## 5 Conclusions  
The paper presents a method allowing one to obtain a quick draft of a metro network. Since the task is computationally complex, the two-stage approach with the use of the genetic algorithms was proposed. The method was applied to prepare a preliminary design of the metro network for the central part of the Upper Silesia region in Southern Poland. In the first stage, the optimal locations of stations accounting for population density were found. In the second stage, the optimal lines topology was established; here, two alternative assumptions were considered: just the network coherency was required, or the high radiation accessibility was expected. Two variants of the metro network with three or four metro lines were checked too.  
The obtained results were the effect of a few hours of calculations using a standard PC with i7 CPU 2.9 GHz and 8 GB RAM. Some effort was required to tune the optimization parameters. The input data were in the form of simple bitmaps, which allowed one to examine different variants of the assumed inputs.  
The presented approach can be helpful regarding preliminary considerations of a metro system structure. As no precise data concerning transportation demands and construction costs were introduced into the model, the obtained results cannot be regarded as the final design of the metro system. This concerns mainly the problem of stations locations--this issue requires additional considerations on street topology and the location of other urban facilities. The presented results can be the basis for discussing some variants of stations layout or lines topology. They can be subjected to the public discussion. They can also be used when estimating the required budget.  
Figure 10: Progress of the process of the optimization of lines topology.  
An important finding is that the requirement of the high radiation accessibility will result in a significant increase of building costs (of about 30%). Otherwise, the increase of the average trip length should be expected (of about 60%). The finally chosen option depends on the budget available. Obviously, a trade-off solution is reasonable as well, but it cannot be found using the presented model as it is currently. At present, the model just minimizes the relative construction costs. Thus, it should be extended to take into account the explicit budget limitations and the real construction costs. It was also shown that the level of service and the costs do not depend significantly on the number of the metro lines.  
Despite the mentioned limitations, the obtained results give an insight into the designed metro system structure. The main advantage of the presented method is the possibility to quickly make a draft of topology of the metro network by introducing only the basic data describing the analyzed region. The simplicity of the presented model makes it possible to easily change the introduced data to analyze different scenarios of the future development of the region.  
All the above remarks do not mean that the applied method--the genetic algorithm--is unable to provide a detailed design of a metro system or any of its components. Artificial intelligence methods, including genetic algorithms, can be applied at any level of the design process. The accuracy of the obtained results is limited only by the model structure, not by the applied optimization method.  
[PERSON] participated in the preparation of the research. He built the numerical models, tuned the controlling parameters, and took part in the optimization analyses. He participated in the writing of the article. [PERSON] took part in the data acquisition and in the optimization analyses. She analyzed the obtained results. She participated in the writing of the article as well.  
This research received no external funding.  
* Publication supported as a part of the Rector's habilitation grant. Silesian University of Technology, grant number 12/050/RGH18/0071.  
The authors declare no conflict of interest.