Compositional Autoconstruc- tive Dynamics Compositional Autoconstructive Dynamics Kyle I. Harrington , Evolutionary Computation Kyle I. Harrington 1 , 2 GA GP Meta-Evolution 1 DEMO lab Autoconstructive Michtom School of Computer Science Evolution Brandeis University, Waltham, MA Push 2 Co-authors: Compositional Autoconstruction Emma Tosch (Brandeis University) Conclusion Lee Spector (Hampshire College, Amherst, MA) Jordan Pollack (Brandeis University) June 29, 2011 - ICCS . . . . . .
Outline Compositional Autoconstruc- tive Dynamics Evolutionary Computation 1 Kyle I. Harrington , Genetic Algorithm Genetic Programming Evolutionary Computation GA GP Meta-Evolution 2 Meta-Evolution Autoconstructive Evolution Autoconstructive Evolution 3 Push Push Compositional Autoconstruction Compositional Autoconstruction Conclusion Conclusion 4 . . . . . .
Evolutionary Computation Evolutionary Algorithm Compositional Evolutionary algorithms are a set of general techniques that can Autoconstruc- tive be applied to many types of problems. Dynamics Kyle I. Harrington , Evolutionary Computation GA GP Meta-Evolution Autoconstructive Evolution Push Compositional Autoconstruction Conclusion A minimal evolutionary algorithm. . . . . . .
Outline Compositional Autoconstruc- tive Dynamics Evolutionary Computation 1 Kyle I. Harrington , Genetic Algorithm Genetic Programming Evolutionary Computation GA GP Meta-Evolution 2 Meta-Evolution Autoconstructive Evolution Autoconstructive Evolution 3 Push Push Compositional Autoconstruction Compositional Autoconstruction Conclusion Conclusion 4 . . . . . .
Genetic Algorithm Overview Compositional Autoconstruc- tive Dynamics Kyle I. Harrington , Developed by John Holland [Holland, 1975]. Evolutionary Computation Evolve a population of individuals that represent potential GA problem solutions. GP Meta-Evolution Autoconstructive Evolution Push Compositional A bit string genome. Autoconstruction Conclusion . . . . . .
Genetic Algorithm Evaluation Compositional Autoconstruc- tive Dynamics Kyle I. Harrington , Dependent upon genotype → phenotype mapping. Evolutionary Computation Ones max : common benchmark, maximize 1’s in genome GA GP Meta-Evolution g ) = ∑ ⃗ f ( g i Autoconstructive Evolution g i ∈ g Push for genome ⃗ g containing g i genes. Compositional Autoconstruction Conclusion . . . . . .
Genetic Algorithm Selection Compositional Autoconstruc- tive Dynamics Kyle I. Choose members of population that reproduce. Harrington , Fitness proportionate roulette: bias selection to better Evolutionary Computation individuals. GA GP Generation(t) Selection Generation(t+1) Genome Score Rel. score Min Max Roulette Genome Score Rel. score Meta-Evolution 1 / 4 1 / 6 01010101 4 0 0.25 0.8147 11000010 3 3 / 16 1 / 6 10001001 3 0.25 0.4375 0.9058 11000010 3 Autoconstructive 1 / 16 2 / 9 00100000 1 0.4375 0.5 0.127 01010101 4 Evolution 5 / 16 1 / 6 11011010 5 0.5 0.8125 0.9134 11000010 3 Push 3 / 16 5 / 18 11000010 3 0.8125 1.0 0.6324 11011010 5 Compositional Total 16 Total 18 Autoconstruction Average 3.2 Averge 3.6 Conclusion Example 8-bit genome for Ones Max . . . . . . .
Genetic Algorithm Variation Compositional Autoconstruc- tive Dynamics Kyle I. Harrington , Evolutionary Computation GA GP Meta-Evolution Autoconstructive Evolution Push Compositional Autoconstruction Conclusion 1-point mutation. 1-point crossover. Determining mutation and crossover probability is a “dark art.” . . . . . .
Outline Compositional Autoconstruc- tive Dynamics Evolutionary Computation 1 Kyle I. Harrington , Genetic Algorithm Genetic Programming Evolutionary Computation GA GP Meta-Evolution 2 Meta-Evolution Autoconstructive Evolution Autoconstructive Evolution 3 Push Push Compositional Autoconstruction Compositional Autoconstruction Conclusion Conclusion 4 . . . . . .
Genetic Programming Overview Compositional First in [Cramer, 1985], popularized in [Koza, 1992]. Autoconstruc- tive Dynamics Evolution of executable computer programs. Kyle I. Used for: symbolic regression, gene-gene interaction Harrington , detection, robot design/control, circuit design, etc. Evolutionary Computation GA GP Meta-Evolution String representation Autoconstructive Evolution Push Compositional Autoconstruction Conclusion f ( x ) = 1 + X ∗ ( X + 1 ) Tree representation Mathematical representation . . . . . .
Genetic Programming Evaluation Compositional Autoconstruc- Target expression: g ( x ) = X 2 + 2 X + 1 tive Dynamics Tree representation Kyle I. Harrington , Evolutionary Computation GA Example individual: GP Meta-Evolution Autoconstructive Evolution Push Mathematical representation Compositional f ( x ) = 1 + X ∗ ( X + 1 ) Autoconstruction X = 0 , f ( X ) = 1 , g ( X ) = 1 Conclusion X = 1 , f ( X ) = 3 , g ( X ) = 4 X = 2 , f ( X ) = 7 , g ( X ) = 9 Individual’s error: 3 . . . . . .
Genetic Programming Mutation Compositional Autoconstruc- tive Dynamics Kyle I. Harrington , Evolutionary Computation GA GP Meta-Evolution Autoconstructive Evolution Push Compositional Autoconstruction Subtree mutation. Conclusion Size-fair mutation, etc. . . . . . .
Genetic Programming Crossover Compositional Autoconstruc- tive Dynamics Kyle I. Harrington , Evolutionary Computation GA GP Meta-Evolution Autoconstructive Evolution Push Compositional Autoconstruction Conclusion Subtree crossover. Size-fair crossover, semantic-aware crossover, etc. . . . . . .
Meta-Evolution Overview Compositional Autoconstruc- tive Dynamics Kyle I. Harrington , Evolutionary Computation Evolve the evolutionary process. GA GP The original meta-evolution algorithm was presented in Meta-Evolution [Schmidhuber, 1987]. Autoconstructive Evolution Introduces the “meta-meta-. . . hook.” Push Compositional Autoconstruction Conclusion . . . . . .
Example: Meta-Genetic Programming Compositional Introduced in [Edmonds, 2001]. Autoconstruc- tive Evolve the variation programs. Dynamics Kyle I. Harrington , Evolutionary Computation GA GP Meta-Evolution Autoconstructive Evolution Push Compositional Autoconstruction Conclusion A meta-evolutionary algorithm. . . . . . .
Meta-Evolution Adaptive Evolution and Self-Adaptation Compositional Autoconstruc- tive Dynamics Kyle I. Harrington , Population-level : adjust variation probabilities based on population performance Evolutionary Computation Individual-level : individual’s have unique variation GA GP probabilities Meta-Evolution Component-level : genes/instructions have unique variation Autoconstructive Evolution probabilities Push Compositional Autoconstruction Conclusion Full review in [Angeline, 1995] . . . . . .
Autoconstructive Evolution Overview Compositional Autoconstruc- Introduced in [Spector and Robinson, 2002]. tive Dynamics Integrate all levels of adaptation (population, individual, Kyle I. component) as part of the program itself. Harrington , Evolutionary Computation GA GP Meta-Evolution Autoconstructive Evolution Push Compositional Autoconstruction Conclusion An autoconstructive evolutionary algorithm. . . . . . .
Outline Compositional Autoconstruc- tive Dynamics Evolutionary Computation 1 Kyle I. Harrington , Genetic Algorithm Genetic Programming Evolutionary Computation GA GP Meta-Evolution 2 Meta-Evolution Autoconstructive Evolution Autoconstructive Evolution 3 Push Push Compositional Autoconstruction Compositional Autoconstruction Conclusion Conclusion 4 . . . . . .
Push Overview Compositional Autoconstruc- tive Dynamics Kyle I. Harrington , Stack-based, multi-typed language designed for EC Evolutionary [Spector and Robinson, 2002]. Computation GA Code is a data type (homoiconicity). GP Meta-Evolution Programs are capable of self-modification via exec stack Autoconstructive [Spector et al., 2005]. Evolution Push Tag-based naming for items on all stacks Compositional Autoconstruction [Spector et al., 2011]. Conclusion . . . . . .
Push Zippers Compositional Autoconstruc- Tree-based data structure introduced in tive [Huet and France, 1997]. Dynamics Kyle I. Supports movement, insertion, removal, and substitution. Harrington , Evolutionary Computation GA GP Meta-Evolution Autoconstructive Evolution Push Compositional Autoconstruction Conclusion An example zipper and potential movement locations. . . . . . .
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