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

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

Page 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?

Page 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

Page 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

Page 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

CGP Principles What heuristics/constraints can be processed

Page 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

Page 9 GP with Strong and Weak Constraints Reproduction Mutation/Crossover PiPi P i+1 Pruned non-uniform distribution Probabilistic Grammars, CGP, EDA

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

Page 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

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

Page 13 GP Crossover / + sin a x y + 4 / + a xy

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

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

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.

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

Reducing Function Set: Basics, Quality

Reducing Function Set: Basics, Efficiency

Reducing Function Set: Combined, Quality

Reducing Function Set: Combined, Efficiency

Constraining Root and Local Structure: Basics, Quality

Constraining Root and Local Structure: Basics,Efficiency

Constraining Root and Local Structure: Combined, Quality

Constraining Root and Local Structure: Combined, Efficiency

Combined Function Set and Structural Heuristics: Quality

Combined Function Set and Structural Heuristics: Efficiency

More Combined Heuristics: Quality

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

Best Heuristics by Inspection: Quality (vs. components)

Best Heuristics by Inspection: Efficiency (vs. components)

Best Heuristics Summary: Quality

Best Heuristics Summary: Efficiency

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

Testing Slightly Different Trails: Same Basic Primitives

Testing Different Trails: Similar Basic Primitives

Learning Probabilistic Heuristics with ACGP

Comparing Probabilistic Heuristics vs. Strong

Page 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

Page 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