Abstract
In this paper we relate information theory and Kolmogorov Complexity (KC) to optimization in the black box scenario. We define the set of all possible decisions an algorithm might make during a run, we associate a function with a probability distribution over this set and define accordingly its entropy. We show that the expected KC of the set (rather than the function) is a better measure of problem difficulty. We analyze the effect of the entropy on the expected KC. Finally, we show, for a restricted scenario, that any permutation closure of a single function, the finest level of granularity for which a No Free Lunch Theorem can hold [7], can be associated with a particular value of entropy. This implies bounds on the expected performance of an algorithm on members of that closure.
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References
Borenstein, Y., Poli, R.: Kolmogorov complexity, optimization and hardness. In: CEC 2006 (2006)
Borenstein, Y., Poli, R.: No free lunch, Kolmogorov Complexity and the information landscape. In: Proceedings of IEEE CEC 2005, vol. 3 (2005)
Droste, S., Jansen, T., Wegener, I.: Upper and lower bounds for randomized search heuristics in black-box optimization. In: ECCC (048) (2003)
English, T.M.: On the structure of sequential search: Beyond ”no free lunch”. In: Gottlieb, J., Raidl, G.R. (eds.) EvoCOP 2004. LNCS, vol. 3004, pp. 95–103. Springer, Heidelberg (2004)
Grunwald, P., Vitanyi, P.: Shannon information and kolmogorov complexity. IEEE Transactions on Information Theory (2004) (in Review)
Grunwald, P., Vitanyi, P.: Algorithmic information theory. In: Handbook on the Philosophy of Information, Elsevier, Amsterdam (to appear)
Schumacher, C., Vose, M.D., Whitley, L.D.: The no free lunch and problem description length. In: Spector, L., et al. (eds.) GECCO 2001, pp. 565–570. Morgan Kaufmann, San Francisco (2001)
Vose, M.D.: The Simple Genetic Algorithm: Foundations and Theory. MIT Press, Cambridge (1998)
Wegener, I.: Towards a theory of randomized search heuristics. In: Rovan, B., Vojtáš, P. (eds.) MFCS 2003. LNCS, vol. 2747, pp. 125–141. Springer, Heidelberg (2003)
Wolpert, D., Macready, W.G.: No free lunch theorems for optimization. IEEE Trans. Evolutionary Computation 1(1), 67–82 (1997)
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Borenstein, Y., Poli, R. (2006). Information Perspective of Optimization. In: Runarsson, T.P., Beyer, HG., Burke, E., Merelo-Guervós, J.J., Whitley, L.D., Yao, X. (eds) Parallel Problem Solving from Nature - PPSN IX. PPSN 2006. Lecture Notes in Computer Science, vol 4193. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11844297_11
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DOI: https://doi.org/10.1007/11844297_11
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