2. Adapting Representation in Genetic Programming Cezary Z. Janikow UMSL Work partly done at NASA/JSC

3. Page 2 Roadmap Search Space and Redundant Representations Constrained GP CGP Technology Adaptable CGPACGP ACGP1.1.1 methodology Some results ACGP2.1 (NEW), future

4. Page 3 GP Search Space Best mappings One-to-one Onto Real life Redundant Many-to-one Work done on redundant space in GA supports Overrepresentation of the best solutions “Closeness” of genotype and phenotype

5. Page 4 GP Search Space 2-dim space –Tree structures constrained by size limits and function arity –Tree instances of specific structures constrained by domain sizes

6. Page 5 Real Life Mappings Allow all (help by closure) Strong pruning Explicit Structure-preserving cross, STGP, CGP, CFG-GP Weak (probabilistic) pruning Implicit: Evolution itself Penalty (explicit on phenotype) Explicit Non-uniform mutation/cross: CGP, ACGP

7. Page 6 GP Crossover – strong vs. weak pruning (non-uniform) / + sin a x 2 + 2 y + 4 / + a xy + 4 2 + 2

8. Page 7 GP Mutation – strong vs. weak pruning / + sin a x 2 / + * c x 2 3

9. Page 8 GP at work Reproduction Mutation/Crossover PiPi P i+1 Unpruned uniform distribution

10. Page 9 Typed GP at work CFG-based, STGP, -GP, CGP, Structure-Preserving Crossover Reproduction Mutation/Crossover PiPi P i+1 Pruned uniform distribution

11. Page 10 CGP: explicit strong and explicit weak pruning Reproduction Mutation/Crossover PiPi P i+1 Pruned non-uniform distribution CSL

12. Page 11 ACGP: strong and weak pruning, adaptable Reproduction Mutation/Crossover PiPi P i+1 Pruned non-uniform distribution CSL

13. CGP Constrained Genetic Programming Principles Technology Examples

14. Page 13 Why CGP? Existing technology for ACGP as is –Efficient existing technology allowing input and processing of strong constraints and weak heuristics –Implemented into lil-gp But no need to couple

15. Page 14 CGP Principles Constraining GP to search only within desired space Constraining options –Strong FT constraints –Strong Data typing –Weak Heuristics –probabilistic (think of shades) pruning

16. Page 15 CGP Current Capabilities Local heuristics and constraints –On specific labels –On data types –Overloaded (polymorphic) functions –Weighted heuristics

17. ACGP - Adaptable CGP Application context Principles ACGP at work Example of Heuristics Results V1.1.1 vs. near-future v2.1 vs. far-future

18. Page 17 ACGP Application Context Learn heuristics off-line to –Knowledge discovery –Solve better next time –Solve harder problem next time –Create a library of heuristics –Most results shown here Learn heuristics on-line during problem solving –hBOA –Some results here

19. Page 18 ACGP Principles Adjust the heuristics changing the probability distribution –Measure utility in mutation/crossover Immediate impact but –Bucket Brigade problem in mutation –modest improvements –Observe applications to surviving chromosomes –Co-evolution Solutions vs. library of heuristics –Observe distribution of local heuristics current ACGP, reported here, better improvements

20. Page 19 ACGP Meta-Loop

21. Page 20 ACGP Iterations

22. Page 21 CGP1.1 and ACGP1.1.1 Heursitics Current node info retained in CGP1.1 tree Current heuristics in ACGP1.1.1 –Updates heuristics at different schedules –Uses info on expressed genes –Could go to deeper heuristics

23. Page 22 ACGP Experiment Domain 11-Multiplexer –3 addresses –8 data bits –pass through one data bit GP settings functions: if/else, and, or, not terminals: addresses and data

24. Page 23 Previously Identified Heuristics DNF or sufficient set (e.g., {and, not}) –No if only is best –if-arg1 {addresses,not} –if-arg2/3 {if,data} –Yes –Improvements Evolution speed Learning speed

25. Page 24 ACGP Multiplexer Results Change in local heuristics distribution –Current distribution vs. reference Distribution: whole population vs. best samples Reference: first generation vs. previous Change in speed of evolution –Current fitness and number of iterations needed Evolved heuristics –Quantitative and qualitative

26. Page 25 Two ACGP Settings 1.Off-line Iteration = 25 generations Can we learn to improve next time? Can we comprehend knowledge? 2.In-line, in-between –Iteration = 1, 5, 10 generation –Impact of regrow –Impact on population size

27. Page 26 Change in First-order Heuristics Distribution Experiment: –Distribution whole and best –Reference first generation –Average of 5 independent runs on single population Note saturation –just vs. first generation reference or the same vs. previous generation?

28. Page 27 Change in First-order Heuristics Distribution Experiment: –Distribution whole and best –Reference previous generation

29. Page 28 Change in Speed of Evolution Experiment: –simultaneous 5 populations average shown –adjust every 25 generations –regrow on –update schedule incremental change in heuristics Can we be more greedy in heuristics? – can we increase updates to replacements?

30. Page 29 Change in Speed of Evolution Experiment: –simultaneous 5 populations average shown –regrow on –replacement schedule Is it really so much faster and better? Note <100%

31. Page 30 Change in First-order Heuristics Experiment: –simultaneous 5 populations average shown –Slow update schedule –Distribution whole population –Reference first generation on iteration Note saturation –learning has saturated

32. Page 31 The Evolved First-order Heuristics Experiment: –simultaneous 5 populations best population shown –slow update schedule –if condition argument Expected yet strange –only a 0, a 1, a 2, not –a 0 high –a 2 low but present –a 1 missing!!! –Note shift in heuristics

33. Page 32 The Evolved First-order Heuristics on not Experiment: –simultaneous 5 populations best population shown –slow update schedule –not argument Mystery solved –a 1 found high –a 2 low additional support –non-recursive

34. Page 33 The Evolved First-order Heuristics on action arguments of if Experiment: –simultaneous 5 populations best population shown –slow update schedule –if action arguments combined Expected –if high to grow needed deep conditions –data present –others missing

35. Page 34 Iteration Length and Regrow

36. Page 35 Iteration Length and Regrow

37. Page 36 Iteration Length and Regrow

38. Page 37 Iteration Length and Regrow

39. Page 38 Population Size Iteration =1, no regrow

40. Page 39 Scalability Library or off-line (long iterations) Working in the same domain Working toward harder problems Mult-11 -> Mult-20 Reusability of first-order heuristics Lack of some first-order heuristics Types will help On-line (iteration=generation) Good for solving new problem in a new domain

41. Page 40 Another Domain – SantaFe Trail Interesting and good heuristics evolved But Some are good independently but not as a group Others bad independently but good as a group Competition between heuristics classes

42. Page 41 Current work: ACGP2.1 CGP2.1 node information ACGP2.1 extracted heuristics

43. Page 42 ACGP2.1 Heuristics On what: Type Functions/Terminals Combination What kind: Zero-order First-order Second order

44. Page 43 ACGP2.1 Heuristics: Type First-order on Type For each type, what type can produce it but each argument individually

45. Page 44 ACGP2.1 Heuristics: Type Second-order on Type For each type, what can produce it as a family Note growing complexity

46. Page 45 ACGP2.1 Heuristics: Labels First-order on Labels For each function, what can label each child individually The only one in ACGP1.1.1

47. Page 46 ACGP2.1 Heuristics: Labels Second-order on Labels For each function, what can label the family Note the growing complexity

48. Page 47 ACGP2.1 Heuristics: Combined Zero-order combined For each type, what labels (same node) produce it

49. Page 48 ACGP2.1 Heuristics: Combined Zero-order combined For each function, what types it produces (same node) Terminals are not overloaded

50. Page 49 ACGP2.1 Heuristics: Combined First-order combined For each function, and each type it needs to produce, what instances do that

51. Page 50 ACGP2.1 Heuristics: Combined First-order combined This one really links three levels Second order would be very complex here

52. Page 51 Proposed Future Work ACGP2.1 Use the heuristics and assess usefulness Higher order heuristics Explicit or propagated To lower the complexity, explore only those promising heuristics Link with population size Scalability Co-evolution Library

53. Page 52 Thank you ?