## 2 State of the Art
### Constraints  
#### 2.1.1 Setup Constraints  
Setup time, also called changeover, is a very important factor in the packaging industry because it may have a significant impact on the overall production cycle. It denotes the required time interval to prepare the necessary material resources. In many real-life situations, a setup often occurs while shifting from one operation to another. Setup time is classified into two categories: sequence-independent setup time and sequence-dependent setup time. Sequence-independent setup time depends solely on the current task regardless of its previous task. Sequence-dependent setup time depends on both the current and immediately preceding task [3; 4].  
There has been a growth in interest in incorporating setup times in many studies. The main reason why researchers have been motivated to utilize this assumption is to solve scheduling problems in a real manner [5] [PERSON] and [PERSON] [6] addressed the problem of \(F_{\rm m}|St_{sd},C_{sd},r_{i}|\sum ST_{i},C_{i}\). They first formulated the problem as an integer programming problem. Then, they employed a Lagrangian relaxation approach and finally developed a search heuristic. Three major types of heuristics were proposed by [PERSON] and [PERSON] [7], who explored the \(F_{\rm m}|St_{sd},C_{sd},r_{i}|\sum C_{i}\) problem, namely insertion heuristics (based on insertion heuristics for the traveling salesman problem), [PERSON]'s algorithm, and a set of naive greedy heuristics. They investigated these three patterns and identified the range of conditions under which each method performs well. [PERSON] et al. [8] proposed a mathematical programming model for \(F_{\rm m}|{\rm fmls},St_{sd}|\sum C_{i}\) as the problem is proven to be strongly NP-hard; two heuristic algorithms, tabu search (TS) and hybrid ant colony optimization (HACO), were developed to solve the problem. In addition, a lower bounding method based on the branch and price algorithm was developed to assess the performance of the metaheuristic algorithms. [PERSON] et al. [9] considered the \(F_{\rm 2}|{\rm wt},St_{sd}|\sum T_{i}\) problem; they developed several dominance properties, lower bounds, and heuristic algorithms and used the latter to develop an efficient branch and bound algorithm. [PERSON] et al. [10] tackled the \(F_{\rm p}|St_{sd}|C_{max}\) problem; they proposed a mixed-integer linear programming model to solve small-sized instances. Due to the strong NP hardness of the research problem, an effective metaheuristic, called pairwise iterated greedy (PIG) algorithm, was proposed to solve medium- and large-sized problems. [PERSON] and [PERSON] [11] proposed a mixed-integer linear programming (MILP) model for \(F_{\rm m}|St_{sd}|\sum T_{i}\) problem. They proposed a method to evaluate the total tardiness of a permutation sequence and also introduced a partial acceleration method to calculate the total tardiness in an insertion neighborhood. In addition, they developed a new heuristic to solve the problem efficiently. This heuristic was then integrated into the best metaheuristics available in the literature. [PERSON] and [PERSON] [12] studied the \(F_{\rm m}|St_{sd}|\sum wT_{i},wE_{i}\) problem. Three evolutionary metaheuristics were proposed.