1 Evolvability Analysis for Evolutionary Robotics Sung-Bae Cho Yonsei University, Korea

2 Agenda l Motivation l Analysis framework of evolution –Adaptive evolution –Adaptive behaviors –Evolutionary pathways l Evolution of fuzzy logic controller l Simulation results l Summary

3 Motivation Chances Innovative functional structures Increased complexity Desirable EvolutionEvolutionary Phenomena Necessity Random genetic drift Adaptivity

4 Evolutionary Routes Motivation l Can the same results be obtained?  Adaptive evolution ( ) l What properties are genetically preferred?  Adaptive behaviors ( ) l How the solutions are formed?  Evolutionary pathways to the solutions ( ) l Behavioral properties?  Emergence ( )

5 Analysis Framework of Evolution

6 Role of Analysis Components l Adaptive evolution –Does the evolving system maintains a good level of evolvability, especially in a real-world problem? l Adaptive behavior –What properties make certain components more adaptive? l Evolutionary pathways –How the solutions have evolved, i.e., evolutionary pathways? Application of the analysis framework to a real-world problem Analysis Framework

7 Definitions of Evolvability l The capacity to produce good solutions via evolution l Genome’s ability to produce adaptive variants when acted on by the genetic system (Wagner and Altenberg, 1996) l Capacity to generate heritable phenotypic variation (Kirshner and Gerhart, 1998) l Capacity to create new adaptations, and especially new kinds of adaptations, through the evolutionary process (Bedau and Packard, 1992) Analysis Framework

8 Evolvability Measures l 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 l Evolutionary activity statistics –By Mark A. Bedau Analysis Framework

9 Evolutionary Activity Statistics (1) l Evolutionary activity –A counter,, of the ith component at time t –Updated as the component persists Inherited with reproduction Initialized when the component changes, e.g. mutation Update function should be chosen carefully according to the problems at hand Analysis Framework

10 Evolutionary Activity Statistics (2) l Mean activity: –D(t) is the number of component I at time t with a i (t)>0 –Represents continual adaptive success of components l New activity: – is the number of components I with a i (t)>0 –Represents adaptive innovations flowing into the system Analysis Framework

11 Evolutionary Activity Statistics (3) l Need to measure evolvability in two models –Target model –Shadow model To screen off non adaptive evolutionary forces Analysis Framework

12 Schema Analysis l Definition (Holland, 1968) –A similarity template that designates a set of chromosomes having same alleles at certain loci l Consists of a set of characters and don’t-cares l Example –Character set = {0,1}, don’t care=# –#0000  {10000, 00000} –#111#  {01110, 01111, 11110, 11111} l Adaptive schema = the size of the set that this schema describes increases Analysis Framework

13 Observational Emergence l Emergence –“creation of new properties” – Morgan, C.L., Emergent Evolution, Williams and Norgate, 1923 l Observational emergence –Proposed by N.A. Bass, 1992 S : structure (system, organization, organism, machine, …) P : property observed by observational mechanism, Obs Analysis Framework

14 Fuzzy Logic Controller for Mobile Robot Evolution of Fuzzy Logic Controller

15 FLC Parameters for Khepera Robot l Input variables : 8 proximity sensors of Khepera mobile robot l Output variables : 2 motors of Khepera mobile robot l Linguistic values of fuzzy sets l Membership function of fuzzy sets Evolution of Fuzzy Logic Controller

16 Gene Encoding of FLC 8 proximity sensors 2 motors Gene representation for an individual Encoding of a membership function of a variable Decoding of a rule Evolution of Fuzzy Logic Controller

17 Experimental Setup l Population size : 50 l Maximum generation : 1000 l Overlapped population by 50% with elitism l Crossover rate : 0.5 l Mutation rate : 0.01 l Evolutionary activity l Measuring evolvability in two models –Target model –Neutral shadow : no selective pressure To screen off non adaptive evolutionary forces Simulation Results

18 Adaptive Evolution Evolutionary activity Mean activity New activity Simulation Results

19 Adaptive Behavior Salient Rules Simulation Results With SR 2 Without SR 2 With SR 8 Without SR 8 With SR 10 Without SR 10

20 Schema Analysis Best Individual Salient Rules Simulation Results: Evolutionary Pathways

21 Rule B 2 and B 7 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

22 Parameters of Emergence Simulation Results: Observational Emergence

23 Turning Around First-order structuresThree Obs 1 s of first- order structures Int A Obs 2 of a second-order structure S 2 The property observed by Obs 2 of S2 constructed through the interactions of three first-order structures is quite different from the properties observed by Obs 1 ( ), l By the definition of observational emergence l Turning around behavior (Obs 2 (S 2 )) is observationally emergent Simulation Results: Observational Emergence

24 Smooth Cornering Int First-order structuresTwo Obs 1 s of the first-order structures A Obs 2 of a second-order structure S2 The property observed by Obs 2 of S2 constructed through the interactions of the two first-order structures is quite different from the properties observed by Obs 1 ( ), l By the definition of observational emergence l Smooth cornering behavior (Obs 2 (S 2 )) is observationally emergent Simulation Results: Observational Emergence

25 Summary l Application of evolvability measure to a real-world problem l Illustration of evolutionary pathways to the best individual l The evolvability measure shows that the performance of the best individual is the results of its rules’ adaptability l Schema analysis shows that most of the rules of the best individual are the combination of the rules of earlier stage of evolution