Abstract
In the paper, we apply logarithmic cooling schedules of inho- mogeneous Markov chains to the flow shop scheduling problem with the objective to minimize the makespan. In our detailed convergence analy- sis, we prove a lower bound of the number of steps which are sufficient to approach an optimum solution with a certain probability. The result is related to the maximum escape depth Γ from local minima of the underlying energy landscape. The number of steps k which are required to approach with probability 1 − δ the minimum value of the makespan is lower bounded by n O(Γ)·logO(1)(1/δ). The auxiliary computations are of polynomial complexity. Since the model cannot be approximated arbitrarily closely in the general case (unless P =NP), the approach might be used to obtain approximation algorithms that work well for the average case.
Research partially supported by the Strategic Research Program at the ChineseUniversity of Hong Kong under Grant No. SRP 9505, by a Hong Kong Government RGC Earmarked Grant, Ref. No. CUHK 4367/99E, and by the HK-Germany Joint Research Scheme under Grant No. D/9800710.
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Steinhöfel, K., Albrecht, A., Wong, CK. (2000). Convergence Analysis of Simulated Annealing-Based Algorithms Solving Flow Shop Scheduling Problems. In: Bongiovanni, G., Petreschi, R., Gambosi, G. (eds) Algorithms and Complexity. CIAC 2000. Lecture Notes in Computer Science, vol 1767. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46521-9_23
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DOI: https://doi.org/10.1007/3-540-46521-9_23
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