Simulated annealing algorithm for solving the single machine early/tardy problem

Recently, several studies have been conducted regarding the application of the simulated annealing (SA) method to solve combinatorial optimization problems. Most of the previous reports have shown that SA has been used to obtain reasonable solutions that are better than some heuristic algorithms and in comparable CPU time. A single machine early/tardy problem is selected in this paper to demonstrate the usefulness of SA. Firstly, based on previous studies, this research uses the factorial experiment to analyse the factors that are critical to the efficiency of SA. Secondly, SA, tuned by the previous step, is compared with branch-and-bound and neighbourhood search methods by solving some test problems. The results show that SA is very sensitive to the cooling schedule, generation mechanism, acceptance criteria and stopping criteria. When SA is used to solve the single machine problem with n ≤ 15, it can converge to the optimal solution quickly. For the single machine problem where n ≥ 30, the branch-and-bound algorithm is not feasible while SA can provide a much better solution than the neighbourhood search method.