Demand-driven timetable and stop pattern cooperative optimization on an urban rail transit line

In order to study the relationship between the accessibility along the urban rail transit line and the change in housing price, GA-BP model, which combining the genetic algorithm(GA) and back propagation neural network(BPNN), was used to predict the housing price along the urban rail transit line. The reliability of the model was verified by taking the price of residential areas along Nanjing Metro Line 10 as an example, and the performance between GA-BP model and the BP model was compared. It was found that the average absolute error rate of GA-BP model is 6.91%, which is 6.45% lower than that of BP model, and the mean square error of prediction results is significantly reduced. It can be seen that the price prediction algorithm based on GA-BP model for those residential areas along the urban rail transit line is reliable and can fully tap the potential relationship between the accessibility of urban transport network and the housing price.

Train timetabling for a double-track urban rail transit line under dynamic passenger demand

Integrated rolling stock deadhead routing and timetabling in urban rail transit lines

Scheduling local and express trains in suburban rail transit lines: Mixed–integer nonlinear programming and adaptive genetic algorithm

A new method is proposed for single-track railway freight train timetable with two-stage solution of train scheduling problem. The method describes train scheduling problem in matrix with the "signaling block" concept. The matrix represents entire block occupancy of trains between inter-stations and internal-stations while decomposing individual train occupancy, making optimization method more flexible in design and use. The "two-stage solution" refers to that of train timetable with "conflict solution" and "timetable optimization." At the beginning, related data for trains are entered to build the initial timetable, which is then transferred and saved as the matrix format. All conflicts between interstations and internal-stations are located; solutions are made with manual scheduling to generate a feasible timetable. In the second stage, departure and stop time of freight trains, and passenger trains if necessary, are adjusted with Fuzzy system. Before optimization, storage is made in ascending amount of extra-time percent in freight train schedule. Execution is made subject to pre-ordered results during optimization for computer program acceleration of current manual spotting solution to find reasonable and feasible solution. The two-stage method also takes less time than the regular railway timetable design methods in cost saving of manual labor and providing higher operation performance and efficiency.

This paper presents a train scheduling and a rescheduling models based on the generation of an alternative graph of the railway network. In the first model, the train scheduling problem has been solved to define the optimal timetable for a set of trains with the objective to minimize the travel times of passengers to reach their destination, outlining the related sequence of nodes and arcs of the graph to be covered by each group of passengers. Subsequently, a train rescheduling model is applied on an optimal timetable became infeasible due to unpredicted failures or disturbances introduced on the network. In this second approach, the objective is restore the railway service quality by reducing the delays for trains and passengers. The main contribution of this paper is to implement railway scheduling and rescheduling problem by linear programming formulations introducing in the second approach the innovative concept to prioritize the train that can access on the block section in case of conflicts on the network. The performances of the solution methods have been tested on real train timetable data related to a portion of railway in Liguria Region, in Italy.

An integrated model for line planning and train scheduling based on the circulation of trains is proposed to reduce passenger dissatisfaction and operation costs for an urban rail transit line. The turnaround operations of trains and their departures from and arrivals at the depot were included in this model. Furthermore, binary variables were introduced to indicate whether train service existed, and a discrete event model was used to determine the order of the train services. In addition, a bi-level optimization approach is proposed to solve the integrated line-planning and train-scheduling problem, in which the number of required train services, the headways between train services, the departure times, and the arrival times were optimized simultaneously on the basis of passenger demand. The performance of the proposed integrated model and bi-level approach is illustrated with a case study of the Beijing Yizhuang line.

Modeling the first train timetabling problem with minimal missed trains and synchronization time differences in subway networks

Solving Integer Linear Programming (ILP) models generally lies in the category of NP-hard problems. Therefore, as the size of ILP models grows, the efficiency of exact algorithms for solving the models reduced significantly and for large models it is not possible to have the result. Genetic Algorithm (GA) is a metaheuristic method capable of adjusting and redesigning parameters and operations according to the characteristics of ILP models. Still GA has huge search space for large models and parallelization is a suitable technique to tackle this problem. This paper presents a scalable parallel GA to solve large ILP models derived from behavioral synthesis of digital circuits. We show that although models have non-binary variables, only binary variables are sufficient for coding chromosomes. We also use ”unknown” values for some genes to decrease the likelihood of inconsistency in the encoded constraints. Our experiments verify the efficiency and scalability of the proposed algorithm on multicore platforms. The proposed method outperforms IBM ILOG CPLEX 12.6 and MI-LXPM algorithm where the ILP models include 550 to 2258 int / binary decision variables. Also, the results indicate that the saturation point of using parallel processing elements for solving the large ILP models is at least 60.

Optimization of composite laminates requires the satisfaction of constraints where the design ply thicknesses and orientations can only take discrete values prescribed by the manufacturers. Heuristics such as particle swarm or genetic algorithms are inefficient in such cases because they provide suboptimal solutions when the number of design variables is large. They also are computationally expensive in handling the combinatorial nature of the problem. In contrast, with the help of binary decision variables, mixed integer programming can be adopted to optimize such laminates efficiently. This paper presents an approach to reformulate lamination parameters and failure constraints as functions of binary decision variables. The buckling load maximization for a simply supported laminated plate is initially demonstrated using integer linear programming. Next, the laminate weight is minimized by varying the number of plies for a given external bi-axial compressive load and subjected to buckling and material failure constraints. A variation of laminate weight minimization is demonstrated by fixing the number of plies and assuming discrete changes in ply thicknesses. This is achieved using a sequential two-level optimization for laminates having uniform ply thickness. Finally, a scalability study is performed to evaluate the performance of mixed integer programming for different problem sizes. It is demonstrated that all three formulations with integer programming achieve significant performance gain and robustness over standard heuristic solvers.

Collaborative optimization of last-train timetables for metro network to increase service time for passengers

Joint optimization of tram timetables and signal timing adjustments at intersections

Timetable Optimization for High-Speed Trains at Chinese Railways

An analytical method for finding the optimal route to be followed by an Unmanned Surface Vehicle (USV) is proposed. The proposed algorithm aims to generate a collision-free route with minimum travel time in reaching some given waypoints. The method comprises of two algorithms. First, a grid map-based algorithm for static obstacle avoidance by forming sub-waypoints at the tangent angle of the obstacle using the weight of each obstacle to generate feasible paths. The obstacle weights are determined based on whether the neighboring cells are also obstacles or not. Second, the dynamic programming-based path planning optimization to find several shortest paths among those feasible paths. The USV is modeled in a Six-Degree-of-Freedom (6-DOF) equations of motion whose parameters are determined based on a physical model USV. Simulation results are presented to show the method successfully guides the USV without crashing into obstacles. As shown, due to the USV's limited maneuverability, the shortest path obtained using dynamic programming is not always the path with the shortest travel distance, and the shortest travel distance does not guarantee the shortest travel time either. As a comparison, a genetic algorithm has been conducted to produce the optimal route. Simulation results show that the proposed algorithm produces an 11.6% reduction in travel time and a 99.55% reduction in computing time than the genetic algorithm.

The natural performance of the location model is a potential tool for allocating an object into one of the two observed groups involving mixtures of continuous and binary variables. In constructing location model, continuous variable is used to estimate parameters while binary variable is utilized to create segmentation in each group. Such segmentation is called as multinomial cells. Basically, the multinomial cells will grow exponentially according to the number of the binary variable. These multinomial cells will become empty when there is no object can be assigned into some of them. Then the occurring of empty cells will lead to unreliable parameter estimation. Consequently, the construction of the discriminant rule based on location model is impossible. Therefore, this paper attempts to discuss how the location model based on maximum likelihood estimation can be constructed even dealing with many measured binary variables. In other word, how is location model able to deal with the issue of many empty ...