Beam search algorithms for the single machine total weighted tardiness scheduling problem with sequence-dependent setups

In this paper, we consider the single machine weighted tardiness scheduling problem with sequence-dependent setups. We present heuristic algorithms based on the beam search technique. These algorithms include classic beam search procedures, as well as the filtered and recovering variants. Previous beam search implementations use fixed beam and filter widths. We consider the usual fixed width algorithms, and develop new versions that use variable beam and filter widths. Two new improvement procedures, based on adjacent pairwise interchanges and 3-swaps, are also presented. The computational results show that the beam search versions with a variable width are marginally superior to their fixed value counterparts, even when a lower average number of beam and filter nodes is used. The best results are given by the filtered beam search algorithms. For large problems, however, these procedures require excessive computation times. The priority beam search algorithms are much faster, and can therefore be used for the largest instances. The 3-swap method is the best of the improvement procedures, giving the largest relative improvement and decreasing the total cost for a larger number of instances.