## 1 Introduction  
Production planning is a priority factor in modern manufacturing systems [1], where a critical aspect is the scheduling of operations and resource allocation [2]. Each industry must find a better solution for its respective production scheduling jobs to execute efficient manufacturing on time or launch new products to meet market demands satisfactorily [3]. This paper analyses the topic of task scheduling with flexible machines, also known as the flexible job shop scheduling problem (FJSSP), especially concerning instances with high flexibility, where many machines can process the same operation. The FJSSP reflects the current problem faced by manufacturing industries in the allocation of limited but highly flexible resources to perform tasks in the shortest possible time [4]. In the FJSSP, the goal is to find the most appropriate job sequencing, with each job involving operations with precedence restrictions, in an environment where several machines can perform the same operation but quite possibly in different processing times. Thus, the FJSSP is an NP-hard combinatorial problem where for a bigger number of jobs, there is an exponentially higher number of possible solutions [5]. It is thus impossible to review all solutions to find the optimal scheduling in a suitable time that minimizes the processing time of all operations [6]. Many mathematical methods have been proposed to resolve scheduling problems [7]; some works have approached the FJSSP using the branch and bound method [8], linear programming [9], or Lagrangian relaxation [10]. These methods ensure global convergence and have worked very well in solving small instances, but their computational time makes them impractical for problems with dozens of scheduling operations [6]. That is why many researchers have chosen to move toward hybrid heuristic and metaheuristic techniques. Over the years, distinct metaheuristic methods have been applied to solve combinatorial problems, including evolutionary algorithms using the survival of the fittest; an example is genetic algorithms (GAs) [11; 12]. Other metaheuristics are ant colony optimization (ACO) [13], particle swarm optimization (PSO) [14], tabu search (TS) [15], etc. These algorithms have been adapted to different programming problems, finding good solutions with low computational time. The FJSSP is an extension of the classic job shop scheduling problem [16]. In the inital problem, the optimal allocation of operations is sought on a set of fixed machines. In the FJSSP, several feasible machines can perform the same operation, often with distinct processing times. Two problems must be considered to solve an instance of the FJSSP: the order of operations and the assignment of machines. In [17], the FJSSP is approached heuristically, applying dispatch rules and tabu search and further introducing 15 instances with different numbers of tasks and machines. Since this work, different heuristics and metaheuristics conducting some hybrid searches have been investigated to solve this problem. An algorithm using TS and a simplified computation of the makespan are explained in [18], highlighting the importance of critical operations for local search. In [19], a hybrid algorithm (HA) using GA and TS is proposed to minimize the makespan. Its model maintains a good balance between exploitation and exploration. In [20], a multi-objective problem (MO-FJSP) is addressed applying the non-sorting genetic algorithm (NSGA-II) together with a bee evolutionary guide (BEG-NSGA-II) to minimize the makespan, the workload of the most-busy machine, and the total workload. In [21], a combination of genetic algorithm and a variable neighborhood descent method is shown to optimize a multi-objective version that takes into account the makespan, the total workload, and the workload of the most-busy machine, using two methods of local search. Another hybrid algorithm using the PSO and TS is presented in [22], again for a multi-objective problem.