Convergence Analysis of Simulated Annealing-Based Algorithms Solving Flow Shop Scheduling Problems

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.