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 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

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

Cezary Z. Janikow

Christopher J MannUMSL


Roadmap

Roadmap

  • GP

    • GP Search Space

    • Local heuristics

  • CGP

  • Heuristics in SantaFe Trail

    • Function/Terminal set

    • Structural

    • Combination

    • Generality

    • Probabilistic heuristics

  • Summary


Gp search space

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 space1

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

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 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 visits the santa fe trail effects of heuristics on gp

CGP

Principles

What heuristics/constraints can be processed


Cgp principles

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

GP with Strong and Weak Constraints

Pruned non-uniform

distribution

Mutation/Crossover

Pi

Pi+1

Reproduction

Probabilistic Grammars, CGP, EDA


Cgp means of processing

CGP Means of Processing

  • Strong constraints

    • Explicit structures and by data typing

  • Overloaded functions on types

  • Weak constraints


Cgp means of processing1

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

/

+

2

x

sin

a

CGP Mutation

/

+

2

x

*

c

3


Gp crossover

+

2

+

y

4

/

+

2

/

x

sin

+

+

+

2

2

a

x

sin

y

4

a

GP Crossover


Santafe experiments

SantaFe Experiments

Problem

Function set

Heuristics exploration

Generality of the heuristics

Comparing vs. ACGP’s probabilistic heuristics (on performance)


Santafe problem

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

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

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, Quality


Reducing function set basics efficiency

Reducing Function Set: Basics, Efficiency


Reducing function set combined quality

Reducing Function Set: Combined, Quality


Reducing function set combined efficiency

Reducing Function Set: Combined, Efficiency


Constraining root and local structure basics quality

Constraining Root and Local Structure: Basics, Quality


Constraining root and local structure basics efficiency

Constraining Root and Local Structure: Basics,Efficiency


Constraining root and local structure combined quality

Constraining Root and Local Structure: Combined, Quality


Constraining root and local structure combined efficiency

Constraining Root and Local Structure: Combined, Efficiency


Combined function set and structural heuristics quality

Combined Function Set and Structural Heuristics: Quality


Combined function set and structural heuristics efficiency

Combined Function Set and Structural Heuristics: Efficiency


More combined heuristics quality

More Combined Heuristics: Quality


More combined heuristics quality1

More Combined Heuristics: Quality


Best heuristics by inspection

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: Quality (vs. components)


Best heuristics by inspection efficiency vs components

Best Heuristics by Inspection: Efficiency (vs. components)


Best heuristics summary quality

Best Heuristics Summary: Quality


Best heuristics summary efficiency

Best Heuristics Summary: Efficiency


Best shortest solution

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 Slightly Different Trails: Same Basic Primitives


Testing different trails similar basic primitives

Testing Different Trails: Similar Basic Primitives


Learning probabilistic heuristics with acgp

Learning Probabilistic Heuristics with ACGP


Comparing probabilistic heuristics vs strong

Comparing Probabilistic Heuristics vs. Strong


Summary 1

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

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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