## 2 Materials and Methods
### Testing of Optimization Results
#### 2.3.2 Optimization Testing  
Most available studies on geodetic network optimization use only one or two sites/networks. This can, however, yield falsely favorable and optimistic results. Such a situation could arise even when using four networks as originally proposed in this paper. For this reason, we performed 500 modifications of each of the basic networks (hereinafter referred to as network variants), which differ in the position of individual points. As shown in the example in Figure 3 (square-like network), these positions were generated pseudo-randomly within a certain range around the original points (detailed in Table A1). For each of the network variants, a calculation using all four algorithms (described in detail in Section 2.2) was performed. In the first test, the optimal number of measurements was determined by brute force, i.e., by scanning all possible combinations and selecting the one that contains the fewest number of measurements (groups of measurements) and meets the desired precision. In subsequent tests, the optimal number of measurements given the computational complexity of the brute force solution was determined as the smallest one found by our algorithm. To be able to compare the efficiency of individual algorithms, the results need to be normalized. In our study, this normalization was calculated as the ratio of the number of measurements acquired using the respective algorithm divided by the optimal number of measurements (if known) or by the best result of all four algorithms, expressed as the percentage. In other words, the optimal solution is 100%, and suboptimal solutions are characterized by numbers >100%. Statistical evaluation was then performed for all algorithms using the results from all 500 network variants for each network and the results are presented as the mean normalized  
Figure 2: Testing networks: (**a**) square-like network; (**b**) triangular network; (**c**) bridge network; (**d**) building network; the coordinates of the points can be found in the Table A1 according to the point numbers. performance (MNP) of the algorithm for the particular network and the percentual success in optimal result detection (ORD). We chose 500 variants as an essentially extreme number in order to make the statistical uncertainty of the results practically negligible. In addition, the best result achieved by the combination of all four algorithms was also evaluated. Multiple tests were performed for each of the networks as will be described below. (1) Brute force evaluation  
To be able to objectively evaluate the success of the optimization method, we need to know the absolute optimal solution, which can only be achieved using brute force calculation, i.e., by calculating all possible solutions and selecting the one that provides the required accuracy with a minimum effort (absolute optimum). This approach is, however, computationally demanding and, as a consequence, it is applicable only for the square-like network (the computational demands grow exponentially with the number of possible measurements in the network), and even this was performed only for 50 network variants. In all, four tests with different required accuracies and measurement accuracies were performed (see Table 2). (2) Large-scale comparison of optimization algorithms on all networks  
The brute force comparison (A1-A4) was, due to the computational demands, only possible for the simplest (square-like) network and a limited number of network variants (50). Hence, a mutual comparison of all algorithms for all networks with a large number of network variants (500) against the absolute objective optimum was not possible. Instead, the result achieved by the algorithm showed the best performance for the network variant and a combination of the parameters served as the reference (100%) for the particular combination of parameters. The reader can note that accuracy requirements differ among networks. This was estimated in view of the network size (maximum distance between points)--with growing