## 1 Introduction  
The optimization of geodetic networks is an important component of geodetic practice. Although methods such as laser scanning or photogrammetry gradually take over in the collection of spatial data over larger extents, measurement using total station remains crucial where local measurements for construction purposes are concerned. This method also remains indispensable in the measurement of deformations of, e.g., human-built objects [1, 2] or natural scenes [3]. The sufficient and known accuracy of survey results [4, 5] is a fundamental prerequisite for the successful construction process, and the aim of geodetic network optimization is to minimize the costs of constructing and maintaining the network while maintaining the required accuracy and reliability. Many methods have been proposed for this purpose; however, not all of them are suitable for the relatively complex mathematical problem of geodetic networks. The geodetic optimization method should be applied wherever the required accuracy of the measurement result is not easily met by the simple use of geodetic instruments, and where the quality of the subsequent construction process or the safety of the building operation depends on the accuracy achieved. These are, e.g., surveying activities in bridge construction [6], the determination of coordinates of staking out geodetic network [7], and the monitoring or measuring of structures above ground [8, 9] or below ground [10, 11, 12]. The basics of optimization in the field of geodetic networks have been laid down in the 1950s to 1970s. The general objective function for geodetic network optimization was introduced by [PERSON] [13]. Recently, [PERSON] followed up on his work [14], comparing the suitability of single-criterion or multi-criterion optimization approaches. Scalar objective functions describing the accuracy and the properties of these functions were investigated in detail by [PERSON] [15]. Together with [PERSON] [16], they defined a matrix objective function using the Taylor-Karman structure of the covariance matrix. [PERSON] then laid down the principles of objective functions for reliability [17]. [PERSON] classified the optimization of geodetic networks into four types, depending on the optimized parameters [15]. Namely, these are termed zero-order design (ZOD) to third-order design (TOD). The ZOD, the basics of which are described by [PERSON] [18], focuses on the coordinate system definition; it has, however, not gained much popularity. The first-order design (FOD) deals with the optimization of the network configuration, i.e., the locations of the network points. It was investigated in detail, in particular by [PERSON] [19], who optimized the position of the points through very small coordinate changes using the Taylor-Karman structure as the objective function. [PERSON] and [PERSON] [20] presented a different approach to the FOD, using a heuristic method of simulated annealing for the optimization of the covariance matrix determinant [21]. They demonstrated this approach using two examples; however, in the more complicated of these examples, the optimization led to the convergence of the optimized points towards the center of gravity, leading to their final position on the borders predefined to limit their further convergence to the center of gravity. This indicates that even though the optimization of the network shape to maximize the accuracy might have seemed an interesting concept, it is not practically applicable as the mathematical solution necessarily always ends up on predefined borders designating the smallest allowed network (as seen, e.g., in [20] or [22]). The cause is simple: the errors generally grow with distance, and the simplest mathematical solution for improving accuracy, therefore, reduces the distances. Without setting the borders and continuing in optimization according to the FOD, the entire network would eventually converge into a single point.