Cooling schedules for optimal annealing
Mathematics of Operations Research
Simulated annealing and Boltzmann machines: a stochastic approach to combinatorial optimization and neural computing
Job shop scheduling by simulated annealing
Operations Research
Journal of Complexity - Special issue for the Foundations of Computational Mathematics conference, Rio de Janeiro, Brazil, Jan. 1997
Local Search in Combinatorial Optimization
Local Search in Combinatorial Optimization
On Various Cooling Schedules for Simulated Annealing Applied to the Job Shop Problem
RANDOM '98 Proceedings of the Second International Workshop on Randomization and Approximation Techniques in Computer Science
Approximability of flow shop scheduling
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
NP-complete scheduling problems
Journal of Computer and System Sciences
Metaheuristic optimization: algorithm analysis and open problems
SEA'11 Proceedings of the 10th international conference on Experimental algorithms
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In the paper, we apply logarithmic cooling schedules of inhomogeneous Markov chains to the flow shop scheduling problem with the objective to minimize the makespan. In our detailed convergence analysis, 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 nO(Γ) ċ 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.