Self-Configuring Crossover

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Presentation transcript:

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

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 Natural Computation Laboratory - Missouri S&T

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

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

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

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

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

The Merge Primitive 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 Merge(1, r, 0.7) Natural Computation Laboratory - Missouri S&T

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

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

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

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

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

Empirical Quality Assessment Compared Against Arithmetic Crossover N-Point Crossover Uniform Crossover On Problems Rosenbrock Rastrigin Offset Rastrigin NK-Landscapes DTrap Problem Comparison SCX Rosenbrock -86.94 (54.54) -26.47 (23.33) Rastrigin -59.2 (6.998) -0.0088 (0.021) Offset Rastrigin -0.1175 (0.116) -0.03 (0.028) NK 0.771 (0.011) 0.8016 (0.013) DTrap 0.9782 (0.005) 0.9925 (0.021) Natural Computation Laboratory - Missouri S&T

Adaptations: Rastrigin Natural Computation Laboratory - Missouri S&T

Adaptations: DTrap Natural Computation Laboratory - Missouri S&T

SCX Overhead 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 Natural Computation Laboratory - Missouri S&T

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

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

Questions? Natural Computation Laboratory - Missouri S&T

Fitness: Rastrigin Natural Computation Laboratory - Missouri S&T

Fitness: NK Natural Computation Laboratory - Missouri S&T

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