## 2 Literature Review
### Transfer Line Balancing Problem  
Transfer lines are production systems that consist of serial stations where operations are continuously performed [1]. TLBP consists of assigning the set of indivisible units of work elements to a set of sequential workstations for certain environments (dedicated, flexible, or reconfigurable transfer line). Transfer line balancing problems were first reported by [PERSON] [5] and first presented by [PERSON] et al. [6] for the dedicated transfer line. Another type of balancing problem, closer to the one considered in this paper, was first introduced by [PERSON] et al. [7]. They considered the flexible or reconfigurable transfer lines. The transfer line has multiple stations that consist of one or more identical machine tools operating a given set of sequenced tasks, and each station is usually equipped with single spindle machine centers. Different from classic TLBP, this has two more relevant problems inside, which are called the line configuration problem and the operation allocation problem. The line configuration problem defines the number of stations and the number of parallel machine tools per station, while the allocation problem defines the operations allocated to each station and their positions in the station operating sequence.  
To our knowledge, this kind of TLBP was first studied by [PERSON] et al. [7]. The authors introduced a mixed integer programming method for which minimizing the number of machine tools was considered as the single objective function. A greedy heuristic-based approach was then presented to solve this problem [8] with the same objective function. Later, an ant colony algorithm [9] and a greedy randomized adaptive search [10] were proposed with a single objective combining the performance of line balancing and the number of stations and of machines. A set partitioning model-based approach was proposed by [PERSON] et al. [11; 12] to solve the problem. The aim was to minimize the number of machine tools. TLBP was transformed into a linear integer program based on the set partitioning model, where the operation sequencing for each station was optimized. A genetic-based approach [13] was also proposed, where the decoding heuristic was designed. This approach considered a single objective function (the total number of  
Figure 1: Three-dimensional model of the four kinds of engine blocks.  
machine tools) introducing a value punishing the infeasible solutions. In addition, the hybrid techniques of Benders decomposition and an ant colony algorithm were proposed by [PERSON] and [PERSON] [14] to obtain the optimal configuration of the production line by minimizing the non-productive time.  
A simultaneous approach was proposed by [PERSON] et al. [15] combining the \"balancing problem\", the \"scheduling problem\", and the \"equipment problem\", and using multi-objective optimization. In this approach, the balancing problem was used to decide the allocation of machining tasks to stations and the number of stations, the scheduling problem focused on sorting machining tasks inside stations, and the equipment problem was used to select the number of parallel machines for each station. Three sub-methods were proposed and combined to sequentially solve the corresponding sub-problems. During the optimization, the authors created a solution pool to carry the feasible plans, where new feasible plans with a lower cycle time would be obtained through combining two solutions as parallel production lines. Finally, Pareto optimizing was introduced to analyze the solution pool.