## 5 Result and Discussion
### Algorithms' Performance Based on an Empirical Evaluation
#### 5.4.1 Performance According to Log Complexity  
The event log complexity depends mainly on the number of trace variants and on how many times each trace variant is repeated in the event log. A trace variant is a particular sequence of activities that can occur multiple times in the event log. This set of experiments evaluates how the algorithms perform under different event log settings: varying the number of trace variants and varying the number of repetitions of each trace variant in the event log. Notice that alignments will be computed for each trace variant and reused for all cases of this variant. Therefore, no significant impact is to be expected when varying the number of repetitions of each trace variant. The configurable process tree contains nine configurable nodes that have mixed dependencies. There are eight configurable nodes that include \(\{H,E\}\) as configurators and one configurable node that has \(\{H,B,E\}\) as configurators. The set of feasible configurations allowed by the configurable process model can be generated based on the Cartesian product, obtaining \(2^{8}\cdot 3^{1}=768\) feasible configurations. Three different target models (universities \(A\), \(B\) and \(C\)) derived from the original configurable process model were used for experimentation; the number of activities for the models corresponding to universities \(A\), \(B\) and \(C\) are 66, 65 and 55, respectively. Based on these target models, different event logs were simulated. Table 7 summarizes the experiments. In the first set of experiments, the number of trace variants is varied. In this case, a random number of trace repetitions between 10 and 20 is considered for each trace variant. The final number of traces is therefore different for each university. In the second set of experiments, the number of trace variants is fixed to 100, and then, the number of trace repetitions is varied. A synthetic event log was created per each experiment; thus, 21 event logs were tested with each algorithm. Table 8 displays the results obtained with each algorithm when varying the log complexity. Exhaustive strategy evaluation:  
As a force-brute method, this strategy searches over all possible configurations that can be applied to the configurable process model. As seen in Figure 15(a), computing time increases linearly when increasing the number of trace variants. For event logs with 500 trace variants, the algorithm takes several hours; in the worst case scenario, the university \(C\), it takes more than 40 h to obtain the optimal derived process model. Figure 15(b) shows how the algorithm performs if we set the number of traces to 100 and we vary the number of trace repetitions. In this case, the computing time is not proportional to the log size as when we vary the number of variants; in fact, the computing time is almost constant. This is a feature of the conformance method applied in our implementation to compute the conformance metric. It uses a cache table: if a trace variant has already been evaluated, it is not evaluated again. Therefore, we can observe that the computing time is only proportional to the number of trace variants in the event log, regardless of the number of trace repetitions. Genetic strategy evaluation:  
As a heuristic method to search for a desirable configuration, the genetic method has some parameters. We set the maximum number of generations to 20 and the population size to 10. For all experiments, the genetic strategy found an optimal configuration, which allows one to obtain an optimal derived process model; in fact, it obtained the same results as the exhaustive strategy. Figure 16(a) shows that there is a linear dependency between the computing time of the genetic strategy and the number of trace variants. Meanwhile, Figure 16(b) depicts the computing time of the genetic strategy, which is nearly constant when varying the number of trace repetitions while keeping constant the number of trace variants.