SR4
SR7
SR6
SR5
SR8
SR9
SR10
SR12
SR
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Best Individual
Salient Rules
Simulation Results: Evolutionary Pathways
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Rule B2 and B7
S{1} S{4}B{2}
Activities of instances of
schemata S{1}, S{4}, and B{2}
Activities of instances of
schemata S{6} and B{7}
S{6} B{7}
Simulation Results: Evolutionary Pathways
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Parameters of Emergence
Simulation Results: Observational Emergence
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Turning Around
First-order structures Three Obs1s of first-order structures
Int
A Obs2 of a second-order structure S2
• The property observed by Obs2 of S2 constructed through the interactions of three first-order structures is quite different from the properties observed by Obs1( ),
By the definition of observational emergence
Turning around behavior (Obs2(S2)) is observationally emergent
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12 111
,, SSS1
1iS }7,5,2{i
Simulation Results: Observational Emergence
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Smooth Cornering
Int
First-order structures Two Obs1s of the first-order structures
A Obs2 of a second-order structure S2
• The property observed by Obs2 of S2 constructed through the interactions of the two first-order structures is quite different from the properties observed by Obs1( ),
By the definition of observational emergence
Smooth cornering behavior (Obs2(S2)) is observationally emergent
1
1iS }5,2{i
17
12 11,SS
Simulation Results: Observational Emergence
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Summary
Application of evolvability measure to a real-world problem
Illustration of evolutionary pathways to the best individual
The evolvability measure shows that the performance of the best individual is the results of its rules’ adaptability
Schema analysis shows that most of the rules of the best individual are the combination of the rules of earlier stage of evolution