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CGP Visits the Santa Fe Trail – Effects of Heuristics on GP. Cezary Z. Janikow Christopher J Mann UMSL. Roadmap. GP GP Search Space Local heuristics CGP Heuristics in SantaFe Trail Function/Terminal set Structural Combination Generality Probabilistic heuristics Summary.

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

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

Cezary Z. Janikow

Christopher J MannUMSL


  • GP

    • GP Search Space

    • Local heuristics

  • CGP

  • Heuristics in SantaFe Trail

    • Function/Terminal set

    • Structural

    • Combination

    • Generality

    • Probabilistic heuristics

  • Summary

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?

GP Search Space

  • 2-D space

    • Tree structures

      • constrained by size limits and function arity

    • Tree instances of specific structures

      • constrained by domain sizes

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

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



What heuristics/constraints can be processed

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

GP with Strong and Weak Constraints

Pruned non-uniform






Probabilistic Grammars, CGP, EDA

CGP Means of Processing

  • Strong constraints

    • Explicit structures and by data typing

  • Overloaded functions on types

  • Weak constraints

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







CGP Mutation






























GP Crossover

SantaFe Experiments


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


turn left, right, move action



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

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

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

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

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