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Evolvability Analysis for Evolutionary Robotics Sung-Bae Cho Yonsei University, Korea 1 Agenda Motivation Analysis framework of evolution – Adaptive evolution – Adaptive behaviors – Evolutionary pathways Evolution of fuzzy logic controller Simulation results Summary 2 Motivation Evolutionary Phenomena Desirable Evolution Chances Innovative functional structures Necessity Random genetic drift Adaptivity 3 Increased complexity Motivation Evolutionary Routes Can the same results be obtained? Adaptive evolution ( 1 ) What properties are genetically preferred? Adaptive behaviors ( 2 ) How the solutions are formed? Evolutionary pathways to the solutions ( Behavioral properties? Emergence ( 4 ) Emergence 4 Desirable Evolutionary Causes and Effects Low probability 3 Good Solution 1 High Evolvability NonAdaptive Evolution Adaptive Evolution 2 Adaptive Behavior High probability Bad Solution 4 Low Evolvability 3 ) Analysis Framework of Evolution 5 Analysis Framework Role of Analysis Components Application of the analysis framework to a real-world problem 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? 6 Analysis Framework 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) 7 Analysis Framework Evolvability Measures Evolvability as the rate of complexity increase – By Chrystopher L. Nehaniv Ev(t ) maxcpx(t 1) maxcpx(t ) – 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 8 Analysis Framework Evolutionary Activity Statistics (1) Evolutionary activity – A counter, ai (t ), of the ith component at time t ai (t ) i (k ) k t – Updated as the component persists Inherited with reproduction Initialized when the component changes, e.g. mutation Update function i (k ) should be chosen carefully according to the problems at hand 9 Analysis Framework Evolutionary Activity Statistics (2) Mean activity: Acum (t ) a (t ) i i D(t ) – D(t) is the number of component I at time t with ai(t)>0 – Represents continual adaptive success of components 1 a1 C (t , a ) New activity: Anew (t ) D(t ) a a0 – C (t , a ) is the number of components I with ai(t)>0 – Represents adaptive innovations flowing into the system 10 Analysis Framework Evolutionary Activity Statistics (3) Need to measure evolvability in two models – Target model – Shadow model To screen off non adaptive evolutionary forces 11 Analysis Framework 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 12 Analysis Framework 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 13 Evolution of Fuzzy Logic Controller Fuzzy Logic Controller for Mobile Robot 14 Evolution of Fuzzy Logic Controller 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 15 Evolution of Fuzzy Logic Controller Gene Encoding of FLC Gene representation for an individual 8 INPUT • 8 proximity sensors • 2 motors VF F M 2 OUTPUT d0 1 C 1 d1 2 1 d2 0 0 d3 3 0 d4 1 0 2 3 4 5 6 7 8 d5 0 0 d6 4 1 d7 3 1 1 VC variable toggle flag rule toggle flag 1 20 RULES v0 v1 2 0 4 2 1 conditional part 2 consequent part 9 10 11 12 13 14 15 16 17 18 19 Decoding of a rule Encoding of a membership function of a variable 16 Simulation Results Experimental Setup Population size : 50 Maximum generation : 1000 Overlapped population by 50% with elitism Crossover rate : 0.5 Mutation rate : 0.01 t n (t )dt if genotype i exists at t Evolutionary activity ai (t ) 0 i 0 otherwise Measuring evolvability in two models – Target model – Neutral shadow : no selective pressure To screen off non adaptive evolutionary forces 17 Simulation Results Adaptive Evolution Evolutionary activity ai (t ) i (k ) k t Mean activity Acum (t ) 3.5 a (t ) New activity i i 1 a1 Anew (t ) C (t , a) D(t ) a0 D(t ) x 10 4 0.12 3 0.1 2 New Activity Total Activity 2.5 Fuzzy Model Neutral Shadow 1.5 1 0.08 0.06 0.04 0.02 0.5 0 0 Fuzzy Model Neutral Shadow 200 400 600 Generation 800 1000 18 0 0 200 400 600 Generation 800 1000 Simulation Results Adaptive Behavior Salient Rules 6000 SR9 5000 SR7 Activation 4000 SR3 SR4 3000 SR1 2000 SR2 SR6 SR8 SR12 SR11 SR5 1000 SR10 0 With SR2 0 100 Without SR2 200 300 400 With SR8 500 Generation 600 19 Without 700 SR8 800 900 1000 With SR10 Without SR10 Simulation Results: Evolutionary Pathways Schema Analysis Salient Rules 6000 SR9 5000 SR7 Activation 4000 SR3 3000 SR1 2000 SR2 SR4 SR6 SR8 SR12 SR11 SR5 1000 SR10 0 0 100 200 300 400 500 600 Generation 700 800 900 1000 Best Individual 20 Simulation Results: Evolutionary Pathways Rule B2 and B7 Activities of instances of schemata S{1}, S{4}, and B{2} S{1} S{4}B{2} Activities of instances of schemata S{6} and B{7} 21 S{6} B{7} Simulation Results: Observational Emergence Parameters of Emergence 22 Simulation Results: Observational Emergence Turning Around Int Three Obs1s of firstorder structures First-order structures • A Obs2 of a second-order structure S2 The property observed by Obs2 of S2 constructed through the interactions of three first-order structures S211 , S511 , S711 is quite different from the properties observed by Obs1( Si1), i {2,5,7} 1 By the definition of observational emergence Turning around behavior (Obs2(S2)) is observationally emergent 23 Simulation Results: Observational Emergence Smooth Cornering Int Two Obs1s of the first-order structures First-order structures • A Obs2 of a second-order structure S2 The property observed by Obs2 of S2 constructed through the interactions 1 1 of the two first-order structures S21 , S71 is quite different from the properties observed by Obs1( Si1), i {2,5} 1 By the definition of observational emergence Smooth cornering behavior (Obs2(S2)) is observationally emergent 24 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 25