The convergence of stochastic algorithms solving flow shop scheduling

In the paper, we apply logarithmic cooling schedules of simulated annealing-based algorithms to !ow shop scheduling. In our problem setting, the objective to minimize the overall completion time which is called the makespan. We prove a lower bound for the number of steps that are su1cient to approach an optimum solution with a certain probability. The result is related to the maximum escape depth from local minima of the underlying energy landscape. In our approach, we need n ) + log(1= ) steps to be in an optimum solution with probability 1− , where n denotes the total number of tasks. The auxiliary computations are of polynomial complexity. Since the model cannot be approximated arbitrarily closely in the general case (unless P=NP), the approach can be used to obtain approximation algorithms that work well in the average case. c © 2002 Elsevier Science B.V. All rights reserved.