Network-oriented household activity pattern problem for system optimization

The recently emerging trend of self-driving vehicles and information sharing technologies, made available by private technology vendors, starts creating a revolutionary paradigm shift in the coming years for traveler mobility applications. By considering a deterministic traveler decision making framework at the household level in congested transportation networks, this paper aims to address the challenges of how to optimally schedule individuals’ daily travel patterns under the complex activity constraints and interactions. We reformulate two special cases of household activity pattern problem (HAPP) through a high-dimensional network construct, and offer a systematic comparison with the classical mathematical programming models proposed by Recker (1995). Furthermore, we consider the tight road capacity constraint as another special case of HAPP to model complex interactions between multiple household activity scheduling decisions, and this attempt offers another household-based framework for linking activity-based model (ABM) and dynamic traffic assignment (DTA) tools. Through embedding temporal and spatial relations among household members, vehicles and mandatory/optional activities in an integrated space-time-state network, we develop two 0–1 integer linear programming models that can seamlessly incorporate constraints for a number of key decisions related to vehicle selection, activity performing and ridesharing patterns under congested networks. The well-structured network models can be directly solved by standard optimization solvers, and further converted to a set of time-dependent state-dependent least cost path-finding problems through Lagrangian relaxation, which permit the use of computationally efficient algorithms on large-scale high-fidelity transportation networks.     

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.     

Optimal speed detector density for the network with travel time information

In the expressway network, detectors are installed on the links for detecting the travel time information while the predicted travel time can be provided by the route guidance system (RGS). The speed detector density can be determined to influence flow distributions in such a way that the precision of the travel time information and the social cost of the speed detectors are optimized, provided that each driver chooses the minimum perceived travel time path in response to the predicted travel time information. In this paper, a bilevel programming model is proposed for the network with travel time information provided by the RGS. The lower-level problem is a probit-based traffic assignment model, while the upper-level problem is to determine the speed detector density that minimizes the measured travel time error variance as well as the social cost of the speed detectors. The sensitivity analysis based algorithm is proposed for the bilevel programming problem. Numerical examples are provided to illustrate the applications of the proposed model and of the solution algorithm.     

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.     

Itinerary choice and advance ticket booking for high-speed-railway network services

This paper formulates and examines the passenger flow assignment (itinerary choice) problem in high-speed railway (HSR) systems with multiple-class users and multiple-class seats, given the train schedules and time-varying travel demand. In particular, we take into account advance booking cost of travelers in the itinerary choice problem. Rather than a direct approach to model advance booking cost with an explicit cost function, we consider advance booking cost endogenously, which is determined as a part of the passenger choice equilibrium. We show that this equilibrium problem can be formulated as a linear programming (LP) model based on a three-dimension network representation of time, space, and seat class. At the equilibrium solution, a set of Lagrange multipliers for the LP model are obtained, which are associated with the rigid in-train passenger capacity constraints (limited numbers of seats). We found that the sum of the Lagrange multipliers along a path in the three-dimension network reflects the advance booking cost of tickets (due to advance/early booking to guarantee availability) perceived by the passengers. Numerical examples are presented to demonstrate and illustrate the proposed model for the passenger assignment problem.     

Application of multiple criteria decision making for network improvement

In this paper we propose application of multiple criteria decision making to problems of a metropolitan network improvement plan. Initially, a bilevel multiple objective network design model is considered in two objectives which are minimal government budget and minimal total travel time of road users. We seek feasible improvement alternatives among those bottleneck links in an existing road network structure and travel demand. We present an effective heuristic algorithm to obtain noninferior solutions; then ELECTRE III multiple criteria decision making and group decision making are used to evaluate and to select a compromise solution among those noninferior solutions. From the design phase in multiple criteria decision making, multiple objective mathematical programming is used to formulate a continuous network design model. However, from the phase of evaluation, multiple criteria decision making to solve the discrete network design problem. The network of metropolitan Taipei is taken as an example to illustrate the operation of this model.     

Estimation of mean and covariance of peak hour origin–destination demands from day-to-day traffic counts

This paper proposes a generalized model to estimate the peak hour origin–destination (OD) traffic demand variation from day-to-day hourly traffic counts throughout the whole year. Different from the conventional OD estimation methods, the proposed modeling approach aims to estimate not only the mean but also the variation (in terms of covariance matrix) of the OD demands during the same peak hour periods due to day-to-day fluctuation over the whole year. For this purpose, this paper fully considers the first- and second-order statistical properties of the day-to-day hourly traffic count data so as to capture the stochastic characteristics of the OD demands. The proposed model is formulated as a bi-level optimization problem. In the upper-level problem, a weighted least squares method is used to estimate the mean and covariance matrix of the OD demands. In the lower-level problem, a reliability-based traffic assignment model is adopted to take account of travelers’ risk-taking path choice behaviors under OD demand variation. A heuristic iterative estimation-assignment algorithm is proposed for solving the bi-level optimization problem. Numerical examples are presented to illustrate the applications of the proposed model for assessment of network performance over the whole year.     

Multicriteria evaluation on accessibility‐based transportation equity in road network design problem

This paper investigates the performance of accessibility‐based equity measurements in transportation and proposes a multiobjective optimization model to simulate the trade‐offs between equity maximization and cost minimization of network construction. The equity is defined as the spatial distribution of accessibilities across zone areas. Six representative indicators were formulated, including GINI coefficient, Theil index, mean log deviation, relative mean deviation, coefficient of variation, and Atkinson index, and incorporated into an equity maximization model to evaluate the performance sensitivity. A bilevel multiobjective optimization model was proposed to obtain the Pareto‐optimal solutions for link capacity enhancement in a stochastic road network design problem. A numerical analysis using the Sioux Falls data was implemented. Results verified that the equity indicators are quite sensitive to the pattern of network scenarios in the sense that the level of equity varies according to the amount of overall capacity enhancement as well as the assignment of improved link segments. The suggested multiobjective model that enables representing the Pareto‐optimal solutions can provide multiple options in the decision making of road network design. Copyright © 2012 John Wiley & Sons, Ltd.     

Customized bus service design for jointly optimizing passenger-to-vehicle assignment and vehicle routing

Emerging transportation network services, such as customized buses, hold the promise of expanding overall traveler accessibility in congested metropolitan areas. A number of internet-based customized bus services have been planned and deployed for major origin-destination (OD) pairs to/from inner cities with limited physical road infrastructure. In this research, we aim to develop a joint optimization model for addressing a number of practical challenges for providing flexible public transportation services. First, how to maintain minimum loading rate requirements and increase the number of customers per bus for the bus operators to reach long-term profitability. Second, how to optimize detailed bus routing and timetabling plans to satisfy a wide range of specific user constraints, such as passengers’ pickup and delivery locations with preferred time windows, through flexible decision for matching passengers to bus routes. From a space-time network modeling perspective, this paper develops a multi-commodity network flow-based optimization model to formulate a customized bus service network design problem so as to optimize the utilization of the vehicle capacity while satisfying individual demand requests defined through space-time windows. We further develop a solution algorithm based on the Lagrangian decomposition for the primal problem and a space-time prism based method to reduce the solution search space. Case studies using both the illustrative and real-world large-scale transportation networks are conducted to demonstrate the effectiveness of the proposed algorithm and its sensitivity under different practical operating conditions.     

The estimation of a time-dependent OD trip table with vehicle trajectory samples

Abstract

In this paper we discuss a dynamic origin–destination (OD) estimation problem that has been used for identifying time-dependent travel demand on a road network. Even though a dynamic OD table is an indispensable data input for executing a dynamic traffic assignment, it is difficult to construct using the conventional OD construction method such as the four-step model. For this reason, a direct estimation method based on field traffic data such as link traffic counts has been used. However, the method does not account for a logical relationship between a travel demand pattern and socioeconomic attributes. In addition, the OD estimation method cannot guarantee the reliability of estimated results since the OD estimation problem has a property named the ‘underdetermined problem.’ In order to overcome such a problem, the method developed in this paper makes use of vehicle trajectory samples with link traffic counts. The new method is applied to numerical examples and shows promising capability for identifying a temporal and spatial travel demand pattern.     

The location selection problem for the household activity pattern problem

In this paper, an integrated destination choice model based on routing and scheduling considerations of daily activities is proposed. Extending the Household Activity Pattern Problem (HAPP), the Location Selection Problem (LSP–HAPP) demonstrates how location choice is made as a simultaneous decision from interactions both with activities having predetermined locations and those with many candidate locations. A dynamic programming algorithm, developed for PDPTW, is adapted to handle a potentially sizable number of candidate locations. It is shown to be efficient for HAPP and LSP–HAPP applications. The algorithm is extended to keep arrival times as functions for mathematical programming formulations of activity-based travel models that often have time variables in the objective.     

Network-based real option models

Building on earlier work to incorporate real option methodologies into network modeling, two models are proposed. The first is the network option design problem, which maximizes the expanded net present value of a network investment as a function of network design variables with the option to defer the committed design investment. The problem is shown to be a generalized version of the network design problem and the multi-period network design problem. A heuristic based on radial basis functions is used to solve the problem for continuous link expansion with congestion effects. The second model is a link investment deferral option set, which decomposes the network investment deferral option into individual, interacting link or project investments. This model is a project selection problem under uncertainty, where each link or project can be deferred such that the expanded net present value is maximized. The option is defined in such a way that a lower bound can be solved using an exact method based on multi-option least squares Monte Carlo simulation. Numerical tests are conducted with the classical Sioux Falls network and compared to earlier published results.     

Regulating hazardous materials transportation by dual toll pricing

We investigate dual-toll setting as a policy tool to mitigate the risk of hazardous material (hazmat) shipment in road networks. We formulate the dual-toll problem as a bi-level program wherein the upper level aims at minimizing the risk, and the lower level explores the user equilibrium decision of the regular vehicles and hazmat carriers given the toll. When the upper level objective is to minimize the risk and all links are tollable, we decompose the formulation into first-stage and second-stage, and suggest a computational method to solve each stage. Our two-stage solution methodology guarantees nonnegative valid dual tolls regardless of the solution accuracy of the first-stage problem. We also consider a general dual-toll setting problem where the regulator rather wishes to minimize a combination of risk and the paid tolls and/or some links are untollable. To solve this truly bilevel problem, we provide heuristic algorithms that decompose the problem into subproblems each being solved by a line search. Case studies based on the Sioux Falls network illustrate the insights on the dual-toll policies.     

Activity-based market equilibrium for capacitated multimodal transport systems

Empirical studies have shown that demand for multimodal transport systems is highly correlated with activity schedules of individuals. Nonetheless, existing analytical equilibrium models of multimodal systems have only considered trip-based demand. We propose a new market equilibrium model that is sensitive to traveler activity schedules and system capacities. The model is based on a constrained mixed logit model of activity schedule choice, where each schedule in the choice set is generated with a multimodal extension of the household activity pattern problem. The extension explicitly accounts for both passenger choices of activity participation and multimodal choices like public transit, walking, and vehicle parking. The market equilibrium is achieved with Lagrangian relaxation to determine the optimal dual price of the capacity constraint, and a method of successive averages with column generation finds an efficient choice set of activity schedules to assign flows over the dynamic network load capacities. An example illustrates the model and algorithm, effects similar to Vickrey’s morning commute model can be observed as a special case. A case study of the Oakville Go Transit station access “last mile” problem in the Greater Toronto Area is conducted with 166 survey samples reflecting 3680 individuals. Results suggest that a $10 fixed parking fee at Oakville station would lead to a reduction of access auto share from 54.8% to 49.5%, an increase in access transit share from 20.7% to 25.9%, and a disutility increase of 11% for the of single-activity residents of Oakville.     

A reliability‐based network design problem

This paper presents a reliability‐based network design problem. A network reliability concept is embedded into the continuous network design problem in which travelers' route choice behavior follows the stochastic user equilibrium assumption. A new capacity‐reliability index is introduced to measure the probability that all of the network links are operated below their capacities when serving different traffic patterns deviating from the average condition. The reliability‐based network design problem is formulated as a bi‐level program in which the lower level sub‐program is the probit‐based stochastic user equilibrium problem and the upper level sub‐program is the maximization of the new capacity reliability index. The lower level sub‐program is solved by a variant of the method of successive averages using the exponential average to represent the learning process of network users on a daily basis that results in the daily variation of traffic‐flow pattern, and Monte Carlo stochastic loading. The upper level sub‐program is tackled by means of genetic algorithms. A numerical example is used to demonstrate the concept of the proposed framework.     

A network option portfolio management framework for adaptive transportation planning

A real option portfolio management framework is proposed to make use of an adaptive network design problem developed using stochastic dynamic programming methodologies. The framework is extended from Smit’s and Trigeorgis’ option portfolio framework to incorporate network synergies. The adaptive planning framework is defined and tested on a case study with time series origin-destination demand data. Historically, OD time series data is costly to obtain, and there has not been much need for it because most transportation models use a single time-invariant estimate based on deterministic forecasting of demand. Despite the high cost and institutional barriers of obtaining abundant OD time series data, we illustrate how having higher fidelity data along with an adaptive planning framework can result in a number of improved management strategies. An insertion heuristic is adopted to run the lower bound adaptive network design problem for a coarse Iran network with 834 nodes, 1121 links, and 10 years of time series data for 71,795 OD pairs.     

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.     

The treatment of uncertainty in the dynamic origin–destination estimation problem using a fuzzy approach

Regardless of existing types of transportation and traffic model and their applications, the essential input to these models is travel demand, which is usually described using origin–destination (OD) matrices. Due to the high cost and time required for the direct development of such matrices, they are sometimes estimated indirectly from traffic measurements recorded from the transportation network. Based on an assumed demand profile, OD estimation problems can be categorized into static or dynamic groups. Dynamic OD demand provides valuable information on the within-day fluctuation of traffic, which can be employed to analyse congestion dissipation. In addition, OD estimates are essential inputs to dynamic traffic assignment (DTA) models. This study presents a fuzzy approach to dynamic OD estimation problems. The problems are approached using a two-level model in which demand is estimated in the upper level and the lower level performs DTA via traffic simulation. Using fuzzy rules and the fuzzy C-Mean clustering approach, the proposed method treats uncertainty in historical OD demand and observed link counts. The approach employs expert knowledge to model fitted link counts and to set boundaries for the optimization problem by defining functions in the fuzzification process. The same operation is performed on the simulation outputs, and the entire process enables different types of optimization algorithm to be employed. The Box-complex method is utilized as an optimization algorithm in the implementation of the approach. Empirical case studies are performed on two networks to evaluate the validity and accuracy of the approach. The study results for a synthetic network and a real network demonstrate the robust performance of the proposed method even when using low-quality historical demand data.     

Appraising large-scale investments in a metropolitan transportation system

A package of large-scale investments in the transportation infrastructure in the Stockholm metropolitan region is currently being proposed. It contains new investments in the railway and subway systems as well as new links in the road system. This paper deals with the issue of appraising this kind of investment program. One major problem is the lack of a unique standard method, and it is argued that several tools should be used in a practical evaluation of large-scale investments in the transportation system.Four different approaches are presented and related to each other. First, one study uses a network-based mode-split/assignment model with a fixed trip matrix. The second study is complementary, as its aim is to also trace the impacts on the spatial distribution of population and jobs by applying an integrated transportation and land use model. Third, the long-run effects of the investments on regional economic growth are discussed within the framework of regional production functions. Fourth, an alternative approach is used, in which benefits from the investments are assessed through their estimated influence on aggregate land values.Abbreviations RA Reference Alternative - IP Investment Proposal - IMREL Integrated Model of Residential and Employment Location - RPFM Regional Production Function Model An earlier version of this paper was presented at the 31th European Congress of the Regional Science Association, Lisbon, August 1991.     

Traffic signal timing problems with environmental and equity considerations

Traffic signal timings in a road network can not only affect total user travel time and total amount of traffic emissions in the network but also create an inequity problem in terms of the change in travel costs of users traveling between different locations. This paper proposes a multi‐objective bi‐level programming model for design of sustainable and equitable traffic signal timings for a congested signal‐controlled road network. The upper level of the proposed model is a multi‐objective programming problem with an equity constraint that maximizes the reserve capacity of the network and minimizes the total amount of traffic emissions. The lower level is a deterministic network user equilibrium problem that considers the vehicle delays at signalized intersections of the network. To solve the proposed model, an approach for normalizing incommensurable objective functions is presented, and a heuristic solution algorithm that combines a penalty function approach and a simulated annealing method is developed. Two numerical examples are presented to show the effects of reserve capacity improvement and green time proportion on network flow distribution and transportation system performance and the importance of incorporating environmental and equity objectives in the traffic signal timing problems. Copyright © 2013 John Wiley & Sons, Ltd.