Multi-objective Algorithms for the Single Machine Scheduling Problem with Sequence-dependent Family Setups Marcelo Ferreira Rego, Marcone Jamilson Freitas Souza DECOM – Universidade Federal de Ouro Preto CEP: 35.400-000 – Ouro Preto – MG – Brazil Email: marcelofr@gmail.com, marcone@iceb.ufop.br Jos´ e Elias Claudio Arroyo DPI – Universidade Federal de Vic ¸osa CEP: 36.571-000 – Vic ¸osa – MG – Brazil Email: jarroyo@dpi.ufv.br Abstract—This work treats the single machine scheduling problem in which the setup time depends on the sequence and the job family. The objective is to minimize the makespan and the total weighted tardiness. In order to solve the problem, two multi-objective algorithms are analyzed: one based on Multi-objective Variable Neighborhood Search (MOVNS) and another on Pareto Iterated Local Search (PILS). Two literature algorithms based on MOVNS are adapted to solve the problem, resulting in the MOVNS Ottoni and MOVNS Arroyo variants. Also, a new perturbation procedure for the PILS is proposed, yielding the PILS1 variant. Computational experiments real- ized over test instances show that PILS1 is statistically better than all other algorithms in relation to the cardinality, average distance, maximum distance, difference of hypervolume and epsilon metrics. Keywords–Single Machine Scheduling; Multi-Objective Opti- mization; Pareto Iterated Local Search; Multi-Objective Variable Neighborhood Search I. I NTRODUCTION Scheduling problems have been extensively studied in the literature. This fact is due to at least two aspects. The first one is the practical interest, since there are various applications on this class of problems in industry field, as for example, textile [1], electronics [2] and iron [3]. The other aspect that interests the study of this kind of problem is the theoretical interest, once most of the scheduling problems belong to the class of NP-hard problems [4]. There is a great amount of different and conflicting objec- tives to the scheduling problems, which can be highlighted [5]: • Makespan, which consists in minimizing the longest completion time of a group of jobs. The makespan’s minimization implies in a good usage of the machine; • Total weighted completion time or total weighted flow time, which measures the stock in process; • Total weighted tardiness, which consists in determining a scheduling whose total tardiness is minimum; • Total weighted earliness, which consists in determining a scheduling whose total earliness is minimum; • Total weighted tardiness-earliness, which consists in determining a scheduling with minimum value for tardi- ness and earliness of the jobs. This objective is related to the Just-in-Time philosophy on the production, in which a job must be completed as closely as possible to its due date; • Maximum lateness, which consists in minimizing the highest difference between ending time and due date of the jobs. Although the scheduling problems of the jobs involve various objectives, in most of the researches on this field only one objective is considered. When more than one is considered, usually it is defined only one objective rep- resented by the linear combination of involved objectives. Thus, the problem is treated normally in a single-objective approach. This work discusses the scheduling problem in single machines, wherein the setup time of the machine depends on the scheduling and the family of the jobs. The grouping of the jobs in the family occurs, for example, in the iron field. In [6], the author shows a manufacturing process of iron products (corner, rebar, bar, etc) on the lamination sector, in which jobs are grouped in families according to the products resembling. In this case, the products from the same family are those which differ between themselves by the thickness. On those circumstances, the setup time is so short and unimportant – when related to the processing time of the jobs – that is usual to consider it equivalent to zero. The advantage on making this grouping, thus, is that the jobs belonging to the same family – when processed sequentially – do not need setup time. On the problem in question, two optimization criteria are considered to be attended: makespan minimization and total weighted tardiness minimization. It means that, instead of looking for a solution which satisfies one or other objective separately, the main goal is to obtain a set of non-dominated solutions. This way, each solution belonging to this set would not be worse than any other one on the two objectives simultaneously. Noticing the computational complexity of the scheduling problems, the most used methods to solve them are the metaheuristic ones. Literature’s reviews have showed that 2012 31st International Conference of the Chilean Computer Science Society 1522-4902/13 $31.00 © 2013 IEEE DOI 10.1109/SCCC.2012.24 142