## 2 Materials and Methods
### Analysis Phase
#### 2.1.1 Scheduling Algorithms  
As briefly described in the introduction, there are a variety of algorithms for solving scheduling problems (Figure 1). Heuristics and metaheuristics find frequent application for AGV scheduling because they provide exact solutions to scheduling problems in favor of fast computational times [22]. However, there are some drawbacks in practice, as the problem and relationship between elements must be well known and heuristics do not guarantee finding an optimal solution [23]. Besides heuristics, metaheuristics have been developed as another promising optimization-solving technique for AGV scheduling problems. Tabu search, simulated annealing, and genetic algorithms are high-level heuristics that guide local search heuristics to escape from local optima [23]. Several studies have shown the effectiveness of metaheuristics for scheduling in comparison to simple dispatching rules [24; 25; 26]. Nevertheless, despite the successful implementation of genetic algorithms for improving optimization problems, tabu search and simulated annealing tend to be more efficient in finding the optimal solution in a reasonable time due to their operation on a single configuration and not on an entire population [27]. Furthermore, evolutionary algorithms such as ant colony algorithms, particle swarm optimization, artificial bee colony, or hybrid water water water optimization are metaheuristics that developed rapidly in recent years. Several authors have conducted research on their application in optimization and scheduling scenarios [28; 29; 30]. Additionally, exact methods mostly provide optimal results. However, mathematical optimization can have difficulties in efficiently handling larger systems, as the computational time often exceeds the time limits for real-time scheduling [31]. Figure 1: Algorithms for AGV scheduling problems identified in the literature. One emerging optimization approach within the exact methods is CP. CP is a type of optimization algorithm that uses constraint satisfaction and search techniques to find solutions for given problems. Constraint-based scheduling is one of the most successful application areas of CP, a mathematical optimization technique that makes use of artificial intelligence logic. Researchers explain its success due to the combination of the best of two fields of research: operations research and artificial intelligence [32]. CP is more flexible in comparison to mathematical programming. This is because the constraints, as well as the objective functions, are more general due to the decision variables, besides representing integer values, real values, and set elements or their subsets of sets [5]. Many researchers make use of CP for machine scheduling problems such as the JSSP and FJSSP [17; 18; 33; 34]. The major drawbacks of CP were long computational processing times for larger problem instances and that the building of models required empirical expertise [33; 34]. Due to developments over the last 15 years, CP solvers are now able to solve even large-scale instances where CP solvers performed worse than heuristics or metaheuristics [9]. Currently, CP solvers perform exceptionally well for most scheduling problems due to the significant improvements in recent years for larger problem instances [9; 17]. Furthermore, the application of artificial intelligence (AI) for solving scheduling problems is becoming more common [2]. One of the main application areas of AI to AGV scheduling that emerged during the review was reinforcement learning [22; 23; 24; 25; 26; 27]. In addition, [PERSON]. [38] proposed a neural-network-based multi-state scheduling algorithm for multi-AGVs in a flexible manufacturing system. Besides the individual application of artificial intelligence to AGV scheduling, more and more studies have focused on the integration of machine learning for traditional scheduling algorithms, and their findings illustrate performance improvements compared to individually applied methods [15; 39; 40].