## 2 Literature Review
The performance criteria considered were the number of workstations (equal to the number of operators) and the variation of workload. [PERSON] and [PERSON] [11] proposed a new evolutionary approach to deal with workload balancing problems in mixed-model U-shaped conveyor assembly lines. The same task on different products is assumed to take the same time. The performance criteria were the same as [PERSON] et al. [25]. A case study was examined as a validity check in collaboration with a manufacturing company. [PERSON] et al. [26] dealt with U-shaped conveyor assembly line balancing problems in which task times are uncertain and corresponding historical information is not available due to technology changes, environmental changes, or the effect of learning on the part of operators. An uncertain programming model that minimizes the number of workstations was proposed first. Then, the uncertain model was transferred into a deterministic model to reduce computational effort. Finally, an algorithm was developed based on a branch and bound memory algorithm to find the optimal solution. AlthoughHwang et al. [25], [PERSON] et al. [11] and [PERSON] et al. [26] dealt with U-shaped conveyor assembly line balancing problems, they ignored walking times. U-shaped assembly line balancing problems are similar to the proposed problem, but most of them also ignored walking times. In recent years, [PERSON] et al. [27] addressed the Type 2 U-shaped robotic assembly line balancing problem, in which the objectives are to minimize the cycle time and energy consumption simultaneously. The Pareto artificial bee colony algorithm (PABC) is extended to tackle this problem. [PERSON] et al. [28] applied an occupational repetitive action method to calculate the ergonomic risk value. A worker assignment and balancing problem of Type 2 for a U-shaped assembly line to minimize cycle time and ergonomic risks was then formulated. A multi-objective restarted iterative Pareto greedy algorithm is proposed to tackle this problem. [PERSON] and [PERSON] [29] described a differential evolution algorithm for solving U-shaped assembly line balancing problems. The objective is to minimize cycle time for a just-in-time production line that produces a single product with a certain number of workstations. [PERSON] [30] considered a U-shaped assembly line balancing problem with stochastic assembly times. Two new chance-constrained non-linear models are proposed. The results are compared with the results of modified ant colony optimization and a piecewise-linear programming model. The study shows that the proposed two models are more effective and successful in solving stochastic U-shaped assembly line balancing problems. [PERSON] and [PERSON] [31] dealt with the parallel adjacent U-shaped assembly line balancing problem. Operators and robots are assigned to execute assembly tasks in the same work cycle. Assembly tasks located in two adjacent U-shaped assembly lines can assigned to the same operator or robot. Moreover, both fully able and disabled operators are considered. A mathematical model with five objective functions is developed. Then, non-dominated sorting teaching-learning-based optimization is proposed to solve the proposed problems. [PERSON] et al. [32] aim to optimize activity-to-station and operator-to-station decisions in a U-shaped assembly line balancing problem. Criteria such as equipment cost, number of stations and quality of activity performance are considered simultaneously. As an approach to solving the problem, classical simulated annealing (SA), variable neighborhood search (VNS), and a genetic algorithm (GA) were adopted for optimization. Very few studies consider walking times in U-shaped assembly line balancing problems. [PERSON] and [PERSON] [33] considered walking times and formulated the optimal operator allocation problem to minimize the overall cycle time and discussed the two operator allocation problem as a special case.