Fair dynamic resource allocation in transit-based evacuation planning

Resource allocation in transit-based emergency evacuation is studied in this paper. The goal is to find a method for allocation of resources to communities in an evacuation process which is (1) fair, (2) reasonably efficient, and (3) able to dynamically adapt to the changes to the emergency situation. Four variations of the resource allocation problem, namely maximum rate, minimum clearance time, maximum social welfare, and proportional fair resource allocation, are modeled and compared. It is shown that the optimal answer to each problem can be found efficiently. Additionally, a distributed and dynamic algorithm based on the Lagrangian dual approach, called PFD²A, is developed to find the proportional fair allocation of resources and update the evacuation process in real time whenever new information becomes available. Numerical results for a sample scenario are presented.     

Robust intermodal hub location under polyhedral demand uncertainty

In this study, we consider the robust uncapacitated multiple allocation p-hub median problem under polyhedral demand uncertainty. We model the demand uncertainty in two different ways. The hose model assumes that the only available information is the upper limit on the total flow adjacent at each node, while the hybrid model additionally imposes lower and upper bounds on each pairwise demand. We propose linear mixed integer programming formulations using a minmax criteria and devise two Benders decomposition based exact solution algorithms in order to solve large-scale problems. We report the results of our computational experiments on the effect of incorporating uncertainty and on the performance of our exact approaches.     

Optimizing one‐way traffic network reconfiguration and lane‐based non‐diversion routing for evacuation

Unfortunately, situations such as flood, hurricanes, chemical accidents, and other events occur frequently more and more. To improve the efficiency and practicality of evacuation management plan, an integrated optimization model of one‐way traffic network reconfiguration and lane‐based non‐diversion routing with crossing elimination at intersection for evacuation is constructed in this paper. It is an integrated model aiming at minimizing the network clearance time based on Cell Transmission Model. A hybrid algorithm with modified genetic algorithm and tabu search method is devised for approximating optimal problem solutions. To verify the effectiveness of the proposed model and solving method, two cases are illustrated in this paper. Through the first example, it can be seen that the proposed model and algorithm can effectively solve the integrated problems, and compared with the objective value of the original network, the network clearance time of the final solution reduces by 47.4%. The calculation results for the realistic topology and size network of Ningbo in China, which locates on the east coast of the Pacific Ocean, justify the practical value of the model and solution method, and solutions under different settings of reduction amount of merging cell capacity embody obvious differences. Copyright © 2015 John Wiley & Sons, Ltd.     

Integrated optimization on train scheduling and preventive maintenance time slots planning

We address the problem of simultaneously scheduling trains and planning preventive maintenance time slots (PMTSs) on a general railway network. Based on network cumulative flow variables, a novel integrated mixed-integer linear programming (MILP) model is proposed to simultaneously optimize train routes, orders and passing times at each station, as well as work-time of preventive maintenance tasks (PMTSs). In order to provide an easy decomposition mechanism, the limited capacity of complex tracks is modelled as side constraints and a PMTS is modelled as a virtual train. A Lagrangian relaxation solution framework is proposed, in which the difficult track capacity constraints are relaxed, to decompose the original complex integrated train scheduling and PMTSs planning problem into a sequence of single train-based sub-problems. For each sub-problem, a standard label correcting algorithm is employed for finding the time-dependent least cost path on a time-space network. The resulting dual solutions can be transformed to feasible solutions through priority rules. Numerical experiments are conducted on a small artificial network and a real-world network adapted from a Chinese railway network, to evaluate the effectiveness and computational efficiency of the integrated optimization model and the proposed Lagrangian relaxation solution framework. The benefits of simultaneously scheduling trains and planning PMTSs are demonstrated, compared with a commonly-used sequential scheduling method.     

A computational model for the probit‐based dynamic stochastic user optimal traffic assignment problem

This paper focuses on computational model development for the probit‐based dynamic stochastic user optimal (P‐DSUO) traffic assignment problem. We first examine a general fixed‐point formulation for the P‐DSUO traffic assignment problem, and subsequently propose a computational model that can find an approximated solution of the interest problem. The computational model includes four components: a strategy to determine a set of the prevailing routes between each origin–destination pair, a method to estimate the covariance of perceived travel time for any two prevailing routes, a cell transmission model‐based traffic performance model to calculate the actual route travel time used by the probit‐based dynamic stochastic network loading procedure, and an iterative solution algorithm solving the customized fixed‐point model. The Ishikawa algorithm is proposed to solve the computational model. A comparison study is carried out to investigate the efficiency and accuracy of the proposed algorithm with the method of successive averages. Two numerical examples are used to assess the computational model and the algorithm proposed. Results show that Ishikawa algorithm has better accuracy for smaller network despite requiring longer computational time. Nevertheless, it could not converge for larger network. Copyright © 2010 John Wiley & Sons, Ltd.     

Routing and charging locations for electric vehicles for intercity trips

This study addresses two problems in the context of battery electric vehicles (EVs) for intercity trips: the EV routing problem and the EV optimal charging station location problem (CSLP). The paper shows that EV routing on the shortest path subject to range feasibility for one origin–destination (O–D) pair, called the shortest walk problem (SWP), as well as a stronger version of the problem – the p-stop limited SWP – can be reduced to solving the shortest path problem on an auxiliary network. The paper then addresses optimal CSLPs in which EVs are range feasible with and without p-stops. We formulate the models as mixed-integer multi-commodity flow problems on the same auxiliary network without path and relay pattern enumeration. Benders decomposition is used to propose an exact solution approach. Numerical experiments are conducted using the Indiana state network.     

Dynamic traffic metering in urban street networks: Formulation and solution algorithm

Traffic metering offers great potential to reduce congestion and enhance network performance in oversaturated urban street networks. This paper presents an optimization program for dynamic traffic metering in urban street networks based on the Cell Transmission Model (CTM). We have formulated the problem as a Mixed-Integer Linear Program (MILP) capable of metering traffic at network gates with given signal timing parameters at signalized intersections. Due to the complexities of the MILP model, we have developed a novel and efficient solution approach that solves the problem by converting the MILP to a linear program and several CTM simulation runs. The solution algorithm is applied to two case studies under different conditions. The proposed solution technique finds solutions that have a maximum gap of 1% of the true optimal solution and guarantee the maximum throughput by keeping some vehicles at network gates and only allowing enough vehicles to enter the network to prevent gridlocks. This is confirmed by comparing the case studies with and without traffic metering. The results in an adapted real-world case study network show that traffic metering can increase network throughput by 4.9–38.9% and enhance network performance.     

Store-and-forward based methods for the signal control problem in large-scale congested urban road networks

The problem of designing network-wide traffic signal control strategies for large-scale congested urban road networks is considered. One known and two novel methodologies, all based on the store-and-forward modeling paradigm, are presented and compared. The known methodology is a linear multivariable feedback regulator derived through the formulation of a linear-quadratic optimal control problem. An alternative, novel methodology consists of an open-loop constrained quadratic optimal control problem, whose numerical solution is achieved via quadratic programming. Yet a different formulation leads to an open-loop constrained nonlinear optimal control problem, whose numerical solution is achieved by use of a feasible-direction algorithm. A preliminary simulation-based investigation of the signal control problem for a large-scale urban road network using these methodologies demonstrates the comparative efficiency and real-time feasibility of the developed signal control methods.     

Location planning for transit-based evacuation under the risk of service disruptions

The effectiveness of transit-based emergency evacuation highly depends on the location of pick-up facilities, resource allocation, and management. These facilities themselves are often subject to service disruptions during or after the emergency. This paper proposes a reliable emergency facility location model that determines both pre-emergency facility location planning and the evacuation operations afterwards, while facilities are subject to the risk of disruptions. We analyze how evacuation resource availability leverages individual evacuees’ response to service disruptions, and show how equilibrium of the evacuee arrival process could be reached at a functioning pick-up facility. Based on this equilibrium, an optimal resource allocation strategy is found to balance the tradeoff between the evacuees’ risks and the evacuation agency’s operation costs. This leads to the development of a compact polynomial-size linear integer programming formulation that minimizes the total expected system cost from both pre-emergency planning (e.g., facility set-up) and the evacuation operations (e.g., fleet management, transportation, and exposure to hazardous surroundings) across an exponential number of possible disruption scenarios. We also show how the model can be flexibly used to plan not only pre-disaster evacuation but also post-disaster rescue actions. Numerical experiments and an empirical case study for three coastal cities in the State of Mississippi (Biloxi, Gulfport, and D’lberville) are conducted to study the performance of the proposed models and to draw managerial insights.     

Optimal fueling strategies for locomotive fleets in railroad networks

Railroad companies spend billions of dollars each year to purchase fuel for thousands of locomotives across the railroad network. Each fuel station charges a site-dependent fuel price, and the railroad companies must pay an additional flat contracting fee in order to use it. This paper presents a linear mixed-integer mathematical model that integrates not only fuel station location decisions but also locomotive fueling schedule decisions. The proposed model helps railroads decide which fuel stations to contract, and how each locomotive should purchase fuel along its predetermined shipment path, such that no locomotive runs out of fuel while the summation of fuel purchasing costs, shipment delay costs (due to fueling), and contracting charges is minimized. A Lagrangian relaxation framework is proposed to decompose the problem into fueling schedule and facility location selection sub-problems. A network shortest path formulation of the fueling schedule sub-problem is developed to obtain an exact optimal solution to the fueling schedule sub-problem. The proposed framework is applied to a large-scale empirical case and is shown to effectively reduce system costs.     

Computing 4D near-optimal trajectories for dynamic air traffic flow management with column generation and branch-and-price

Abstract

The current air traffic system faces recurrent saturation problems. Numerous studies are dedicated to this issue, including the present research on a new dynamic regulation filter holding frequent trajectory optimisations in a real-time sliding horizon loop process. We consider a trajectory optimisation problem arising in this context, where a feasible four-dimensional (4D) trajectory is to be built and assigned to each regulated flight to suppress sector overloads while minimising the cost of the chosen policy. We model this problem with a mixed integer linear programme and solve it with a branch-and-price approach. The pricing sub-problem looks for feasible trajectories in a dynamic three-dimensional (3D) network and is solved with a specific algorithm based on shortest path labelling algorithms and on dynamic programming. Each algorithm is tested on real-world data corresponding to a complete traffic day in the European air traffic system; experimental results, including computing times measurement, validate the solution process.     

Constraint handling methods in pavement maintenance programming

The problem of pavement maintenance management at the network level is one of maintaining as high a level of serviceability as possible for a pavement network system through reactive and proactive repair actions, whilst optimising the use of available resources. This problem has traditionally been solved using techniques like mathematical programming and heuristic methods. Lately, the use of genetic algorithms (GAs) to solve resource allocation problems like the network pavement maintenance problem has received increased attention from researchers. GAs have been demonstrated to be better than traditional techniques in terms of solution quality and diversity. However, the performance of the GAs is affected by the method used to handle the many constraints present in the formulation of such resource allocation methods. Penalty as well as generate and repair methods are the usual techniques used to handle constraints, but these have their drawbacks in terms of computational efficiency and tendency to get trapped in sub-optimal solution spaces. The paper proposes a third method that is computationally more efficient than the previous methods. The method is based on prioritised allocation of resources to maintenance activities and the maximum utilisation of resources. Constraints on maximum resource availability are no longer used passively to check on solution feasibility (as in the previous methods) but are used to help generate feasible solutions during the resource allocation phase of the algorithm itself. It is demonstrated that the GA with the prioritised resource allocation method (PRAM) outperforms the traditional GA with repair or penalty methods. PRAM was able to consistently outperform the other two GA based methods, both in terms of solution quality as well as computational time. It is concluded that PRAM can be used as the basis of more efficient resource allocation procedures in the area of pavement maintenance management.     

Optimizing the freight train connection service network of a large-scale rail system

This paper presents a formulation and solution for the train connection services (TCSs) problem in a large-scale rail network in order to determine the optimal freight train services, the frequency of services, and the distribution of classification workload among yards. TCS problem is modeled as a bi-level programming problem. The upper-level is intended to find an optimal train connection service, and the lower-level is used for assigning each shipment to a sequence of train services and determining the frequency of services.Our model solves the TCS problem of the China railway system, which is one of the largest railway systems in the world. The system consists of 5544 stations, and over 520,000 shipments using this system for a year period. A subnetwork is defined with 127 yards having some minimum level of reclassification resources and 14,440 demands obtained by aggregating 520,000 shipments to the subnetwork. We apply a simulated annealing algorithm to the data for optimal computation after pre-processing and get an excellent result. Comparing our optimal solution with the existing plan result, there are improvements of about 20.8% in the total cost.     

A mixed-integer linear program for optimizing sensor locations along freeway corridors

How to optimally allocate limited freeway sensor resources is of great interest to transportation engineers. In this paper, we focus on the optimal allocation of point sensors, such as loop detectors, to minimize performance measurement errors. Although it has been shown that the minimization problem can be intuitively formulated as a nonlinear program, the formulation is so complex that only heuristic approaches can be used to solve the problem. In this paper, we transform the nonlinear program into an equivalent mixed-integer linear model. The linearized model is shown to have a graphical interpretation and can be solved using resource constrained shortest path algorithms. A customized Branch-and-Bound technique is then proposed to solve the resource constrained shortest path problem. Numerical experiments along an urban freeway corridor demonstrate that this sensor location model is successful in allocating loop detectors to improve the accuracy of travel time estimation.     

A bilevel flow model for hazmat transportation network design

In this work we consider the following hazmat transportation network design problem. A given set of hazmat shipments has to be shipped over a road transportation network in order to transport a given amount of hazardous materials from specific origin points to specific destination points, and we assume there are regional and local government authorities that want to regulate the hazmat transportations by imposing restrictions on the amount of hazmat traffic over the network links. In particular, the regional authority aims to minimize the total transport risk induced over the entire region in which the transportation network is embedded, while local authorities want the risk over their local jurisdictions to be the lowest possible, forcing the regional authority to assure also risk equity. We provide a linear bilevel programming formulation for this hazmat transportation network design problem that takes into account both total risk minimization and risk equity. We transform the bilevel model into a single-level mixed integer linear program by replacing the second level (follower) problem by its KKT conditions and by linearizing the complementary constraints, and then we solve the MIP problem with a commercial optimization solver. The optimal solution may not be stable, and we provide an approach for testing its stability and for evaluating the range of its solution values when it is not stable. Moreover, since the bilevel model is difficult to be solved optimally and its optimal solution may not be stable, we provide a heuristic algorithm for the bilevel model able to always find a stable solution. The proposed bilevel model and heuristic algorithm are experimented on real scenarios of an Italian regional network.     

Liner shipping network design with emission control areas: A genetic algorithm-based approach

To curb emissions, containerized shipping lines face the traditional trade-off between cost and emissions (CO₂ and SO_x) reduction. This paper considers this element in the context of liner service design and proposes a mixed integer linear programming (MILP) model based on a multi-commodity pickup and delivery arc-flow formulation. The objective is to maximize the profit by selecting the ports to be visited, the sequence of port visit, the cargo flows between ports, as well as the number/operating speeds of vessels on each arc of the selected route. The problem also considers that Emission Control Areas (ECAs) exist in the liner network and accounts for the vessel carrying capacity. In addition to using the MILP solver of CPLEX, we develop in the paper a specific genetic algorithm (GA) based heuristic and show that it gives the possibility to reach an optimal solution when solving large size instances.     

Network design for personal rapid transit under transit-oriented development

This study addresses guideway network design for personal rapid transit (PRT) favoring transit-oriented development. The guideway network design problem seeks to minimize both the guideway construction cost and users’ travel time. In particular, a set of optional points, known as Steiner points, are introduced in the graph to reduce the guideway length. The model is formulated as a combined Steiner and assignment problem, and a Lagrangian relaxation based solution algorithm is developed to solve the optimal solution. Numerical studies are carried on a real-sized network, and illustrate that the proposed model and solution algorithm can solve the PRT guideway network design problem effectively.     

A dual decomposition method for sector capacity constrained traffic flow optimization

An aggregate air traffic flow model based on a multicommodity network is used for traffic flow management in the National Airspace System. The problem of minimizing the total travel time of flights in the National Airspace System of the United States, subject to sector capacity constraints, is formulated as an Integer Program. The resulting solution achieves optimal delay control. The Integer Program implemented for the scenarios investigated has billions of variables and constraints. It is relaxed to a Linear Program for computational efficiency. A dual decomposition method is applied to solve the large scale Linear Program in a computationally tractable manner. A rounding algorithm is developed to map the Linear Program solution to a physically acceptable result, and is implemented for the entire continental United States. A 2-h traffic flow management problem is solved with the method.     

Global optimization methods for the discrete network design problem

This paper addresses the discrete network design problem (DNDP) with multiple capacity levels, or multi-capacity DNDP for short, which determines the optimal number of lanes to add to each candidate link in a road network. We formulate the problem as a bi-level programming model, where the upper level aims to minimize the total travel time via adding new lanes to candidate links and the lower level is a traditional Wardrop user equilibrium (UE) problem. We propose two global optimization methods by taking advantage of the relationship between UE and system optimal (SO) traffic assignment principles. The first method, termed as SO-relaxation, exploits the property that an optimal network design solution under SO principle can be a good approximate solution under UE principle, and successively sorts the solutions in the order of increasing total travel time under SO principle. Optimality is guaranteed when the lower bound of the total travel time of the unexplored solutions under UE principle is not less than the total travel time of a known solution under UE principle. The second method, termed as UE-reduction, adds the objective function of the Beckmann-McGuire-Winsten transformation of UE traffic assignment to the constraints of the SO-relaxation formulation of the multi-capacity DNDP. This constraint is convex and strengthens the SO-relaxation formulation. We also develop a dynamic outer-approximation scheme to make use of the state-of-the-art mixed-integer linear programming solvers to solve the SO-relaxation formulation. Numerical experiments based on a two-link network and the Sioux-Falls network are conducted.     

Large-scale evacuation network optimization: a bi-level control method with uncertain arterial demand

To improve the efficiency of large-scale evacuations, a network aggregation method and a bi-level optimization control method are proposed in this paper. The network aggregation method indicates the uncertain evacuation demand on the arterial sub-network and balances accuracy and efficiency by refining local road sub-networks. The bi-level optimization control method is developed to reconfigure the aggregated network from both supply and demand sides with contraflow and conflict elimination. The main purpose of this control method is to make the arterial sub-network to be served without congestion and interruption. Then, a corresponding bi-objective network flow model is presented in a static manner for an oversaturated network, and a Genetic Algorithm-based solution method is used to solve the evacuation problem. The numerical results from optimizing a city-scale evacuation network for a super typhoon justify the validity and usefulness of the network aggregation and optimization control methods.