## 4 Evaluation Results  
In our experiments, we have used the dataset from [16]. It contains data over three months linked to the ADLs performed by 10 older adults (ids 1 to 10) daily in their own homes. The data were acquired using a monitoring infrastructure based on wearable sensors and Beacons technology. Each ADL features a start and end time and one of the following activity labels: sleeping, eating (i.e., breakfast, lunch, snack, dinner), personal hygiene, reading, spare time/TV, walking, and outside. Not all the activities are registered for each person. Some of them do not perform specific activities such as going outside, or walking is highly dependent on their health state. The monitored older adults who volunteered to participate are aged between 70 and 85 years. All of them suffer from cardiovascular diseases. They live alone but have the support of their family. The ten apartments in which they live have similar plans and devices. They have the same number and types of devices that they use in their homes. Compared to the classification-based solutions where the number of persons in the dataset may influence the quality of the results obtained, in the case of our genetic solution, this is not the case. For each person, a different search space is created based on the daily activities' length intervals and probabilities for activities transition. They are rather personal and driven by individual conditions, wishes, and needs. They are encoded into the chromosomes and used in the reproduction phases to guide and balance the exploration and exploitation of the search space. No search information is being translated and used across the different persons' individual search spaces. To analyze the characteristics of the dataset used in experiments, we conducted an exploratory analysis using statistical graphs. Figure 8 shows the distribution of the average durations of each ADL for each person in the dataset, while Figure 9 illustrates the frequency of appearance of each ADL. Figure 8: The average duration of each ADL per person. Different colors are used for different persons: blue for id = 1, orange for id = 2, gray for id = 3, yellow for id = 4, lilac for id = 5, green for id = 6, red for id = 7, pink for id = 8, fuchsia for id = 9, brown for id = 10. The sleep activity has the longest average duration for all the persons in the dataset and the frequency of occurrence of breakfast, lunch, and dinner activities has a high degree of similarity for all the persons in the dataset. Higher differences in the frequency of occurrence are observed in the case of sleep, personal hygiene, or spare time/TV and reading activities. Moreover, there are persons with missing activities such as snacks, walking, reading, or outside. This is due either to the fact that the sensor did not record that activity, or because the person did not do that activity. The duration of activities, their frequency of appearance as well as the potential transitions among the activities influence the dimension of the search space:  
\[\prod_{ADL_{i},\ \ \ ADL_{j}\in ADLs}C^{2}_{ADL_{i}\to ADL_{j}} \left(\sum_{ADL\in ADLs}(\prod_{\textit{freq}\ (ADL)}*\mathcal{C}^{duration}_{ADL}\right)) \tag{15}\]  
where \(ADLs\) represent the set of activity labels from the dataset, \(C^{2}_{ADL_{i}\to ADL_{j}}\) the combinations of transitions among two activities in the dataset, \(freq\ (ADL)\) is the frequency of appearance of an activity and \(\mathcal{C}^{duration}_{ADL}\) all combinations of activities with their duration. Figure 10 also shows the distribution of sleep activity duration for a person. As can be seen, there is a variety of durations for each activity which makes the search space for daily routines quite big and difficult to be processed in a reasonable time by deterministic algorithms requiring the use of heuristics. Figure 10: Distribution of sleep activity duration over the days. Figure 9: The frequency of occurrence of each ADL per person.