###### Abstract  
Modern cities heavily rely on public transport systems to enhance citizen access to urban services and promote sustainability. To optimize public transport, intelligent computer-aided tools play a pivotal role in decision making. This article tackles the complex challenge of bus timetabling, specifically focusing on improving multi-leg trips or transfers. It introduces a novel multi-objective Mixed-Integer Programming Linear (MILP) model that concurrently maximizes passenger transfers and minimizes budgetary costs, while also adhering to the minimum required quality-of-service constraints for regular (non-multi-leg) trips, and an exact resolution approach based on the \(\varepsilon\)-constraint method to obtain a set of efficient solutions is used. The competitiveness of the model is validated via a computational experimentation performed over real-world scenarios from the public transportation system of Montevideo, Uruguay. The findings evinced that the MILP model was able to compute a set of Pareto efficient solutions that explore the tradeoff between the number of successful transfers and the cost of the system. Moreover, the best tradeoff solutions surpass the current city timetable, excelling in both the number of transfers and cost efficiency. s +
Footnote †: journal: Applied Sciencestransportation over private vehicles, the operation of public transport systems must be adapted to the needs of inhabitants [8; 9], which requires a careful planning stage of the public transport modes. Planning and operation of public transport systems involves several decision-making problems including route design, timetabling, and drivers' scheduling, among others [10]. This work focuses on the timetabling problem, i.e., determining bus trip frequencies for a specific operating period [11]. Achieving synchronization of multi-leg (transfer) trips is a critical aspect of the timetabling problem. Synchronization implies ensuring that passengers that have to combine different modes of transport (e.g., different bus lines) to reach their destination have sufficient time to aligth from one mode of transport and board the other mode of transport in intermediate stops [12]. Among the diverse modes of transport, the synchronization of timetables of bus lines is widely recognized as a highly complex problem in public transport [13; 14; 15]. Experienced public transportation planners and managers often resort to custom intuitive approaches to ensure a satisfactory level of service for citizens. In our previous publications [16; 17; 18], we have proposed exact and metaheuristic approaches to address an expanded version of the multi-trips synchronization problem, which takes into account extended transfer zones. This article extends our previous work \"Smart mobility for public transport systems: Improved bus timetabling for synchronizing transfers\", presented in V Ibero-American Congress of Smart Cities, 2022. The new contents include (i) a new mathematical formulation which aims to simultaneously maximize successful transfers and minimize the budgetary cost; (ii) the implementation of an exact resolution algorithm to solve the bi-objective optimization problem and obtain a set of Pareto efficient solutions; and (iii) an extended experimental evaluation of over 25 problem instances including instances with a diverse number of bus lines based on the city of Montevideo. This article is organized as described in the following. Section 2 presents the bi-objective Bus Synchronization Problem (BSP), including the main related work, the bus occupation and cost models, and the mathematical formulation. Section 3 describes the proposed methodology for solving the problem. Section 4 presents the computational experimentation, with a description of the implementation details, the instances used, and the main numerical results. Lastly, Section 5 provides a summary of the key findings from this study and suggests potential directions for future research.