## 2 Literature Review  
[PERSON] and [PERSON] [22] conducted the first study that proposed an exact methodology for UALBPs [23]. They developed a mathematical model of a UALBP, and then they proposed a dynamic programming procedure to balance small-sized problems. For larger problems, a greedy heuristic based on ranked positional weight was proposed. The UALAP then became a classic problem [24] and has been widely studied in the literature [25]. [PERSON] and [PERSON] [26] dealt with workload balancing problems in mixed-model U-shaped lines and designed an amelioration structure with a genetic algorithm (ASGA) to improve it. To implement the proposed algorithm, experiments were carried out on three test problems and a small-/medium-sized subsidiary factory of a major boiler-producing company in Japan. [PERSON] et al. [25] developed a genetic algorithm (GA) to balance a mixed-model U-shaped production system. They assumed that extra time is required for crossover workstations. In their proposed mathematical model, the objective was to minimize the number of crossover stations and maximize line efficiency at the same time. [PERSON] et al. [2] proposed a critical path method (CPM) to assign tasks to workstations in a U-shaped assembly line. They evaluated labor productivity in U-shaped line systems and straight-line systems, and they showed that the proposed CPM can reduce the minimum number of workstations for the assignment of tasks in a U-shaped line layout below the number needed in a straight-line layout. [PERSON] et al. [27] proposed an imperialist competitive algorithm (ICA) to simultaneously minimize the number of workstations and the variation in workload in a UALBP. The computational results show that the proposed algorithm outperforms GA, especially in large-sized test problems. [PERSON] and [PERSON] [4] proposed a simulated annealing (SA) algorithm for a resource-dependent UALBP, in which the duration of the task is dependent on equipment type and any assistance available. However, regular operators are available in a sufficient number to operate workstations but equipment and assistants are limited. The results show that the proposed SA algorithm is able to efficiently solve most small-to-moderate-sized problems to optimality or close to optimality. [PERSON] and [PERSON] [5] dealt with a robust UALBP, in which operation times were modeled using intervals, and a robust optimization model was developed. An iterative approximate algorithm was proposed and tested with some computational experiments. They concluded that the model and solution algorithm developed could form a good base for further research on the robust design and balancing of assembly lines, and related results can be found in [28; 29]. [PERSON] et al. [23] assumed that all workers carry out all tasks with unequal performance levels and formulated a mathematical model for worker assignment in a UALBP. Then, an Artificial Bee Colony Algorithm and a genetic algorithm were used to solve it. [PERSON] et al. [3] dealt with a UALBP and formulated an integer programming model. In the model, it is assumed that each task's time depends on the performance of the worker who performs it and that it is different for each worker. Moreover, a worker may not be capable of performing all of the tasks. They proposed a novel heuristic approach based on multiple rules to minimize the cycle time with a given number of stations. [PERSON] and [PERSON] [30] developed an efficient solution method for a UALBP. They compared six different solution methods. The results show that the proposed grouping genetic algorithm (GGA) with problem-specific crossover and mutation operators produces better solutions than the mathematical formulations and other solution methods available in the literature to solve different types of assembly line balancing problems. [PERSON] et al. [1] proposed a novel particle swarm optimization algorithm to solve a UALBP with stochastic task times. The results of the computational study show that the proposed approach performs quite effectively.