The effect of spin-flip symmetry on the performance of the simple GA
We use the one-dimensional nearest neighbor interaction functions (NNIs) to show how the presence of symmetry in a fitness function greatly influences the convergence behavior of the simple genetic algorithm (SGA). The effect of symmetry on the SGA supports the statement that it is not the amount of interaction present in a fitness function, measured e.g. by Davidor's epistasis variance and the experimental design techniques introduced by Reeves and Wright, which is important, but the kind of interaction. The NNI functions exhibit a minimal amount of second order interaction, are trivial to optimize deterministically and yet show a wide range of SGA behavior. They have been extensively studied in statistical physics; results from this field explain the negative effect of symmetry on the convergence behavior of the SGA. This note intends to introduce them to the GA-community.
KeywordsDomain Wall Fitness Function Ising Model Convergence Behavior Order Function
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- 1.L. Altenberg. Fitness distance correlation analysis: an instructive counterexample. In Th. Bäck, editor, Proceedings of the 7th International Conference on Genetic Algorithms, pages 57–64. Morgan Kaufmann Publishers, 1997.Google Scholar
- 2.Y. Davidor. Epistasis variance: a viewpoint on GA-hardness. In G. J. E. Rawlins, editor, Foundations of Genetic Algorithms, pages 23–35. Morgan Kaufmann Publishers. 1991.Google Scholar
- 3.E. Ising. Beitrag zur Theorie des Ferromagnetismus. Z. Physik, 31:235, 1924.Google Scholar
- 5.S. A. Kauffman. Adaptation on rugged fitness landscapes. In Lectures in the Sciences of Complexity, volume I of SFI studies, pages 619–712. Addison Wesley, 1989.Google Scholar
- 7.T. M. Liggett. Interacting Particle Systems. Springer Verlag, 1985.Google Scholar
- 8.B. Naudts. Measuring GA-hardness. PhD thesis, University of Antwerp, RUCA, Belgium, 1998.Google Scholar
- 9.B. Naudts and A. Verschoren. SGA search dynamics on second order functions. In J.-K. Hao, E. Lutton, E. Ronald, M. Schoenauer, and D. Snyers, editors, Artificial Evolution 97. Springer Verlag, 1998.Google Scholar
- 12.C. Reeves and C. Wright. An experimental design perspective on genetic algorithms. In L. D. Whitley and M. D. Vose, editors, Foundations of Genetic Algorithms 3, pages 7–22. Morgan Kaufmann Publishers, 1995.Google Scholar