Lexicographic optimization-based clustering search metaheuristic for the multiobjective flexible job shop scheduling problem

In recent years, the flexible job shop scheduling problem (FJSP) has received a great deal of attention from researchers not only due to its complexity but also due to its wide range of applications in the industry. The FJSP extends the job shop scheduling problem (JSP) by allowing operations to be processed by a set of alternative machines. Many of the studies found in the literature consider the objective of minimizing the largest completion time of the jobs, that is, the makespan. However, in the real context of industries, considering more than one criterion is often relevant. Thus, the present work addresses two additional criteria besides the makespan: minimizing the maximum workload of the machines and minimizing the total workload of the machines. Aiming at real cases, where it is necessary to define priorities among the criteria, a clustering search (CS) algorithm was implemented using a lexicographic classification of the objectives for solving the multiobjective FJSP (MOFJSP). The results of this study show that compared to the state-of-the-art approach, CS is an effective alternative to solve the MOFJSP.