# Area Division Using Affinity Propagation for Multi-Robot Coverage Path Planning
## 5 Experimental Results
This larger grid serves to emulate more complex real-world scenarios, thereby demonstrating the scalability and adaptability of the proposed AP algorithm in diverse, challenging situations. The computational experiments were conducted on a dedicated testbed configured to ensure accurate and consistent results. The hardware setup encompassed a high-performance workstation equipped with an Intel Core i7-9700K 8-core processor clocked at 3.60 GHz, bolstered with 32 GB of DDR4 RAM and enabling efficient data handling and manipulation, which were particularly critical given the size of the datasets and complexity of operations involved in Affinity Propagation. Table 1 shows the experimental results for each setup. For each algorithm, we conducted 20 experiments using the aforementioned parameters. The table shows the average values for the number of generated clusters and the cluster quality. It is worth mentioning that it is difficult to evaluate the proposed algorithm by directly comparing it with others found in the literature, since these algorithms are not configurable to identify the different cell types, elevation, and importance factor. Therefore, we could only compare the results of these algorithms by taking into account the quality of the clustering. The quality of clustering was calculated using the Silhouette Coefficient (SC) [28]. The SC, also known as Silhouette Score, is a well-established and popular metric for evaluating the quality of a clustering algorithm. The essence of this method lies in its dual-faceted measurement approach, quantifying both cohesion and separation simultaneously for each individual cell. It operates by comparing the average distance of a cell to all other points within its own cluster (cohesion) against the average distance to points in the nearest cluster (separation). The coefficient thus provides an aggregate measure of how similar a given data point is to its own cluster relative to other clusters. Higher values of the SC suggest that the cell is well-clustered and lower values imply that the specific cell might have been better assigned to a neighboring cluster. It is widely regarded well due to its intuitive interpretation, its capability to work with any distance metric (in our example the normalized distance as presented in Algorithm 1), and its agnosticism towards the specific clustering algorithm used. To properly evaluate the proposed algorithm, we calculated the SC not only for the average distances but also for the similarity with regard to elevation and floor type. The total SC calculated was weighted based on the respective weights of floor type and elevation. A more nuanced evaluation of the proposed algorithm was achieved by conducting multiple runs in the same environment but with varied importance factors attached to floor type and elevation. This exploratory approach aimed to investigate the algorithm's capability to adapt and respond to shifts in preference and the importance of environmental features. For this experiment, the main focus was on gauging the homogeneity of the resulting clusters. Homogeneity here was defined as the proportion of a cluster that exhibits uniformity in terms of either floor type or elevation. When the importance factor assigned to floor type was modified, we anticipated observing clusters that largely contain the same floor type. Consequently, the algorithm's sensitivity to floor type would be reflected by the degree of homogeneity of the resulting clusters. Analogously, when the emphasis is shifted to elevation, the homogeneity of the clusters, in terms of their elevation, becomes the pivotal measure of algorithm performance. The experimental results are presented in Table 2.  
The experimental results indicate that the importance factors affect the final clusters and their cells. It is important, however, to fine tune the exact values for each multi-robot CPP task, based on the capabilities of the available robots.