## 2 Related Works
### Towards Process Model Optimization
Here, the authors merge similar behaviour after an alternative using folding equivalence. This typically generalizes the behaviour of the net and reduces its complexity. So, aggregation techniques are good options to abstract a process model and possibly simplify it at the price of losing some information. Unsupervised learning has found uses in different tasks and fields including PM. It is common for trace clustering to be applied in a discovery step. In this regard, the event log is divided into sub-logs to produce more accurate process models for each cluster. However, the clustering techniques need a robust similarity metric [37]. They also should incorporate PM quality measures since data mining criteria only assume the improvement of discovery results. Thus, the authors in [38] propose a semi-supervised method with a selection step for a greedy accuracy optimization for each cluster. Despite the high computational complexity, the novel approach performed better than MRA-based clustering in terms of accuracy. A \"slice-mine-dice\" technique is proposed in [39] to cluster traces reaching the specified complexity threshold. The results showed improvement in the number of clusters and process model cumulative size in comparison to three existing trace clustering methods. Contextual information is utilized in [40] in a modified k-medoids clustering algorithm. Standard process is assumed to be more frequent and stable in a time perspective. So, occurrence frequencies and overall cycle times are included to support grouping of similar process variants. Using the first \(k\) most frequent processes as medoids has improved the clustering quality in several heterogeneous cases. However, identifying the proper value for \(k\) is still an open issue. In [41], the coefficient of variation is used to determine the number of clusters of clinical pathways represented as state (department in a hospital) sequences. The clusters with an insufficient number of sequences were discarded before the discovery, where identification of typical pathways is based on an alignment algorithm from bioinformatics. Clustering can be performed not only for traces but for events, too. A two-level clustering approach is proposed in [42] to categorize complex events first and to group obtained processes after, as well as to distill clinical pathways in real cases. Such approaches aid the abstraction of undesired details and, therefore, simplify models, but mostly in an uncontrolled manner. The automated control of finding a simple and/or precise process model can be explicitly defined as an optimization problem. For example, [PERSON] et al. [44] optimized the accuracy of a business process simulation model discovered by the Split Miner. They searched for optimal hyper-parameters of the miner to maximize the accuracy measured using a timed string-edit distance between the original and the one simulated by the model event logs. However, there is always the trade-off between several quality dimensions [3], where the most common one is between model complexity and its fitness/precision. Within integer linear programming, the authors in [35] define the process model optimization problem mathematically, where a linear constraint is a complexity threshold (a maximum number of nodes and arcs) and a replayability score aimed to be maximized. They solve the optimization task with a tabu search algorithm utilizing element frequencies to quickly identify promising moves. The approach outperforms commercial tool results in terms of replayability for small and middle complexity (from 1 to 50 nodes). A similar problem is formulated in [45] but including time-related information in the replayability score of discovered grid process models. The tabu search with optimized edges is shown to be more efficient than other methods for a small event diversity. In [46], rule discovery hybrid particle swarm optimization is proposed to find near-optimal process models. Here, the simulated annealing is applied on each particle position when it is updated.