Filtered and Recovering beam search algorithms for the early/tardy scheduling problem with no idle time

In this paper we consider the single machine earliness/tardiness scheduling problem with no idle time. We present heuristic algorithms based on the filtered and recovering beam search techniques and compare them with existing neighbourhood search and dispatch rule heuristics. Filtering procedures using both priority evaluation functions and problem-specific properties have been considered. Extensive preliminary tests were performed to determine appropriate parameter values for the beam search algorithms and the neighbourhood search procedure. The computational results show that the recovering beam search algorithms outperform their filtered counterparts in both solution quality and computational requirements, while the priority-based filtering procedure proves superior to the rules-based alternative. The best solutions are given by the neighbourhood search algorithm, but this procedure is computationally intensive and can therefore only be applied to small or medium size instances. The recovering beam search heuristic provides results that are close in solution quality and is significantly faster, so it can be used to solve even large instances.