  This paper concerns the single machine total weighted tardiness scheduling
with sequence-dependent setup times, usually referred as $1|s_{ij}|\sum
w_jT_j$. In this $\mathcal{NP}$-hard problem, each job has an associated
processing time, due date and a weight. For each pair of jobs $i$ and $j$,
there may be a setup time before starting to process $j$ in case this job is
scheduled immediately after $i$. The objective is to determine a schedule that
minimizes the total weighted tardiness, where the tardiness of a job is equal
to its completion time minus its due date, in case the job is completely
processed only after its due date, and is equal to zero otherwise. Due to its
complexity, this problem is most commonly solved by heuristics. The aim of this
work is to develop a simple yet effective limitation strategy that speeds up
the local search procedure without a significant loss in the solution quality.
Such strategy consists of a filtering mechanism that prevents unpromising moves
to be evaluated. The proposed strategy has been embedded in a local search
based metaheuristic from the literature and tested in classical benchmark
instances. Computational experiments revealed that the limitation strategy
enabled the metaheuristic to be extremely competitive when compared to other
algorithms from the literature, since it allowed the use of a large number of
neighborhood structures without a significant increase in the CPU time and,
consequently, high quality solutions could be achieved in a matter of seconds.
In addition, we analyzed the effectiveness of the proposed strategy in two
other well-known metaheuristics. Further experiments were also carried out on
benchmark instances of problem $1|s_{ij}|\sum T_j$.
