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Energy-efficient train speed profile optimization problem in urban rail transit systems has attracted much attention in recent years because of the requirement of reducing operation cost and protecting the environment. Traditional methods on this problem mainly focused on formulating kinematical equations to derive the speed profile and calculate the energy consumption, which caused the possible errors due to some assumptions used in the empirical equations. To fill this gap, according to the actual speed and energy data collected from the real-world urban rail system, this paper proposes a data-driven model and integrated heuristic algorithm based on machine learning to determine the optimal speed profile with minimum energy consumption. Firstly, a data-driven optimization model (DDOM) is proposed to describe the relationship between energy consumption and discrete speed profile processed from actual data. Then, two typical machine learning algorithms, random forest regression (RFR) algorithm and support vector machine regression (SVR) algorithm, are used to identify the importance degree of velocity in the different positions of profile and calculate the traction energy consumption. Results show that the calculation average error is less than 0.1 kwh, and the energy consumption can be reduced by about 2.84% in a case study of Beijing Changping Line. Tis work is supported by the China National Funds for Distinguished Young Scientists (71525002), National Nature Science Foundation of China (71890972/71890970, 71771018, and 71621001), and Beijing Municipal Natural Science Foundation (L181008)

Traditional models of timetable generation for last trains do not account for the fact that decision-maker (DM) often incorporates transfer demand variability within his/her decision-making process. This study aims to develop such a model with particular consideration of the decision-makers’ risk preferences in subway systems under uncertainty. First, we formulate an optimization model for last-train timetabling based on mean-variance (MV) theory that explicitly considers two significant factors including the number of successful transfer passengers and the running time of last trains. Then, we add the mean-variance risk measure into the model to generate timetables by adjusting the last trains’ departure times and running times for each line. Furthermore, we normalize two heterogeneous terms of the risk measure to provide assistance in getting reasonable results. Due to the complexity of MV model, we design a tabu search (TS) algorithm with specifically designed operators to solve the proposed timetabling problem. Through computational experiments involving the Beijing subway system, we demonstrate the computational efficiency of the proposed MV model and the heuristic approach.

Train scheduling aims to seek a set of space-time paths for multiple trains on a railway line such that resources can be utilized efficiently with respect to prespecified criteria. By representing the train trajectory through a time-space path in its space-time network, this paper proposes an integer programming model for train scheduling on a single-track railway line, in which velocity choice is particularly considered to further decrease the expected energy consumption and interactions between different trains, and the link energy consumption is derived by the Davis formula with respect to different train speeds. The proposed model is implemented in the GAMS optimization software to solve an approximate optimal solution. Numerical examples show that the optimal timetable with optimized velocities can further decrease the energy consumption and coupling effects in comparison to the fixed velocity based schedule.

Within the morning and evening rush hour, the two-way road flows are always unbalanced in opposite directions. In order to make full advantage of the existing lanes, the two-way road lane has to be reallocated to play the best role in managing congestion. On the other hand, an effective tradable credit scheme can help to reduce the traffic demand and improve fairness for all travelers. So as to alleviate the commute congestion in urban transportation network, a discrete bilevel programming model is established in this paper. In the bilevel model, the government at the upper level reallocates lanes on the two-way road to minimize the total system cost. The traveler at the lower level chooses the optimal route on the basis of both travel time and credit charging for the lanes involved. A numerical experiment is conducted to examine the efficiency of the proposed method.

In order to investigate different route choice criteria in a competitive highway/park-and-ride (P&R) network with uncertain travel times on the road, a bilevel programming model for solving the problem of determining parking fees and modal split is presented. In the face of travel time uncertainty, travelers plan their trips with a prespecified on-time arrival probability. The impact of three route choice criteria: the mean travel time, the travel time budget, and mean-excess travel time, is compared for parking pricing and modal split. The model at user equilibrium is described as a minimization model. And the analytic solutions are given. Analytic solutions show that both flow and travel time at equilibrium are independent of the price difference of travel expense on money. The main findings from the numerical results are elaborated. While given a confidence level, the flow on the highway changed significantly with the criteria, although the differences of the travel times are small. Travelers can be guided to choose their modes coordinately by improving the quality of the transit service. The optimal parking fees can be affected markedly by the confidence level. Finally, the influence of the log-normal distribution parameters is tested and analyzed.

This paper develops an adjustable robust optimization approach for a network design problem explicitly incorporating traffic dynamics and demand uncertainty. In particular, a cell transmission model based network design problem of linear programming type is considered to describe dynamic traffic flows, and a polyhedral uncertainty set is used to characterize the demand uncertainty. The major contribution of this paper is to formulate such an adjustable robust network design problem as a tractable linear programming model and justify the model which is less conservative by comparing its solution performance with the robust solution from the usual robust model. The numerical results using one network from the literature demonstrate the modeling advantage of the adjustable robust optimization and provided strategic managerial insights for enacting capacity expansion policies under demand uncertainty.

We study the effect of the parking on heterogeneous commuters' travel choice in a competitive transportation system which consists of a subway and a parallel road with a bottleneck of limited service capacity. Every morning, commuters either use their private cars only or drive their cars to the bottleneck, park there, and then take the subway to the destination. Considering the effects caused by body congestion in carriage and the parking fees, we developed a bottleneck model to describe the commuters' travel choice. There exist several types of equilibrium that corresponds to user equilibrium. We investigated the influence of the capacity of the bottleneck and the total travel demand on the travel behaviors and on the total social cost. It is shown that there exists a scheme with suitable subway fare and parking fees to implement the minimum total social cost.