Abstract
In previous work of the second author a rigorous mathematical foundation for re-encoding one evolutionary search algorithm by another has been developed. A natural issue to consider then is the complexity of deciding whether or not a given evolutionary algorithm can be re-encoded by one of the standard classical evolutionary algorithms such as a binary genetic algorithm. In the current paper we prove that, in general, this decision problem is NP-complete.
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References
Davis, L.: Applying Adoptive Algorithms to Epistatic Domains. In: Proceedings of the International Joint Conference on Artificial Intelligence, pp. 162–164 (1985)
Garey, M., Johnson, D.: Computers and Intractability. A Guide to the Theory of NP-Completeness. W. H. Freeman and Company, New York (1979)
Mac Lane, S.: Categories for the Working Mathematician. Graduate Texts in Mathematics 5. Springer, Heidelberg (1971)
Michalewicz, Z.: Genetic algorithms + data structures = evolution programs. Springer, Heidelberg (1996)
Mitavskiy, B.: Crossover invariant subsets of the search space for evolutionary algorithms. Evolutionary Computation 12(1), 19–46 (2004), http://www.math.lsa.umich.edu/~bmitavsk/
Mitavskiy, B.: Comparing evolutionary computation techniques via their representation. In: Cantú-Paz, E., et al. (eds.) Proceedings of the Genetic and Evolutionary Computation Conference (GECCO), vol. 1, pp. 1196–1209. Springer, Heidelberg (2003)
Mitavskiy, B.: A category theoretic method for comparing evolutionary computation techniques via their representation. In: ten-Cate, B. (ed.) Proceedings of the Eighth ESSLLI Student Session, pp. 201–210 (2003)
Poli, R.: Hyperschema Theory for GP with One-Point Crossover, Building Blocks, and Some New Results in GA Theory. In: Poli, R., Banzhaf, W., Langdon, W.B., Miller, J., Nordin, P., Fogarty, T.C. (eds.) EuroGP 2000. LNCS, vol. 1802, pp. 163–180. Springer, Heidelberg (2000)
Radcliffe, N.: The algebra of genetic algorithms. Annals ofMathematics and Artificial Intelligence 10, 339–384 (1994), http://users.breathemail.net/njr/papers/amai94.pdf
Rothlauf, F., Goldberg, D., Heinzl, A.: Network random keys - a tree representation scheme for genetic and evolutionary algorithms. Evolutionary Computation 10(1), 75–97 (2002)
Rowe, J., Vose, M., Wright, A.: Group properties of crossover and mutation. Evolutionary Computation 10(2), 151–184 (2002)
Stephens, C.: Some exact results from a coarse grained formulation of genetic dynamics. In: Proceedings of the Genetic and Evolutionary Computation Conference (GECCO), pp. 631–638 (2001)
Vose, M.: The Simple Genetic Algorithm: Foundations and Theory. MIT Press, Cambridge (1999)
Vose, M., Wright, A.: Form invariance and implicit parallelism. Evolutionary Computation 9(3), 355–370 (2001)
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Blass, A., Mitavskiy, B. (2005). NP-Completeness of Deciding Binary Genetic Encodability. In: Wright, A.H., Vose, M.D., De Jong, K.A., Schmitt, L.M. (eds) Foundations of Genetic Algorithms. FOGA 2005. Lecture Notes in Computer Science, vol 3469. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11513575_4
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DOI: https://doi.org/10.1007/11513575_4
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