## 2 Literature Review
According to the results of the survey regarding the FJSP [19], it was found that 88 publications (44.67%) utilized makespan as the only objective function, while another 78 papers (39.59%) used makespan in conjunction with another objective function. The same survey shows that hybrid techniques were used to solve problems in 35% of the case studies, evolutionary algorithms in 23% of the case studies, heuristic techniques in 9% of the case studies, and other techniques in the remaining 33% of case studies. Since then, several metaheuristics have been proposed to solve the problem. By considering the characteristics of the FJSP, [PERSON] and [PERSON] [20] proposed a kind of adaptive discrete cat swarm optimization algorithm with three objectives to be optimized simultaneously, i.e., makespan, maximal machine workload, and total workload, and they employed a heuristic-based strategy to generate the initial population. [PERSON] et al. [21] performed an evaluation with a combined improved version of nondominated sorting GA II and a surrogate measure to address the FJSP objectives, namely, makespan and robustness. [PERSON] et al. [22] proposed an efficient optimization algorithm that is a hybrid of the iterated greedy and simulated annealing algorithms to solve the FJSP with two objectives, which are simultaneously considered, namely, the minimization of the maximum completion time and the energy consumption during machine processing and material transportation. [PERSON] et al. [23] introduced a biobjective hybrid GA-hypervolume contribution measure that integrates GA with a multisearch algorithm and uses a hypervolume contribution measure (\(\Delta\)s) in its two-level selection strategy. A suitable method for solving the FJSP that belongs to evolutionary algorithms is the GA, since, in most cases, it can find the global optimum with a very high probability [11]. One of the GA's main characteristics is to directly operate on the problem structure without derivation and function continuity limitations. GAs also have inherent implicit parallelism and global searching ability and can adjust search directions automatically and self-adaptively [24]. In recent years, the usage of GAs to solve optimal scheduling problems has increased. A GA employs a set or population of individual solutions as its searching space and is extremely resistant to a hasty approach to the local extreme [11]. [PERSON] et al. [25] compared meta-heuristic algorithms GA, Tabu search, and Ant colony optimization (ACO) to solve the FJSP in a flexible manner and to choose dominant solutions. Based on the literature sources supplied, a job or working order may be characterized as a sequence of distributed machine actions. Each job or distributed operation in the searching space represents a viable solution to the optimization problem. The basis of genetic engineering is the alteration of individual genes. As the gene sequence represents the individual, it is evident that if an adequate method of representing the job sequence as the individual is utilized, GAs can be very suitable for solving scheduling issues. Given the foregoing, a GA was selected as a solution to solve the problem described in this research. It should be noted that the efficiency of the GA is dependent on the genetic operators of crossover and mutation, which differ depending on the issue type [11]. In the literature, optimization of a single criterion, namely, optimizing the schedule of manufacturing processes to minimize the time necessary for their execution, predominates. Nonetheless, it is vital to meet the makespan criterion, particularly for service-selling businesses. Even if makespan is minimized in a given time, the company's earnings must be sufficient to ensure its market viability. In this study, this sort of problem is considered.