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Self-Configuring Crossover

Self-Configuring Crossover. Brian W. Goldman Daniel R. Tauritz. Motivation. Performance Sensitive to Crossover Selection Identifying & Configuring Best Traditional Crossover is Time Consuming Existing Operators May Be Suboptimal Optimal Operator May Change During Evolution.

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Self-Configuring Crossover

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  1. Self-Configuring Crossover Brian W. Goldman Daniel R. Tauritz Natural Computation Laboratory - Missouri S&T

  2. Motivation Natural Computation Laboratory - Missouri S&T Performance Sensitive to Crossover Selection Identifying & Configuring Best Traditional Crossover is Time Consuming Existing Operators May Be Suboptimal Optimal Operator May Change During Evolution

  3. Some Possible Solutions Natural Computation Laboratory - Missouri S&T • Meta-EA • Exceptionally time consuming • Self-Adaptive Algorithm Selection • Limited by algorithms it can choose from

  4. Self-Configuring Crossover (SCX) Offspring Crossover Swap(3, 5, 2) Merge(1, r, 0.7) Swap(r, i, r) Natural Computation Laboratory - Missouri S&T • Each Individual Encodes a Crossover Operator • Crossovers Encoded as a List of Primitives • Swap • Merge • Each Primitive has three parameters • Number, Random, or Inline

  5. Applying an SCX Concatenate Genes 1.0 5.0 2.0 6.0 3.0 7.0 4.0 8.0 Parent 1 Genes Parent 2 Genes Natural Computation Laboratory - Missouri S&T

  6. The Swap Primitive Swap(3, 5, 2) Natural Computation Laboratory - Missouri S&T • Each Primitive has a type • Swap represents crossovers that move genetic material • First Two Parameters • Start Position • End Position • Third Parameter Primitive Dependent • Swaps use “Width”

  7. Applying an SCX Concatenate Genes 5.0 1.0 2.0 6.0 3.0 7.0 8.0 4.0 Offspring Crossover Swap(3, 5, 2) 3.0 4.0 5.0 6.0 Merge(1, r, 0.7) Swap(r, i, r) Natural Computation Laboratory - Missouri S&T

  8. The Merge Primitive Merge(1, r, 0.7) Natural Computation Laboratory - Missouri S&T • Third Parameter Primitive Dependent • Merges use “Weight” • Random Construct • All past primitive parameters used the Number construct • “r” marks a primitive using the Random Construct • Allows primitives to act stochastically

  9. Applying an SCX Concatenate Genes 1.0 3.0 2.0 4.0 5.0 7.0 6.0 8.0 Offspring Crossover Swap(3, 5, 2) 0.7 g(i) = α*g(i) + (1-α)*g(j) Merge(1, r, 0.7) g(1) = 1.0*(0.7) + 6.0*(1-0.7) g(2) = 6.0*(0.7) + 1.0*(1-0.7) 2.5 4.5 Swap(r, i, r) Natural Computation Laboratory - Missouri S&T

  10. The Inline Construct Swap(r, i, r) Natural Computation Laboratory - Missouri S&T Only Usable by First Two Parameters Denoted as “i” Forces Primitive to Act on the Same Loci in Both Parents

  11. Applying an SCX Concatenate Genes 2.5 3.0 2.0 4.0 5.0 7.0 4.5 8.0 Offspring Crossover 2.0 4.0 Swap(3, 5, 2) Merge(1, r, 0.7) Swap(r, i, r) Natural Computation Laboratory - Missouri S&T

  12. Applying an SCX Remove Exess Genes Concatenate Genes 2.5 3.0 4.0 2.0 5.0 7.0 4.5 8.0 Offspring Genes Natural Computation Laboratory - Missouri S&T

  13. Evolving Crossovers Parent 2 Crossover Parent 1 Crossover Offspring Crossover Swap(r, 7, 3) Swap(3, 5, 2) Merge(i, 8, r) Swap(4, 2, r) Merge(1, r, 0.7) Merge(r, r, r) Swap(r, i, r) Natural Computation Laboratory - Missouri S&T

  14. Empirical Quality Assessment Natural Computation Laboratory - Missouri S&T • Compared Against • Arithmetic Crossover • N-Point Crossover • Uniform Crossover • On Problems • Rosenbrock • Rastrigin • Offset Rastrigin • NK-Landscapes • DTrap

  15. Adaptations: Rastrigin Natural Computation Laboratory - Missouri S&T

  16. Adaptations: DTrap Natural Computation Laboratory - Missouri S&T

  17. SCX Overhead Natural Computation Laboratory - Missouri S&T • Requires No Additional Evaluation • Adds No Significant Increase in Run Time • All linear operations • Adds Initial Crossover Length Parameter • Testing showed results fairly insensitive to this parameter • Even worst settings tested achieved better results than comparison operators

  18. Conclusions Natural Computation Laboratory - Missouri S&T Remove Need to Select Crossover Algorithm Better Fitness Without Significant Overhead Benefits From Dynamically Changing Operator

  19. Future Work Natural Computation Laboratory - Missouri S&T Extension to Permutation Representations Compare With State-of-the-Art Crossovers Test Effectiveness on Real World Problems Further Improve Crossover Evolution Methods

  20. Questions? Natural Computation Laboratory - Missouri S&T

  21. Fitness: Rastrigin Natural Computation Laboratory - Missouri S&T

  22. Fitness: NK Natural Computation Laboratory - Missouri S&T

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