An Iterated Local Search heuristic for the single machine total weighted tardiness scheduling problem with sequence-dependent setup times

The single machine total weighted tardiness problem with sequence-dependent setup times (often known as problem <inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="tprs_a_883472_ilm0001.gif"></inline-graphic>) requires a given set of jobs to be sequenced on a single machine, where a setup time is required before the processing of each job that depends on both the preceding job and the job to be processed next. The goal is to minimise the sum of weighted tardiness, where the tardiness of a job is zero if it is completed by its due date and is equal to its completion time minus its due date otherwise. In this paper, we develop an Iterated Local Search (ILS) heuristic and compare its performance with the state-of-the-art metaheuristic algorithms from the literature. The proposed ILS algorithm obtains high-quality solutions using computation times that is comparable to its competitors.