Abstract
We investigate the convergence of simulated annealing with emphasis on the probability 1-δ to be in an optimum solution. The analysis is carried out for a logarithmic cooling schedule c(k) = Γ/ln(k + 2), i.e., the temperature is lowered at any step k. We prove that after k > (n/δ)O(Γ) steps the probability to be in an optimum solution is larger than 1-δ, where n is an upper bound for the size of local neighbourhoods. The parameter Γ is problem specific and depends on the underlying energy landscape. By counting the occurrences of configurations, we demonstrate for an application with known optimum solutions that the lower bound indeed ensures the stated probability for a relatively small constant in O(Γ).
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Albrecht, A.A. (2004). A Problem-Specific Convergence Bound for Simulated Annealing-Based Local Search. In: Laganá, A., Gavrilova, M.L., Kumar, V., Mun, Y., Tan, C.J.K., Gervasi, O. (eds) Computational Science and Its Applications – ICCSA 2004. ICCSA 2004. Lecture Notes in Computer Science, vol 3045. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24767-8_42
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DOI: https://doi.org/10.1007/978-3-540-24767-8_42
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