Parallel path relinking method for the single machine total weighted tardiness problem with sequence-dependent setups

We propose a new method of sequential and parallel speeding up of the process of solving a single machine scheduling problem with total tardiness cost function. This improvement is done on two levels: generating a neighborhood inside path relinking method (basing on new approach—blocks in solutions) and parallelization of generating paths. The obtained results are compared to the benchmark ones taken from the literature. It was possible to find new the best solutions for many benchmark instances by using the proposed method.