Convergence analysis of simulated annealing-based algorithms solving flow shop scheduling problems

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 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) · 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.