Repeated anticipatory network traffic control using iterative optimization accounting for model bias correction

Anticipatory signal control in traffic networks adapts the signal timings with the aim of controlling the resulting (equilibrium) flows and route choice patterns in the network. This study investigates a method to support control decisions for successful applications in real traffic systems that operate repeatedly, for instance from day to day, month to month, etc. The route choice response to signal control is usually predicted through models; however this leads to suboptimality because of unavoidable prediction errors between model and reality. This paper proposes an iterative optimizing control method to drive the traffic network towards the real optimal performance by observing modeling errors and correcting for them. Theoretical analysis of this Iterative Optimizing Control with Model Bias Correction (IOCMBC) on matching properties between the modeled optimal solution and the real optimum is presented, and the advantages over conventional iterative schemes are demonstrated. A local convergence analysis is also elaborated to investigate conditions required for a convergent scheme. The main innovation is the calculation of the sensitivity (Jacobian) information of the real route choice behavior with respect to signal control variables. To avoid performing additional perturbations, we introduce a measurement-based implementation method for estimating the operational Jacobian that is associated with the reality. Numerical tests confirm the effectiveness of the proposed IOCMBC method in tackling modeling errors, as well as the influence of the optimization step size on the reality-tracking convergence.     

An iterative route construction and improvement algorithm for the vehicle routing problem with soft time windows

The solution of routing problems with soft time windows has valuable practical applications. Soft time window solutions are needed when: (a) the number of routes needed for hard time windows exceeds the number of available vehicles, (b) a study of cost-service tradeoffs is required, or (c) the dispatcher has qualitative information regarding the relative importance of hard time-window constraints across customers. This paper proposes a new iterative route construction and improvement algorithm to solve vehicle routing problems with soft time windows. Due to its modular and hierarchical design, the solution algorithm is intuitive and able to accommodate general cost and penalty functions. Experimental results indicate that the average run time performance is of order O(n²). The solution quality and computational time of the new algorithm has been compared against existing results on benchmark problems. The presented algorithm has improved thirty benchmark problem solutions for the vehicle routing problems with soft time windows.     

A quantum evolutionary algorithm for the second-best congestion pricing problem in urban traffic networks

This paper investigates the congestion pricing problem in urban traffic networks. A first-best strategy, a second-best strategy for toll leveling in closed cordons and a second-best strategy for determining both toll levels and toll points are considered. The problem is known to be a mixed integer programming model and formulated as a bi-level optimization problem, with an objective of maximizing the social welfare. A method is presented to solve the problem, based on a novel metaheuristic algorithm, namely quantum evolutionary algorithm (QEA). To verify the proposed method, the widely used genetic algorithm (GA) is also applied to solve the problem. The problem is solved for a medium-size urban traffic network and the results of the QEA are compared against the conventional GA. Computational results show that the QEA outperforms the GA in solution quality.     

A stochastic optimization model for transit network timetable design to mitigate the randomness of traveling time by adding slack time

Transit network timetabling aims at determining the departure time of each trip of all lines in order to facilitate passengers transferring either to or from a bus. In this paper, we consider a bus timetabling problem with stochastic travel times (BTP-STT). Slack time is added into timetable to mitigate the randomness in bus travel times. We then develop a stochastic integer programming model for the BTP-STT to minimize the total waiting time cost for three types of passengers (i.e., transferring passengers, boarding passengers and through passengers). The mathematical properties of the model are characterized. Due to its computational complexity, a genetic algorithm with local search (GALS) is designed to solve our proposed model (OPM). The numerical results based on a small bus network show that the timetable obtained from OPM reduces the total waiting time cost by an average of 9.5%, when it is tested in different scenarios. OPM is relatively effective if the ratio of the number of through passengers to the number of transferring passengers is not larger than a threshold (e.g., 10 in our case). In addition, we test different scale instances randomly generated in a practical setting to further verify the effectiveness of OPM and GALS. We also find that adding slack time into timetable greatly benefits transferring passengers by reducing the rate of transferring failure.     

A heuristic algorithm for the multi-vehicle advance request dial-a-ride problem with time windows

A heuristic algorithm is described for a time-constrained version of the advance-request, multi-vehicle, many-to-many Dial-A-Ride Problem (DARP). The time constraints consist of upper bounds on: (1) the amount of time by which the pick-up or delivery of a customer can deviate from the desired pick-up or delivery time; (2) the time that a customer can spend riding in a vehicle. The algorithm uses a sequential insertion procedure to assign customers to vehicles and to determine a time schedule of pick-ups and deliveries for each vehicle. A flexible objective function balances the cost of providing service with the customers' preferences for pick-up and delivery times close to those requested, and for short ride times. Computational experience with the algorithm is described, including a run with a real database of 2600 customers and some 20 simultaneously active vehicles. The scenario for the application of the algorithm is also discussed in detail.     

An augmented Lagrangian origin‐based algorithm for link‐capacitated traffic assignment problem

The origin‐based algorithm is embedded into the augmented Lagrangian method for the link‐capacitated traffic assignment problem. In order to solve the “nonexistence” problem due to the second partial derivatives of the augmented Lagrangian function at some specific points, the approximate expressions of the second partial derivatives are amended in the origin‐based algorithm. The graph of last common nodes is developed on the basis of the restricted single‐origin network. A method is proposed for finding n–1 last common nodes of the restricted single‐origin network, resulting in computational complexity of O(n²) in finding last common nodes. Numerical analysis on the Sioux Falls network and Chicago Sketch network demonstrated the effectiveness and characteristics of the proposed algorithm. Copyright © 2014 John Wiley & Sons, Ltd.     

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 column generation algorithm for the bus driver scheduling problem

Bus driver scheduling aims to find the minimum number of bus drivers to cover a published timetable of a bus company. When scheduling bus drivers, contractual working rules must be enforced, thus complicating the problem. In this research, we develop a column generation algorithm that decomposes this complicated problem into a master problem and a series of pricing subproblems. The master problem selects optimal duties from a set of known feasible duties, and the pricing subproblem augments the feasible duty set to improve the solution obtained in the master problem. The proposed algorithm is empirically applied to the realistic problems of several bus companies. The numerical results show that the proposed column generation algorithm can solve real‐world problems and obtain bus driver schedules that are better than those developed and used by the bus companies. Copyright © 2016 John Wiley & Sons, Ltd.     

A differential evolution approach for the vehicle routing problem with backhauls and time windows

This paper presents a differential evolution algorithm (DEA) to solve a vehicle routing problem with backhauls and time windows (VRPBTW) and applied for a catering firm. VRPBTW is an extension of the vehicle routing problem, which includes capacity and time window constraints. In this problem, customers are divided into two subsets: linehaul and backhaul. Each vehicle starts from a depot and goods are delivered from the depot to the linehaul customers. Goods are subsequently brought back to the depot from the backhaul customers. The objective is to minimize the total distance that satisfies all of the constraints. The problem is formulated using mixed integer programming and solved using DEA. Proposed algorithm is tested with several benchmark problems to demonstrate effectiveness and efficiency of the algorithm and results show that our proposed algorithm can find superior solutions for most of the problems in comparison with the best known solutions. Hence, DEA was carried out for catering firm to minimize total transportation costs. Copyright © 2013 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.     

Constraint reformulation and a Lagrangian relaxation-based solution algorithm for a least expected time path problem

Using a sample-based representation scheme to capture spatial and temporal travel time correlations, this article constructs an integer programming model for finding the a priori least expected time paths. We explicitly consider the non-anticipativity constraint associated with the a priori path in a time-dependent and stochastic network, and propose a number of reformulations to establish linear inequalities that can be easily dualized by a Lagrangian relaxation solution approach. The relaxed model is further decomposed into two sub-problems, which can be solved directly by using a modified label-correcting algorithm and a simple single-value linear programming method. Several solution algorithms, including a sub-gradient method, a branch and bound method, and heuristics with additional constraints on Lagrangian multipliers, are proposed to improve solution quality and find approximate optimal solutions. The numerical experiments investigate the quality and computational efficiency of the proposed solution approach.     

A method for solving the multi‐objective transit frequency optimization problem

Frequency setting takes place at the strategic and tactical planning stages of public transportation systems. The problem consists in determining the time interval between subsequent vehicles for a given set of lines, taking into account interests of users and operators. The result of this stage is considered as input at the operational level. In general, the problem faced by planners is how to distribute a given fleet of buses among a set of given lines. The corresponding decisions determine the frequency of each line, which impacts directly on the waiting time of the users and operator costs. In this work, we consider frequency setting as the problem of minimizing simultaneously users' total travel time and fleet size, which represents the interest of operators. There is a trade‐off between these two measures; therefore, we face a multi‐objective problem. We extend an existing single‐objective formulation to account explicitly for this trade‐off, and propose a Tabu Search solving method to handle efficiently this multi‐objective variant of the problem. The proposed methodology is then applied to a real medium‐sized problem instance, using data of Puerto Montt, Chile. We consider two data sets corresponding to morning‐peak and off‐peak periods. The results obtained show that the proposed methodology is able to improve the current solution in terms of total travel time and fleet size. In addition, the proposed method is able to efficiently suggest (in computational terms) different trade‐off solutions regarding the conflicting objectives of users and operators. Copyright © 2017 John Wiley & Sons, Ltd.     

A cooperative waiting strategy based on elliptical areas for the Dynamic Pickup and Delivery Problem with Time Windows

The purpose of this paper to present a cooperative scheduling algorithm for solving the Dynamic Pickup and Delivery Problem with Time Windows (DPDPTW). The idea behind cooperative waiting strategies is to calculate simultaneously the waiting times for all nodes in the solution. Classical non‐cooperative scheduling algorithms perform the scheduling for each route independently of the scheduling of the other routes. We present the Cooperative Scheduling Problem (CSP) based on the elliptical areas generated by vehicles waiting at their nodes. The CSP is solved by means of a genetic algorithm and is evaluated by using a set of benchmarks based on real‐life data found in the literature. Initially, two waiting strategies are presented: Wait‐Early‐Time scheduling and Balanced‐Departure scheduling. Extensive empirical simulations have been carried out by analyzing the degree of dynamism and the average waiting time, a new concept defined to take into account the gap between the time windows of pickup and delivery nodes. Copyright © 2016 John Wiley & Sons, Ltd.     

Design and development of a hybrid artificial bee colony algorithm for the environmental vehicle routing problem

The vehicle routing problem (VRP) is a critical and vital problem in logistics for the design of an effective and efficient transportation network, within which the capacitated vehicle routing problem (CVRP) has been widely studied for several decades due to the practical relevance of logistics operation. However, CVRP with the objectives of minimizing the overall traveling distance or the traveling time cannot meet the latest requirements of green logistics, which concern more about the influence on the environment. This paper studies CVRP from an environmental perspective and introduces a new model called environmental vehicle routing problem (EVRP) with the aim of reducing the adverse effect on the environment caused by the routing of vehicles. In this research, the environmental influence is measured through the amount of the emission carbon dioxide, which is a widely acknowledged criteria and accounts for the major influence on environment. A hybrid artificial bee colony algorithm (ABC) is designed to solve the EVRP model, and the performance of the hybrid algorithm is evaluated through comparing with well-known CVRP instances. The computational results from numerical experiments suggest that the hybrid ABC algorithm outperforms the original ABC algorithm by 5% on average. The transformation from CVRP to EVRP can be recognized through the differentiation of their corresponding optimal solutions, which provides practical insights for operation management in green logistics.     

A route-based solution algorithm for dynamic user equilibrium assignments

The aim of this study is to establish a method to calculate good quality user equilibrium assignments under time varying conditions. For this purpose, it introduces a dynamic network loading method that can maintain correct flow propagation as well as flow conservation, and it shows a novel route-based solution algorithm. This novel algorithm turns out to be convenient and logically plausible compared to the conventional [Frank, M., Wolfe, P., 1956. An algorithm for quadratic programming. Naval Research Logistics Quarterly 3, 95–110] algorithm, because the former does not require evaluation of an objective function and it finds solutions maintaining correct flow propagation in the time-varying network conditions. The application of novel dynamic network loading method and solution algorithm to test networks shows that we can find high quality dynamic user equilibrium assignment. This is illustrated in an example network using the deterministic queuing model for a link performance function and associating costs and flows in a predictive way in discrete time.     

A geometry-based algorithm to provide guidance for electric vehicle charging

Electric vehicles (EVs) have been regarded as effective options for solving the environmental and energy problems in the field of transportation. However, given the limited driving range and insufficient charging stations, searching and selecting charging stations is an important issue for EV drivers during trips. A smart charging service should be developed to help address the charging issue of EV drivers, and a practical algorithm for charging guidance is required to realise it. This study aims to design a geometry-based algorithm for charging guidance that can be effectively applied in the smart charging service. Geographic research findings and geometric approaches are applied to design the algorithm. The algorithm is practical because it is based on the information from drivers’ charging requests, and its total number of calculations is significantly less than that of the conventional shortest-first algorithm. The algorithm is effective because it considers the consistency of direction trend between the charging route and the destination in addition to the travel distance, which conforms to the travel demands of EV drivers. Moreover, simulation examples are presented to demonstrate the proposed algorithm. Results of the proposed algorithm are compared with those of the other two algorithms, which show that the proposed algorithm can obtain a better selection of charging stations for EV drivers from the perspective of entire travel chains and take a shorter computational time.     

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.     

Global optimization method for mixed transportation network design problem: A mixed-integer linear programming approach

This paper proposes a global optimization algorithm for solving a mixed (continuous/discrete) transportation network design problem (MNDP), which is generally expressed as a mathematical programming with equilibrium constraint (MPEC). The upper level of the MNDP aims to optimize the network performance via both expansion of existing links and addition of new candidate links, whereas the lower level is a traditional Wardrop user equilibrium (UE) problem. In this paper, we first formulate the UE condition as a variational inequality (VI) problem, which is defined from a finite number of extreme points of a link-flow feasible region. The MNDP is approximated as a piecewise-linear programming (P-LP) problem, which is then transformed into a mixed-integer linear programming (MILP) problem. A global optimization algorithm based on a cutting constraint method is developed for solving the MILP problem. Numerical examples are given to demonstrate the efficiency of the proposed method and to compare the results with alternative algorithms reported in the literature.