CGP Visits the Santa Fe Trail – Effects of Heuristics on GP

1. CGP Visits the Santa Fe Trail – Effects of Heuristics on GP Cezary Z. Janikow Christopher J MannUMSL

2. Roadmap • GP • GP Search Space • Local heuristics • CGP • Heuristics in SantaFe Trail • Function/Terminal set • Structural • Combination • Generality • Probabilistic heuristics • Summary

3. GP Search Space • Best mappings • One-to-one, onto • Real life • Large function/terminal set • Redundancy • Many-to-one • Can domain-specific knowledge improve GP performance? • Can we learn some domain-specific knowledge from GP?

4. GP Search Space • 2-D space • Tree structures • constrained by size limits and function arity • Tree instances of specific structures • constrained by domain sizes

5. Pruning/Constraining GP Search Space • Tree structures • Hard to accomplish directly w/o instantiations • Indirect by adjusting possible instantiations • Tree instances • Strong constraints • prohibit some instantiations (labelings) • Structure-preserving cross, STGP, CGP, CFG-GP • Weak probabilistic constraints • favor some instantiations over others • CGP, Probabilistic Tree Grammars

6. GP Design • GP only explores a well defined subspace of the potential search space • Later generations search smaller subspaces • Initial choice of the root node has significant impact on search and final solution • Called the GP Design • Daida, Langdon, Hall and Soule • Heuristics can alter the design and redirect later generations toward specific subspaces • Conversely, observing the designs tells us about problem-specific heuristics - ACGP

7. CGP Principles What heuristics/constraints can be processed

8. CGP Principles • Strong input constraints • Prune the search space in such a way that valid parent(s) guarantee valid offspring • Start with valid initialization • Weak probabilistic constraints • Adjust probabilities of specific mutations/crossovers • Only local heusristics • Both with minimal linear overhead

9. GP with Strong and Weak Constraints Pruned non-uniform distribution Mutation/Crossover Pi Pi+1 Reproduction Probabilistic Grammars, CGP, EDA

10. CGP Means of Processing • Strong constraints • Explicit structures and by data typing • Overloaded functions on types • Weak constraints

11. CGP Means of Processing • Explicit labeling constraints • First order only • Parent-child • Can be with probability • Data typing constraints • Propagated through overloaded functions • This links first-order information

12. / + 2 x sin a CGP Mutation / + 2 x * c 3

13. + 2 + y 4 / + 2 / x sin + + + 2 2 a x sin y 4 a GP Crossover

14. SantaFe Experiments Problem Function set Heuristics exploration Generality of the heuristics Comparing vs. ACGP’s probabilistic heuristics (on performance)

15. SantaFe Problem 32x32 grid Food trail, 144 cells long, with 21 turns and 89 pieces of food Start northwest corner of the grid facing east Fitness is the number of food pieces consumed in up to 400 moves

16. SantaFe Functions/Terminals Terminals turn left, right, move action Functions if-food-ahead test the position directly ahead for food, and if true perform the first action, otherwise perform the second action progn2, progn3 take two and three arguments, respectively, and execute them sequentially.

17. Experimental Methodology Analyze and propose heuristics Reducing function set Constraining root and local structures Combing the above Assess heuristics using 10 independent runs Learning curves – average of best Efficiency – average tree size in populations

18. Reducing Function Set: Basics, Quality

19. Reducing Function Set: Basics, Efficiency

20. Reducing Function Set: Combined, Quality

21. Reducing Function Set: Combined, Efficiency

22. Constraining Root and Local Structure: Basics, Quality

23. Constraining Root and Local Structure: Basics,Efficiency

24. Constraining Root and Local Structure: Combined, Quality

25. Constraining Root and Local Structure: Combined, Efficiency

26. Combined Function Set and Structural Heuristics: Quality

27. Combined Function Set and Structural Heuristics: Efficiency

28. More Combined Heuristics: Quality

29. More Combined Heuristics: Quality

30. Best Heuristics by Inspection Analyze best trees constrain progn2 and progn3 so that neither can call neither (P!P2!P3) constrain root to always test for food (ifroot) constrain if-food-ahead to always move first if there is food ahead (if0m), while disallowing testing for food again if there is no food ahead (if1!if). Best heuristics even though individual components were not best

31. Best Heuristics by Inspection: Quality (vs. components)

32. Best Heuristics by Inspection: Efficiency (vs. components)

33. Best Heuristics Summary: Quality

34. Best Heuristics Summary: Efficiency

35. Best Shortest Solution (if-food-ahead move (progn3 right (if-food-ahead move (progn3 left left (if-food-ahead move right))) move))

36. Testing Slightly Different Trails: Same Basic Primitives

37. Testing Different Trails: Similar Basic Primitives

38. Learning Probabilistic Heuristics with ACGP

39. Comparing Probabilistic Heuristics vs. Strong

40. Summary 1 • Heuristics improve GP search • Learning curve improves • Learning complexity improves • Timing improves because if low overhead • Complex heuristics may be better even if their components are not very good • Good components do not guarantee better combination

41. Summary 2 • Probabilistic heuristics can easily outperform strong heuristics • But may be less comprehensible if information sought • Heuristics are specific to a problem • Help on similar problems • More specific are less less generalizing • Conversely, learning heuristics may tell us about domain knowledge