ILS Heuristics for the Single-Machine Scheduling Problem with Sequence-Dependent Family Setup Times to Minimize Total Tardiness

Abstract

This paper addresses a single-machine scheduling problem with sequence-dependent family setup times. In this problem the jobs are classified into families according to their similarity characteristics. Setup times are required on each occasion when the machine switches from processing jobs in one family to jobs in another family. The performance measure to be minimized is the total tardiness with respect to the given due dates of the jobs. The problem is classified asNP-hard in the ordinary sense. Since the computational complexity associated with the mathematical formulation of the problem makes it difficult for optimization solvers to deal with large-sized instances in reasonable solution time, efficient heuristic algorithms are needed to obtain near-optimal solutions. In this work we propose three heuristics based on the Iterated Local Search (ILS) metaheuristic. The first heuristic is a basic ILS, the second uses a dynamic perturbation size, and the third uses a Path Relinking (PR) technique as an intensification strategy. We carry out comprehensive computational and statistical experiments in order to analyze the performance of the proposed heuristics. The computational experiments show that the ILS heuristics outperform a genetic algorithm proposed in the literature. The ILS heuristic with dynamic perturbation size and PR intensification has a superior performance compared to other heuristics.

A Novel Disruptive Innovation-Like Algorithm for Single-Machine Scheduling with Sequence-Dependent Family Setup Times

“…We coded the DILA in C++ and executed it on an Intel Core i7 PC with a 3.4 GHz CPU and 4 GB RAM. A series of computational experiments were conducted to compare the results of all the combinations of the algorithms with the benchmark instances provided by Jacob and Arroyo [9]. The problem instances are characterized by four factors: the number of jobs n, number of families F, due-date range r, and setup-time range η.…”

“…The second set of experiments investigated the performance of the DILA using the best parameter values determined in the first set of experiments. We compared the performance of the proposed DILA with four heuristics [9]: HGA, ILS_BASIC, ILS_DP, and ILS_DP + PR. The results of the four heuristics are provided by Jacob and Arroyo [9].…”

“…We compared the performance of the proposed DILA with four heuristics [9]: HGA, ILS_BASIC, ILS_DP, and ILS_DP + PR. The results of the four heuristics are provided by Jacob and Arroyo [9]. For a fair comparison of these algorithms, 30 runs of the DILA were intentionally performed with a time limit of n*0.5 s for 1440 test instances, which is in the same stop condition as in Jacob and Arroyo [9].…”

A Novel Approach for Optimum Planning of Bobbin Boilers in Textile Industry

“…In sequence dependent setup, the setup time is variable according to the sequentially processed jobs. In sequence independent setup this period varies only according to the job to be processed (independent from the previous one) [26].…”