## 1 Introduction  
Public transport is considered an important backbone of sustainable urban development, as it enables more efficient movement around cities. However, public transportation systems often struggle to provide a good level of service at an affordable price for public administration and users. These systems must provide a high quality of service that is attractive to users. They must also be affordable for low-income segments of the population. To achieve this objective, public systems inevitably require subsidies, which society is increasingly questioning [1]. Public passenger transport is an important area of public service that affects the standard of living and lifestyle of a population. As a mediator of transport relations in a territory, it influences the formation and development of settlements, economies, and landscape structures [2]. The efficiency of a transport system depends on several elements, such as the available technology, government policies, planning processes, and control strategies. The interaction between these elements is quite complex, which results in intractable decision-making problems [3]. The development of sustainable transportation is a priority in cities. Its objective is to increase the number of trips using public transport while minimising social costs and negative impacts on the environment [4]. However, operators often do not change the existing lines, stops, or timetables, which they justify based on passenger habits. This approach can create a mismatch between the availability and demand for public transport services. Therefore, planning and improving a public transport system should be based on a thorough analysis [5]. It is necessary to ensure the preference for public passenger transport over individual automobile transportation. The organisation and support of integrated transport systems is a trend in the public passenger transport sector [6]. The goal of integrated transport systems is to combine the advantages of individual types of transport and create a common, complex system of transport services in a defined region [7]. Regional public passenger transport is implemented within a larger territorial unit (e.g., a self-governing region) while ensuring connections between individual settlements in the region, especially between larger cities and between each municipality and its catchment city [8]. Regional transportation has become increasingly important. Current urbanisation processes place great demands on regional transport, as many people consider it more advantageous to live in smaller settlements in a region. This trend was made possible by automobile transport and rising living standards. In the case of passenger transport, it is therefore necessary to create mass transport systems capable of competing with individual automobile transport. Line-planning models differ in terms of the decisions involved (determining train routes, setting frequency of trains, or both) and take into consideration infrastructural and operational aspects, objective functions, and the way passenger decisions are considered in the decision-making process. The goal of route planning is to determine routes that are regularly served by a vehicle (trains, buses, trans, etc.) and the frequency of these connections. Route planning is a strategic public transport problem that was addressed early in the development of conventional public transport. The result, the so-called line concept, is then used as a basis for further decisions such as scheduling and vehicle planning. A condition for the design of public passenger transport lines is knowledge of the transport behaviour of the region's inhabitants, its causes, and development forecasts [9]. The proposal of a public transport system is a two-level optimisation problem. At the higher level, the system is designed by the operator, and at the lower level, passengers in the system choose travel that optimises their individual goal function.