## 2 Literature Review  
Trip planning is a key process in public transport, wherein passengers are informed how to best use a given public transport system for their individual travel needs. A common feature of most available journey planners is that they assume deterministic travel times; however, public transport vehicles often deviate from their schedules. In a previous study [10], the problem of finding path plans in a stochastic environment was investigated. To take full advantage of the flexibility inherent in multiservice public transport systems, the authors suggest using a routing concept instead of a linear route plan. One of the basic problems in the strategic planning of public and railway transportation is the line-planning problem [11] for determining the system of lines and related frequencies. The goals of the planning process are typically multiple and often conflicting. The operator wants to minimise costs, while passengers want to have the smallest possible fares, without any or with only small transfers between different lines. Previous research [12] has combined route-planning models and a transport assignment model to overcome this problem. Public transport planning at the strategic level refers to the design of a public transport network, which includes the determination of public transport stations and the development of public transport routes [13]. The modelling and solution planning of public transport lines have been described in [14]. Network designs can respond to slight fluctuations in passenger demand if designed robustly [15]. In previous research [16], the authors showed that, instead of further optimising each individual step, it would be more beneficial to consider the entire process in an integrated manner. The authors proposed a custom model that they applied to three planning phases and showed how it can be used to design iterative algorithms as heuristics for an integrated problem. The planning process for public transport is the first step of the route design, and schedule calculation is the second step. Finally, the vehicle and crew schedules are planned. The authors proposed a change in the order of the classic sequence of the planning steps. In their new approach, they first designed vehicle routes, divided them into lines, and finally calculated a (periodic) timetable [17]. A more detailed overview of line-planning concepts and models is described in [18]. In [19], the challenges of network design, operational planning, and control of intelligent public transport systems were discussed. Defining suitable lines in a public transport system (bus, rail, tram, or metro) is an important real-world problem. The authors in [20] investigated the problem of designing lines in a public transport system, wherein they included the user's optimal choice of route [21]. There have been many studies aimed at optimising the network of public passenger transport lines using linear programming models and optimisation algorithms [22]. The authors in [23] presented a mixed-integer linear programming model that they developed to design tools for finding solutions for planning lines and timetables in automated urban metro networks. Despite the recent progress in the field of automatic public transport route optimisation, there is a clear gap between the development of optimisation algorithms and their applications in real planning processes [24]. For each planning area, the approach in [25] uses a network reduction process that requires relatively few network evaluations. The network reduction process begins with a network of the shortest lines. The lines are then gradually deleted, merged, or shortened using an optimisation algorithm. Nonlinear integer formulations for power lines that connect main lines and minimise transfer times were investigated in [26]. Further research [27] resolves the public transport network model based on layer operations; Ref. [28] solves the network route design of a public transport system with network evolution; Ref.