## 1 Introduction
The use of different variable neighborhoods (VNs) to refine the local search is proposed in [23] to minimize the makespan. Another algorithm combining TS and VNs is described in [24] for a different multi-target version of the FJSSP. In [25], the FJSSP is studied considering maintenance costs, where a hybrid genetic algorithm (HGA) uses a local search based on simulated annealing (SA). The combination of the Harmony Search (HS) algorithm with other heuristic and random techniques is analyzed in [26] to handle two discrete vectors, one for the sequence of operations and the other for machine allocation, to minimize makespan. Another hybrid algorithm between artificial bees and TS is presented in [27], where the quality and diversity of solutions is rated with three metrics. Task rescheduling is investigated in [28], for which another hybrid technique was proposed using a two-stage artificial bee colony algorithm with three rescheduling strategies. Another hybrid method is introduced in [29] by applying an artificial bee colony algorithm (ABC) and a TS, introducing new reprogramming processes. In [30], a hybrid algorithm is implemented using PSO with random-restart hill-climbing (RRHC), obtaining a competitive and straightforward algorithm compared with other techniques. Another hybrid algorithm based on GA is presented in [31] for a new specification of the FJSSP that considers the human factor as a multi-objective problem. In [32], a PSO-GA hybrid algorithm is proposed to minimize the workload and the makespan. The minimization of inventory costs and total workflow are studied in [33], which involves a hybrid algorithm between the ABC algorithm and the modified migrating birds optimization (MMBO) algorithm to obtain satisfactory results. Another hybrid method is put forth in [34] based on SA and saving heuristics to minimize the energy consumption of machines, taking into account their deterioration to determine the precise processing time. In [35], the FJSSPwith fuzzy times is solved with a hybrid multi-verse optimization (HMVO) algorithm. A hybrid approach to general scheduling problems is discussed in [36], considering batch dimensions, rework, and shelf-life constraints for defective items. The algorithm applies late acceptance hill-climbing (LAHC) and analytic procedures to accelerate the process. The computational results show the benefits of using hybridization techniques. In [37], a two-stage GA (2 SGA) is developed; the first stage is to choose the order of operations and the selection of machines simultaneously, and the second is to include new variants that avoid population stagnation. A hybrid algorithm that combines brain storming optimization (BSO) with LAHC is advanced in [38]; the BSO is adapted to the FJSSP to explore the search space by grouping the solutions, and the exploitation is performed with the LAHC. The hybridization of the human learning optimization (HLO) algorithm and the PSO is analyzed in [39], again applying the HLO for global search and an adaptation of the PSO to refine the local search. The above-mentioned works suggest that hybrid approaches are still a developing research trend in solving the FJSSP and its variants, for which many of these works use GA in conjunction with another technique for local search. However, to our knowledge, no work has applied GA operators based on a cellular automata-inspired neighborhood to explore solutions and their hybridization with the RRHC for the refinement of these solutions. This article proposes a new hybrid technique called GA-RRHC that combines two metaheuristic techniques: the first for global search using genetic algorithm (GA) operators and a neighborhood based on concepts of cellular automata (CA) used mostly on the programming of the order of operations. As a second step, each solution is refined by a local search that applies random-restart hill-climbing (RRHC), in particular, to make the best selection of machines for critical operations, which is more convenient for problems with high flexibility.