###### Abstract  
This article addresses timetable synchronization in public transportation, an important problem in modern smart cities, in order to guarantee a proper quality of service to citizens. Two variants of the bus timetabling synchronization problem considering extended transfer zones are studied: optimizing offsets and optimizing offsets and headways for each line. An exact mixed integer programming and an evolutionary algorithm are developed to solve both problem variants. The algorithms are evaluated on 45 instances of a real case study, the intelligent transportation system of Montevideo, Uruguay. Experimental results reported significant improvements over the current timetable implemented by the city administration. The number of successful synchronizations improved up to 66.6% and 179.9% for the first and second problem variant, respectively. The average waiting times for transfers improved, especially in tight problem instances (up to 57.8% and 158.3% for the first and second problem variant, respectively). The proposed planning methods are useful to help decision makers to configure public transportation systems. timetable synchronization; public transportation planning; mixed integer programming; evolutionary algorithms; real case study; smart cities +
Footnote †: 2021  
between media are fairly regular along some reference time-window. The considered public transportation system consists of a mesh of routes operated by vehicles with similar capacities. Given origin-destination matrices for trips, expectations of passengers, technical features of buses, and operational costs, a historical design problem defines the lines to be deployed and their routes throughout each city in order to obtain a network with a proper trade-off between cost and quality of service [3]. Regarding the scope of this work, lines and routes are assumed fixed and known in advance, and timetable modifications are explored to allow for better overall efficiency [6]. Two variants of the bus timetabling synchronization problem considering extended transfer zones for every pair of bus stops in a city are formulated: optimizing the offset for each line and optimizing the offset and headways for each line. A realistic formulation is included to model the transfer demands of passengers. Two computational methods, exact mixed integer programming and the evolutionary algorithm (EA), are developed to efficiently solve both problem variants. The algorithms are evaluated on 45 instances of a real-world application case in Montevideo, Uruguay. Problem instances are defined using real data about lines, headways, and transfer demands, gathered from the intelligent transportation system of Montevideo. Results are compared with the real timetable currently implemented by the city administration. The public transportation system of Montevideo is flexible, providing several options for passengers to reach a destination. Many passengers complete end-to-end trips by using a sole line, but either due to feasibility or convenience, many users transfer between lines to fulfill end-to-end trips. Transfers are implemented in the automatic Metropolitan Transportation System (STM). Users are charged through radio frequency identification cards, which allow them to pay and easily transfer between lines, even between different (geographically separated) bus stops.The STM keeps historical ticket sales and travel times via GPS-integrated controller units on buses. Records include user trip details along any day and time-stamped and geo-referenced transfers, etc. This dataset is a primordial asset for authorities, and it is used to adjust the configuration of lines. A relevant adjustment is the timetable, i.e., the schedule of departures each line must conform to. The STM dataset indicates that there are time-windows where the load of the system is regular, that is, with low deviation from mean values of traveling times, number of passengers in each bus, and the number of transfers between them [7].