Multiple-phase train trajectory optimization with signalling and operational constraints

The train trajectory optimization problem aims at finding the optimal speed profiles and control regimes for a safe, punctual, comfortable, and energy-efficient train operation. This paper studies the train trajectory optimization problem with consideration of general operational constraints as well as signalling constraints. Operational constraints refer to time and speed restrictions from the actual timetable, while signalling constraints refer to the influences of signal aspects and automatic train protection on train operation. A railway timetable provides each train with a train path envelope, which consists of a set of positions on the route with a specified target time and speed point or window. The train trajectory optimization problem is formulated as a multiple-phase optimal control model and solved by a pseudospectral method. This model is able to capture varying gradients and speed limits, as well as time and speed constraints from the train path envelope. Train trajectory calculation methods under delay and no-delay situations are discussed. When the train follows the planned timetable, the train trajectory calculation aims at minimizing energy consumption, whereas in the case of delays the train trajectory is re-calculated to track the possibly adjusted timetable with the aim of minimizing delays as well as energy consumption. Moreover, the train operation could be affected by yellow or red signals, which is taken into account in the train speed regulation. For this purpose, two optimization policies are developed with either limited or full information of the train ahead. A local signal response policy ensures that the train makes correct and quick responses to different signalling aspects, while a global green wave policy aims at avoiding yellow signals and thus proceed with all green signals. The method is applied in a case study of two successive trains running on a corridor with various delays showing the benefit of accurate predictive information of the leading train on energy consumption and train delay of the following train.     

Modeling and simulation of vehicle projection arrival–discharge process in adaptive traffic signal controls

Real‐time signal control operates as a function of the vehicular arrival and discharge process to satisfy a pre‐specified operational performance. This process is often predicted based on loop detectors placed upstream of the signal. In our newly developed signal control for diamond interchanges, a microscopic model is proposed to estimate traffic flows at the stop‐line. The model considers the traffic dynamics of vehicular detection, arrivals, and departures, by taking into account varying speeds, length of queues, and signal control. As the signal control is optimized over a rolling horizon that is divided into intervals, the vehicular detection for and projection into the corresponding horizon intervals are also modeled. The signal control algorithm is based on dynamic programming and the optimization of signal policy is performed using a certain performance measure involving delays, queue lengths, and queue storage ratios. The arrival–discharge model is embedded in the optimization algorithm and both are programmed into AIMSUN, a microscopic stochastic simulation program. AIMSUN is then used to simulate the traffic flow and implement the optimal signal control by accessing internal data including detected traffic demand and vehicle speeds. Sensitivity analysis is conducted to study the effect of selecting different optimization criteria on the signal control performance. It is concluded that the queue length and queue storage ratio are the most appropriate performance measures in real‐time signal control of interchanges. Copyright © 2010 John Wiley & Sons, Ltd.     

Lane‐based optimization of traffic equilibrium settings for area traffic control

Area traffic control is an important element in Intelligent Transportation System (ITS). This paper extends the lane‐based optimization method to a traffic equilibrium network, which improves the operational performance of signal‐controlled network. We formulate a decomposition approach to simultaneously optimize the lane markings and signal settings for a signal‐controlled network that comprises two levels of optimization. At the junction level, the lane markings, control sequence, and other aspects of the signal settings are optimized for individual junctions, whereas at the network level, the group‐based signal settings are optimized to take into account the re‐routing characteristics of travelers and signal coordination effects that are based on a TRANSYT traffic model, which is a well‐known procedure for evaluating the performance of signal‐controlled networks. We use a numerical example to demonstrate the effectiveness of the proposed methodology.     

A driver advisory system with dynamic losses for passenger electric multiple units

Driver advisory systems, instructing the driver how to control the train in an energy efficient manner, is one the main tools for minimizing energy consumption in the railway sector. There are many driver advisory systems already available in the market, together with significant literature on the mathematical formulation of the problem. However, much less is published on the development of such mathematical formulations, their implementation in real systems, and on the empirical data from their deployment. Moreover, nearly all the designed driver advisory systems are designed as an additional hardware to be added in drivers’ cabin. This paper discusses the design of a mathematical formulation and optimization approach for such a system, together with its implementation into an Android-based prototype, the results from on-board practical experiments, and experiences from the implementation. The system is based on a more realistic train model where energy calculations take into account dynamic losses in different components of the propulsion system, contrary to previous approaches. The experimental evaluation shows a significant increase in accuracy, as compared to a previous approach. Tests on a double-track section of the Mälaren line in Sweden demonstrates a significant potential for energy saving.     

Predicting and planning airport acceptance rates in metroplex systems for improved traffic flow management decision support

Efficient planning of Airport Acceptance Rates (AARs) is key for the overall efficiency of Traffic Management Initiatives such as Ground Delay Programs (GDPs). Yet, precisely estimating future flow rates is a challenge for traffic managers during daily operations as capacity depends on a number of factors/decisions with very dynamic and uncertain profiles. This paper presents a data-driven framework for AAR prediction and planning towards improved traffic flow management decision support. A unique feature of this framework is to account for operational interdependency aspects that exist in metroplex systems and affect throughput performance. Gaussian Process regression is used to create an airport capacity prediction model capable of translating weather and metroplex configuration forecasts into probabilistic arrival capacity forecasts for strategic time horizons. To process the capacity forecasts and assist the design of traffic flow management strategies, an optimization model for capacity allocation is developed. The proposed models are found to outperform currently used methods in predicting throughput performance at the New York airports. Moreover, when used to prescribe optimal AARs in GDPs, an overall delay reduction of up to 9.7% is achieved. The results also reveal that incorporating robustness in the design of the traffic flow management plan can contribute to decrease delay costs while increasing predictability.     

Robust optimization of distance-based tolls in a network considering stochastic day to day dynamics

This paper investigates the nonlinear distance-based congestion pricing in a network considering stochastic day-to-day dynamics. After an implementation/adjustment of a congestion pricing scheme, the network flows in a certain period of days are not on an equilibrium state, thus it is problematic to take the equilibrium-based indexes as the pricing objective. Therefore, the concept of robust optimization is taken for the congestion toll determination problem, which takes into account the network performance of each day. First, a minimax model which minimizes the maximum regret on each day is proposed. Taking as a constraint of the minimax model, a path-based day to day dynamics model under stochastic user equilibrium (SUE) constraints is discussed in this paper. It is difficult to solve this minimax model by exact algorithms because of the implicity of the flow map function. Hence, a two-phase artificial bee colony algorithm is developed to solve the proposed minimax regret model, of which the first phase solves the minimal expected total travel cost for each day and the second phase handles the minimax robust optimization problem. Finally, a numerical example is conducted to validate the proposed models and methods.     

Eco-efficiency management program (EEMP)—a model for road fleet operation

Fuel consumption has always been a matter of economic concern in road fleet management, giving rise to many initiatives aimed at fostering more efficient energy use. The increasingly awareness of environmental problems now requires these programs to include environmental aspects. A structured Eco-efficiency Management Program (EEMP) is proposed for road fleet operation, taking into account the traditional approach that strives to minimise fuel consumption as well as wider economic and environmental aspects. The EEMP has its potential evaluated in a case study undertaken for INFRAERO, Brazilian’s airport authority, on the operation of its road fleet supporting aircraft ground operations at Rio de Janeiro International Airport. The paper looks at EEMP’s implementation by identifying the program’s phases, its participants and their competencies, eco-efficiency indicators, and performance targets.     

Energy consumption and cost-benefit analysis of hybrid and electric city buses

This paper presents a cost-benefit analysis (CBA) of hybrid and electric city buses in fleet operation. The analysis is founded on an energy consumption analysis, which is carried out on the basis of extensive simulations in different bus routes. A conventional diesel city bus is used as a reference for the CBA. Five different full size hybrid and electric city bus configurations were considered in this study; two parallel and two series hybrid buses, and one electric city bus. Overall, the simulation results indicate that plug-in hybrid and electric city buses have the best potential to reduce energy consumption and emissions. The capital and energy storage system costs of city buses are the most critical factors for improving the cost-efficiency of these alternative city bus configurations. Furthermore, the operation schedule and route planning are important to take into account when selecting hybrid and electric city buses for fleet operation.     

Multi-objective optimization of train routing problem combined with train scheduling on a high-speed railway network

Based on train scheduling, this paper puts forward a multi-objective optimization model for train routing on high-speed railway network, which can offer an important reference for train plan to provide a better service. The model does not only consider the average travel time of trains, but also take the energy consumption and the user satisfaction into account. Based on this model, an improved GA is designed to solve the train routing problem. The simulation results demonstrate that the accurate algorithm is suitable for a small-scale network, while the improved genetic algorithm based on train control (GATC) applies to a large-scale network. Finally, a sensitivity analysis of the parameters is performed to obtain the ideal parameters; a perturbation analysis shows that the proposed method can quickly handle the train disturbance.     

A fuzzy-stochastic optimization model for the intermodal fleet management problem of an international transportation company

ABSTRACT

In this paper, a fuzzy-stochastic optimization model is developed for an intermodal fleet management system of a large international transportation company. The proposed model integrates various strategic, tactical and operational level decisions simultaneously. Since real-life fleet planning problems may involve different types of uncertainty jointly such as randomness and fuzziness, a hybrid chance-constrained programming and fuzzy interactive resolution-based approach is employed. Therefore, stochastic import/export freight demand and fuzzy transit times, truck/trailer availabilities, the transport capacity of Ro-Ro vessels, bounds on block train services, etc. can also be taken into account concurrently. In addition to minimize overall transportation costs, optimization of total transit times and CO₂ emission values are also incorporated in order to provide sustainable fleet plans by maximizing customer satisfaction and environmental considerations. Computational results show that effective and efficient fleet plans can be produced by making use of the proposed optimization model.     

Data-driven linear decision rule approach for distributionally robust optimization of on-line signal control

We propose a two-stage, on-line signal control strategy for dynamic networks using a linear decision rule (LDR) approach and a distributionally robust optimization (DRO) technique. The first (off-line) stage formulates a LDR that maps real-time traffic data to optimal signal control policies. A DRO problem is solved to optimize the on-line performance of the LDR in the presence of uncertainties associated with the observed traffic states and ambiguity in their underlying distribution functions. We employ a data-driven calibration of the uncertainty set, which takes into account historical traffic data. The second (on-line) stage implements a very efficient linear decision rule whose performance is guaranteed by the off-line computation. We test the proposed signal control procedure in a simulation environment that is informed by actual traffic data obtained in Glasgow, and demonstrate its full potential in on-line operation and deployability on realistic networks, as well as its effectiveness in improving traffic.     

Dynamic optimization of ship energy efficiency considering time-varying environmental factors

Nowadays, optimization of ship energy efficiency attracts increasing attention in order to meet the requirement for energy conservation and emission reduction. Ship operation energy efficiency is significantly influenced by environmental factors such as wind speed and direction, water speed and depth. Owing to inherent time-variety and uncertainty associated with these various factors, it is very difficult to determine optimal sailing speeds accurately for different legs of the whole route using traditional static optimization methods, especially when the weather conditions change frequently over the length of a ship route. Therefore, in this paper, a novel dynamic optimization method adopting the model predictive control (MPC) strategy is proposed to optimize ship energy efficiency accounting for these time-varying environmental factors. Firstly, the dynamic optimization model of ship energy efficiency considering time-varying environmental factors and the nonlinear system model of ship energy efficiency are established. On this basis, the control algorithm and controller for the dynamic optimization of ship energy efficiency (DOSEE) are designed. Finally, a case study is carried out to demonstrate the validity of this optimization method. The results indicate that the optimal sailing speeds at different time steps could be determined through the dynamic optimization method. This method can improve ship energy efficiency and reduce CO₂ emissions effectively.     

A joint optimization model for liner container cargo assignment problem using state-augmented shipping network framework

This paper proposes a state-augmented shipping (SAS) network framework to integrate various activities in liner container shipping chain, including container loading/unloading, transshipment, dwelling at visited ports, in-transit waiting and in-sea transport process. Based on the SAS network framework, we develop a chance-constrained optimization model for a joint cargo assignment problem. The model attempts to maximize the carrier’s profit by simultaneously determining optimal ship fleet capacity setting, ship route schedules and cargo allocation scheme. With a few disparities from previous studies, we take into account two differentiated container demands: deterministic contracted basis demand received from large manufacturers and uncertain spot demand collected from the spot market. The economies of scale of ship size are incorporated to examine the scaling effect of ship capacity setting in the cargo assignment problem. Meanwhile, the schedule coordination strategy is introduced to measure the in-transit waiting time and resultant storage cost. Through two numerical studies, it is demonstrated that the proposed chance-constrained joint optimization model can characterize the impact of carrier’s risk preference on decisions of the container cargo assignment. Moreover, considering the scaling effect of large ships can alleviate the concern of cargo overload rejection and consequently help carriers make more promising ship deployment schemes.     

A decomposition approach to determining fleet size and structure with network flow effects and demand uncertainty

This paper presents a new methodology to determine fleet size and structure for those airlines operating on hub‐and‐spoke networks. The methodology highlights the impact of stochastic traffic network flow effects on fleet planning process and is employed to construct an enhanced revenue model by incorporating the expected revenue optimization model into fleet planning process. The objective of the model is to find a feasible allocation of aircraft fleet types to route legs using minimum fleet purchasing cost, thus ensuring that the expected fleet profit is maximized subject to several critical resource constraints. By using a linear approximation to the total network revenue function, the fleet planning model with enhanced revenue modeling is decomposed into the nonlinear aspects of expected revenue optimization and the linear aspects of determining fleet size and structure by optimal allocation of aircraft fleet types to route legs. To illustrate this methodology and its economic benefits, an example consisting of 6 chosen aircraft fleet types, 12 route legs, and 57 path‐specific origin‐destination markets is presented and compared with the results found using revenue prorated fleet planning formulation. The results show that the fleet size and structure of the methodology proposed in this paper gain 211.4% improvement in fleet profit over the use of the revenue prorated fleet planning approach. In addition, comparison with the deterministic model reveals that the fleet size and structure of this proposed methodology are more adaptable to the fluctuations of passenger demands. Copyright © 2016 John Wiley & Sons, Ltd.     

Global optimization method for network design problem with stochastic user equilibrium

In this paper, we consider the continuous road network design problem with stochastic user equilibrium constraint that aims to optimize the network performance via road capacity expansion. The network flow pattern is subject to stochastic user equilibrium, specifically, the logit route choice model. The resulting formulation, a nonlinear nonconvex programming problem, is firstly transformed into a nonlinear program with only logarithmic functions as nonlinear terms, for which a tight linear programming relaxation is derived by using an outer-approximation technique. The linear programming relaxation is then embedded within a global optimization solution algorithm based on range reduction technique, and the proposed approach is proved to converge to a global optimum.     

Transit network design based on travel time reliability

This paper presents a transit network optimization method, in which travel time reliability on road is considered. A robust optimization model, taking into account the stochastic travel time, is formulated to satisfy the demand of passengers and provide reliable transit service. The optimization model aims to maximize the efficiency of passenger trips in the optimized transit network. Tabu search algorithm is defined and implemented to solve the problem. Then, transit network optimization method proposed in this paper is tested with two numerical examples: a simple route and a medium-size network. The results show the proposed method can effectively improve the reliability of a transit network and reduce the travel time of passengers in general.     

The time slot allocation problem under uncertain capacity

This paper presents two stochastic programming models for the allocation of time slots over a network of airports. The proposed models address three key issues. First, they provide an optimization tool to allocate time slots, which takes several operational aspects and airline preferences into account; second, they execute the process on a network of airports; and third they explicitly include uncertainty. To the best of our knowledge, these are the first models for time slot allocation to consider both the stochastic nature of capacity reductions and the problem’s network structure. From a practical viewpoint, the proposed models provide important insights for the allocation of time slots. Specifically, they highlight the tradeoff between the schedule/request discrepancies, i.e., the time difference between allocated time slots and airline requests, and operational delays. Increasing schedule/request discrepancies enables a reduction in operational delays. Moreover, the models are computationally viable. A set of realistic test instances that consider the scheduling of four calendar days on different European airport networks has been solved within reasonable – for the application’s context – computation times. In one of our test instances, we were able to reduce the sum of schedule/request discrepancies and operational delays by up to 58%. This work provides slot coordinators with a valuable decision making tool, and it indicates that the proposed approach is very promising and may lead to relevant monetary savings for airlines and aircraft operators.     

Sequential optimization approach for the multi‐class user equilibrium problem in a continuous transportation system

We consider a city region with several facilities that are competing for customers of different classes. Within the city region, the road network is dense, and can be represented as a continuum. Customers are continuously distributed over space, and they choose a facility by considering both the transportation cost and market externalities. More importantly, the model takes into account the different transportation cost functions and market externalities to which different customer classes are subjected. A logit‐type distribution of demand is specified to model the decision‐making process of users' facility choice. We develop a sequential optimization approach to decompose the complex multi‐class and multi‐facility problem into a series of smaller single‐class and single‐facility sub‐problems. An efficient solution algorithm is then proposed to solve the resultant problem. A numerical example is given to demonstrate the effectiveness and potential applicability of the proposed methodology.     

A new algorithm for optimal signal control in congested networks

Optimization of traffic lights in a congested network is formulated as a linear programming problem. The formulation adapted here takes into account particular capacity constraints for road links and for intersections. A necessary prerequisite for the determination of optimal green times is that representative a-priori information about the origin-destination and route choice pattern inside the network is available. Because any particular control strategy temporarily alters the effective turning rates at intersections, an iterative procedure is proposed here which accomplishes convergence of optimal signal control and resulting O-D flows. The efficiency of this optimization procedure is demonstrated in a case study for a network with fifteen intersections.     

A joint bottom-up solution methodology for system-level pavement rehabilitation and reconstruction

We present a methodology for the joint optimization of rehabilitation and reconstruction activities for heterogeneous pavement systems under multiple budget constraints. The proposed bottom-up approach adopts an augmented condition state to account for the history-dependent properties of pavement deterioration, and solves for steady-state policies for an infinite horizon. Genetic algorithms (GAs) are implemented in the system-level optimization based on segment-specific optimization results. The complexity of the proposed algorithm is polynomial in the size of the system and the policy-related parameters. We provide graphical presentations of the optimal solutions for various budget situations. As a case study, a subset of California’s highway system is analyzed. The case study results demonstrate the economic benefit of a combined rehabilitation and reconstruction budget compared to separate budgets.