Abstract
In the case where the search space has a group structure, classical genetic operators (mutation and two-parent crossover) which respect the group action are completely characterized by formulas defining them in terms of the search space and its group operation. This provides a representation-free implementation for those operators, in the sense that the genotypic encoding of search space elements is irrelevant. The implementations are parameterized by distributions which may be chosen arbitrarily, and which are analogous to specifying distributions for mutation and crossover masks.
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References
Biggs, N.L.: Finite groups of automorphisms. Cambridge University Press, Cambridge, UK (1971)
Rockmore, D., Hordijk, W., Kostelec, P., Stadler, P.: Fast fourier transforms for fitness landscapes. Applied and Computational Harmonic Analysis 12(1), 57–76 (2002)
Rowe, J.E., Vose, M.D., Wright, A.H.: Group properties of crossover and mutation. Evolutionary Computation 10, 151–184 (2002)
Rowe, J.E., Vose, M.D., Wright, A.H.: Structural search spaces and genetic operators. Evolutionary Computation 12, 461–494 (2004)
Rowe, J.E., Vose, M.D., Wright, A.H.: Coarse graining selection and mutation. In: Wright, A.H., Vose, M.D., De Jong, K.A., Schmitt, L.M. (eds.) FOGA 2005. LNCS, vol. 3469, pp. 176–191. Springer, Heidelberg (2005)
Rowe, J.E., Vose, M.D., Wright, A.H.: Differentiable coarse graining. Theoretical Computer Science 361, 111–129 (2006)
Stadler, P.F.: Landscapes and their correlation functions. Journal of Mathematical Chemistry 20(1), 1–45 (1996)
Vose, M.D.: Random heuristic search. Theoretical Computer Science 229, 103–142 (1999)
Vose, M.D.: The Simple Genetic Algorithm: Foundations and Theory. MIT Press, Cambridge, MA (1999)
Weinberger, E.D.: Fourier and taylor series on fitness landscapes. Biological Cybernetics 65(5), 321–330 (1991)
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Rowe, J.E., Vose, M.D., Wright, A.H. (2007). Neighborhood Graphs and Symmetric Genetic Operators. In: Stephens, C.R., Toussaint, M., Whitley, D., Stadler, P.F. (eds) Foundations of Genetic Algorithms. FOGA 2007. Lecture Notes in Computer Science, vol 4436. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73482-6_7
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DOI: https://doi.org/10.1007/978-3-540-73482-6_7
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