## 1 Introduction  
A scheduling problem (SP) involves the efficient assignment of disposable resources (processors or machines) to complete one or several related tasks (jobs) over time [1]. SP is a relevant topic in science and engineering with a wide range of applications in diverse areas such as telecommunications [2], industry [3, 4], health [5, 6], agriculture [7], and education [8]. Due to its importance and impact on all aspects of human activity, SP is a well-studied problem in the scientific community. Many techniques and procedures have been proposed to solve its diverse variants. Almost any SP variant is NP-hard [9, 10]. Its study is essential to provide better solutions, take advantage of technological development, and implement more efficient solution procedures. A job shop SP (JSSP) is where a set of jobs, each composed of several operations, is processed on several machines without violating the precedence relations between the operations of all the jobs [11]. Two well-known JSSP variants are the flow shop SP (FSP) and the open shop SP (OSP). In a JSSP, jobs are processed on machines in identical order, visiting all or some of them. OSP has no precedence relations. Furthermore, an FSP is named as _flexible_ FSP when a job uses only one machine available of those arranged in parallel in each stage of its processing sequence. These variants can be subject to several constraints derived from real problem conditions, such as (1) blocking constraints, if there is no intermediate storage (buffer) between consecutive machines, and the current machine processing the job is blocked until the next one is available [12]; (2) no-wait constraints, if all the operations of one job need to be processed without any interruption [13]; and (3) sequence-dependent setup time constraints, when the machines need to be adjusted (setup time) before processing their following jobs [14]. In particular, an SP with sequence-dependent setup times is among the most challenging classes of scheduling problems [15]. With the implementation of flexible manufacturing systems (FMS) [16] and the increased use of information technologies in Industry 4.0, flexibility on production lines has become crucial for achieving a companies' objectives. Flexibility in FSP allows for the increasing of a factory's capacities and also a reduction in the bottleneck impact on conflicting stages [17]. Therefore, the flexible FSP (FFSP) has been used to model real-world cases, like that described by [PERSON] et al. [18] for one tile factory with four stages (pressing, glazing, furnace, and sorting and packing) using four identical machines in each one. Also, [PERSON] et al. [19] model an FFSP for the steelmaking process of an iron and steel complex in China which has three consecutive stages (steelmaking, refining, and continuous casting). Here, seven jobs were processed using several identical machines in each stage. As with other scheduling problem variants, branch-and-bound-based techniques, heuristics, and metaheuristics have been used to solve FFSP instances. Only sequential and parallel algorithms have been implemented in all of them, and the use of distributed algorithms in grid environments has been scarcely documented in the existing literature. Furthermore, few manuscripts address the FFSP with sequence-dependent setup times, and they are restricted to particular cases as no-wait or permutation schedules. For example, [PERSON] [20] describes a particle swarm optimization (PSO) algorithm used to solve several FFSP instances. This approach uses a random key scheme to transform the real-valued agents used by the PSO into valid schedules. The authors evaluate this proposal with several instances using several combinations of 30 and 100 jobs, two, four, and eight stages, and two, four, and ten parallel machines. Furthermore, [PERSON] [21] uses the same FFSP instances to evaluate several PSO-based versions such as standard PSO, passive congregation PSO, attraction repulsion PSO, discrete PSO, and hybrid discrete PSO with a local search (DPSO-LS).