# Integrated Framework for Bus Timetabling and Scheduling in Multi-Line Operation Mode
## 1 Introduction
[16] present two integer linear programming models for the TT and VS problems and combine them in a bi-objective integrated model. [PERSON] and [PERSON] [17] use a weighted sum approach to combine both objectives and propose a hybrid metaheuristic framework to decompose the problem into a scheduling component and a balancing component. [PERSON] et al. [18] propose a bi-objective multi-period planning model for the synchronization of TT and VS. [PERSON] et al. [19] offer a two-level planningmodel for the M-TT/VS problem and solve it by tabu and enumeration algorithms. [PERSON] [20] considers optimizing the timetable and the vehicle circulation schedule jointly. In these studies, recursive [9; 17] and hierarchical [19; 20] methods are the most used. These methods obtain satisfactory solutions by adjusting the TT decision within limits according to the feedback of the VS result. That is, the TT decision and VS decision are not solved and optimized simultaneously. Therefore, it is hard to find the global optimum solution with these methods, and repeated recursive calculations also increase solving time. In addition, most researchers stipulate the periodicity [18] or the frequency [16; 17] of timetables within a period. Under these rules, changes to the plans are limited. With the development of computer and information technology, bus travel demand information requires more details to be known. When we need to satisfy known demand patterns,  
Figure 1: Schematic diagram of vehicle centralized management in the multi-line operation mode. the timetable-based operation is more appropriate than the frequency-based operation [5]. Therefore, the design of an integrated approach to relate timetable-based TT decision and VS decision is a vital part of the research. Targeting the above research contents and difficulties, this paper proposes a new integrated framework for the M-TT/VS problem. The M-TT/VS problem we studied is a static planning problem, in which passenger flow demand and trip running time are estimated in advance as inputs. Firstly, the determination processes of TT and VS are correlated by constructing multiple vehicles' trip-link chains with departure time information to facilitate simultaneous optimization. The departure time can be adjusted in minutes to accommodate fluctuating demand. Secondly, a multi-objective optimization model is constructed for the M-TT/VS problem. The multi-objective optimization model considers higher service quality and lower operating costs as objectives [14; 16; 21]. Logic and operational rules are considered as constraints to ensure the implementation of the solutions. Thirdly, a heuristic solution algorithm is designed to find the Pareto frontier solutions, including two main sub-algorithms: a feasible solution generation algorithm based on greedy rules (CEG) and an optimization algorithm based on neighborhood search (HNS). Finally, a case study of Chongqing, China, is carried out to analyze and verify the effectiveness and efficiency of the framework. The contributions of this paper are summarized as follows:  
1. A new multi-objective integrated framework for the M-TT/VS problem is proposed, which constructs a vehicle-based solution structure to facilitate simultaneous optimization. 2. A heuristic algorithm, including a feasible solution generation algorithm, CEG, and an optimization algorithm, HNS, is designed to find the Pareto frontier solutions. A heuristic method and a comprehensive tabu table are designed to improve optimization efficiency. 3. A case study of Chongqing, China, is carried out to analyze and verify the effectiveness and efficiency of the framework. The Pareto frontier solutions are provided to bus operators as alternative operation schemes.