## 5 Numerical Experiments  
This section represents the practical part of the paper because, here, we report the results of the performed numerical experiments. The main goal of the following computational study was to analyze the suggested algorithm from the viewpoint of Pareto front approximation quality and computational requirements measured by consumed computational time. As far as available technical research support is concerned, a common PC equipped with the Intel(r) Core(tm) i7 4790 CPU@ 3.60 GHz processor and 8 GB RAM was used to implement all necessary functionalities. The suggested algorithm was coded in Java, making use of the NetBeans IDE 8.2 toolkit. The benchmark dataset that was employed came from our earlier research projects, the findings of which may be seen in [21; 22; 27; 28]. As all problem instances have their exact Pareto fronts, it is simple to assess the effectiveness of a suggested heuristic method. The dataset consists of the middle-sized instances representing real EMS systems operated in selected self-governing regions of Slovakia. The list of regions contains Bratislava (BA), Nitra (NR), Trencin (TN), Trnava (TT), and Zilina (ZA). The abbreviation in the brackets after each region name references a particular instance in the following tables reporting the achieved results. In the test problems, all inhabited network nodes represent both the set of candidates for an EMS station and the set of patients' locations. As the system criterion described by Expression (3) assumes that urgent pre-hospital healthcare is provided by the closest available service center, the parameter \(r\) was set to three. The associated probability coefficients \(q_{k}\) for \(k=1\),..., \(r\) were set in percentage  
Figure 3: The black circles correspond to the Pareto front members, and the empty circles denote the solutions met during the minimization process in the direction \(\mathbf{d}\). as follows: \(q_{1}=77.063\), \(q_{2}=16.476\), and \(q_{3}=100-q_{1}-q_{2}\). These values come from a simulation model of the EMS system in Slovakia [10]. The parameter \(T\) used in (4) was set to 10 min [21; 22; 27; 28]. Table 1 summarizes the basic characteristics of all studied problem instances. The left part of the table contains the problem size defined by the cardinality of the set of candidates for locating an EMS station. This value is denoted by \(m\). Then, the number \(p\) of located service centers is reported. The remaining part of the table reports the information about the exact Pareto fronts of included system designs. The symbol _NoS_ denotes the number of Pareto front members. The total area of the polygon that the Pareto front's members created is given in the column designated by _Area_. The right part of the table contains some additional information about the exact Pareto front for each benchmark. For each instance, we report four characteristics: Let _MLM_ denote the leftmost component of the Pareto front and let _MRM_ identify the rightmost one. Then, let \(f_{1}(\textit{MLM})\) denote the objective function value (3) for _MLM_, and similarly, let \(f_{2}(\textit{MLM})\) express Criterion (4) for _MLM_. We will follow the above-mentioned denotation also for the rightmost element, _MRM_. These four values can serve quite well to evaluate the Pareto front approximation quality when studying the heuristic method. Let us focus now on the experiments aimed at the suggested approach to Pareto front approximation. The obtained results are summarized in the following two tables. The left part of Table 2, denoted by _Exact_, contains the number of solutions _NoS_ forming the exact Pareto front together with the corresponding value of _Area_. The value of _Area_ expresses the absolute size of the polygon formed by all members of the Pareto front. The middle part of the table, denoted by _Currently available_, is used to report the results of the previously developed method, the results of which were published in [28].