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Phase Transitions and Symmetry Breaking in Genetic Algorithms with Crossover

Phase Transitions and Symmetry Breaking in Genetic Algorithms with Crossover
Phase Transitions and Symmetry Breaking in Genetic Algorithms with Crossover
In this paper, we consider the role of the crossover operator in genetic algorithms. Specifically, we study optimisation problems that exhibit many local optima and consider how crossover affects the rate at which the population breaks the symmetry of the problem. As an example of such a problem, we consider the subset sum problem. In so doing, we demonstrate a previously unobserved phenomenon, whereby the genetic algorithm with crossover exhibits a critical mutation rate, at which its performance sharply diverges from that of the genetic algorithm without crossover. At this critical mutation rate, the genetic algorithm with crossover exhibits a rapid increase in population diversity. We calculate the details of this phenomenon on a simple instance of the subset sum problem and show that it is a classic phase transition between ordered and disordered populations. Finally, we show that this critical mutation rate corresponds to the transition between the genetic algorithm accelerating or preventing symmetry breaking and that the critical mutation rate represents an optimum in terms of the balance of exploration and exploitation within the algorithm.
genetic algorithm, phase transition, symmetry breaking
0304-3975
121-141
Rogers, Alex
f9130bc6-da32-474e-9fab-6c6cb8077fdc
Prügel-Bennett, Adam
b107a151-1751-4d8b-b8db-2c395ac4e14e
Jennings, N. R.
ab3d94cc-247c-4545-9d1e-65873d6cdb30
Rogers, Alex
f9130bc6-da32-474e-9fab-6c6cb8077fdc
Prügel-Bennett, Adam
b107a151-1751-4d8b-b8db-2c395ac4e14e
Jennings, N. R.
ab3d94cc-247c-4545-9d1e-65873d6cdb30

Rogers, Alex, Prügel-Bennett, Adam and Jennings, N. R. (2006) Phase Transitions and Symmetry Breaking in Genetic Algorithms with Crossover. Theoretical Computer Science, 358 (1), 121-141.

Record type: Article

Abstract

In this paper, we consider the role of the crossover operator in genetic algorithms. Specifically, we study optimisation problems that exhibit many local optima and consider how crossover affects the rate at which the population breaks the symmetry of the problem. As an example of such a problem, we consider the subset sum problem. In so doing, we demonstrate a previously unobserved phenomenon, whereby the genetic algorithm with crossover exhibits a critical mutation rate, at which its performance sharply diverges from that of the genetic algorithm without crossover. At this critical mutation rate, the genetic algorithm with crossover exhibits a rapid increase in population diversity. We calculate the details of this phenomenon on a simple instance of the subset sum problem and show that it is a classic phase transition between ordered and disordered populations. Finally, we show that this critical mutation rate corresponds to the transition between the genetic algorithm accelerating or preventing symmetry breaking and that the critical mutation rate represents an optimum in terms of the balance of exploration and exploitation within the algorithm.

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More information

Published date: 2006
Keywords: genetic algorithm, phase transition, symmetry breaking
Organisations: Agents, Interactions & Complexity, Southampton Wireless Group

Identifiers

Local EPrints ID: 262413
URI: https://eprints.soton.ac.uk/id/eprint/262413
ISSN: 0304-3975
PURE UUID: c9fab915-bbb7-4308-bcf7-499943a9da76

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Date deposited: 26 Apr 2006
Last modified: 19 Jul 2019 22:31

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Contributors

Author: Alex Rogers
Author: Adam Prügel-Bennett
Author: N. R. Jennings

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