1. Evolutionary Robotics The Genotype-to-Phenotype Map The genotype to phenotype map: the algorithm that transforms the genotype into the phenotype. Direct mapping: Each element in the genotype code for one element in the phenotype. Indirect mapping: Each element in the genotype codes for, or influences, zero or more elements in the phenotype. [0.8, 1.0, -0.9, …, -0.2] 0.8 -0.2

2. Evolutionary Robotics The Genotype-to-Phenotype Map Indirect mapping: Each element in the genotype codes for, or influences, zero or more elements in the phenotype. Q: How would you encode an indirect mapping for this robot? What are the different symmetries here that may be important? What if the robot is evaluated with different numbers of segments? …

3. Evolutionary Robotics The Genotype-to-Phenotype Map More biologically realistic. Example: Genetic Regulatory Networks Bongard, J. C. and R. Pfeifer (2001) Repeated Structure and Dissociation of Genotypic and Phenotypic Complexity in Artificial Ontogeny, in Proceedings of The Genetic and Evolutionary Computation Conference, GECCO-2001. pp. 829-836.

5. The growing robot body and brain The genome, a copy of which resides in each morphological unit Transcription factors, produced by genes contained in the genome, diffuse through the robot's body, causing phenotypic change Evolutionary Robotics

6. The genome, a copy of which resides in each morphological unit Evolutionary Robotics ABC If gene A is on, It tries to turn gene C on: gene A “enhances” gene C. If gene B is on, It tries to turn gene C off: gene A “represses” gene B.

7. Evolutionary Robotics

8. Evolved neural circuits

9. An evolved genetic regulatory network Regulatory gene Targetted regulatory gene Structural gene affecting morphogenesis Structural gene affecting neurogenesis

10. 2 2 1 1 Evolutionary Robotics Phenotypes (here, robots) can become more complex without the genome growing too large: developmental encodings can be more scalable than direct encodings.

11. Evolutionary Robotics Genotype to phenotype encodings should be… (they can encode phenotypes of increasing complexity) (they can alter many aspects of the phenotype such as body plan, neural architecture and neural parameters) (beneficial mutations are produced with a probability > 0 ), but pleiotropy (one gene can affect several phenotypic characters) can negatively affect evolvability:

12. Evolutionary Robotics Genotype to phenotype encodings should be… evolvable (beneficial mutations are produced with a probability > 0 ), but pleiotropy (one gene can affect several phenotypic characters) can negatively affect evolvability: Modular mapping Non-modular mapping G1,G2,…G6 = genes 1 through 6 P1,P2,P3,P4 = Phenotypic characters (eg. P1=CTRNN taus, P2=CTRNN weights) C1,C2 = Phenotypic complexes (C1=CTRNN for locomotion, C2=CTRNN for grasping) F1,F2 = functions (eg. F1=locomotion, F2=grasping)

13. Evolutionary Robotics G1,G2,…G6 = genes 1 through 6 P1,P2,P3,P4 = Phenotypic characters (eg. P1=CTRNN taus, P2=CTRNN weights) C1,C2 = Phenotypic complexes (C1=CTRNN for locomotion, C2=CTRNN for grasping) F1,F2 = functions (eg. F1=locomotion, F2=grasping)

14. Evolutionary Robotics Research questions: What kinds of evolutionary pressures will cause a genotype-to-phenotype mapping to become more (or less) modular? How to create genotype-to-phenotype maps that are compact, expressive and evolvable? If an encoding is compact, expressive and evolvable for one fitness function, will the same encoding be so for another fitness function?