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This study provides a gradient projection (GP) algorithm to solve the combined modal split and traffic assignment (CMSTA) problem. The nested logit (NL) model is used to consider the mode correlation under the user equilibrium (UE) route choice condition. Specifically, a two-phase GP algorithm is developed to handle the hierarchical structure of the NL model in the CMSTA problem. The Seoul transportation network in Korea is adopted to demonstrate an applicability in a large-scale multimodal transportation network. The results show that the proposed GP solution algorithm outperforms the method of the successive averages (MSA) algorithm and the classical Evan's algorithm. [ABSTRACT FROM AUTHOR]

Traffic equilibrium models under uncertainty characterize travelers’ route choice behaviors under travel time variability. In this paper, we develop a link -based mean-excess traffic equilibrium (L-METE) model by integrating the sub-additivity property and complete travel time variability characterization of mean-excess travel time (METT), and the computationally tractable additive route cost structure of the conventional user equilibrium (UE) problem. Compared to the majority of relevant models formulated in the route domain, the link -based modeling has two desirable features on modeling flexibility and algorithmic development. First, it avoids the normal route travel time distribution assumption (uniformly imposed for all routes) that inherits from the Central Limit Theorem in most route -based models, permitting the use of any suitable link travel time distributions from empirical studies. Second, the additive route cost structure makes the L-METE model solvable by readily adapting existing UE algorithms without the need of storing/enumerating routes while avoiding the computationally demanding nonadditive shortest path problem and route flow allocations in route-based models, which is a significant benefit for large-scale network applications under uncertainty. [ABSTRACT FROM AUTHOR]

Highlights: [•] We provide a general unconstrained optimization formulation for the CDA problem. [•] We prove the equivalence and uniqueness of the solution. [•] We formulate two logit CDA models with closed-form solution. [•] We develop a self-regulated averaging (SRA) descent algorithm. [•] We demonstrate the proposed formulations and algorithm with a real network. [ABSTRACT FROM AUTHOR]

Highlights: [•] An unconstrained minimization program is developed for the MNW-SUE model. [•] The MNW-SUE model considers non-identical perception variances for different trip lengths. [•] Equivalency and uniqueness of the MNW-SUE model are provided. [•] A link-based algorithm is developed for solving the MNW-SUE model. [•] Several extensions for future research are provided. [ABSTRACT FROM AUTHOR]

Highlights: [•] A path-size weibit (PSW) stochastic user equilibrium (SUE) model is developed. [•] The PSW-SUE model accounts for both route overlapping and route-specific perception variance. [•] Equivalency and uniqueness of the PSW-SUE model are provided. [•] A path-based algorithm is developed for solving the PSW-SUE model. [•] Numerical results using a real network are presented. [Copyright &y& Elsevier]

Combined travel demand models (CTDM) that integrate trip generation, trip distribution, modal split, and traffic assignment have been developed to resolve the inconsistency problem between the level-of-service and flow values of the sequential four-step travel demand forecasting procedure. In this paper, an improved partial linearization algorithm for solving the logit-based combined travel-destination-mode-route choice model formulated as a convex mathematical programming is developed. The improvements mainly focus on exploring recent advances in line search strategies to minimize the computational efforts required to determine a suitable stepsize that guarantees convergence. Specifically, the quadratic interpolation and the self-regulated averaging schemes are examined. Numerical results show that the self-regulated averaging line search scheme is more effective and efficient for solving the convex mathematical programming with a complex objective function in terms of solution quality and computational effort. [ABSTRACT FROM AUTHOR]

This article considers the stochastic user equilibrium (SUE) problem with the route choice model based on the C-logit function. The C-logit model has a simple closed-form analytical probability expression and requires relatively lower calibration efforts and represents a more realistic route choice behaviour compared with the multinomial logit model. This article proposes two versions of the C-logit SUE model that captures the route similarity using different attributes in the commonality factors. The two versions differ with respect to the independence assumption between cost and flow. The corresponding stochastic traffic equilibrium models are called the length-based and congestion-based C-logit SUE models, respectively. To formulate the length-based C-logit SUE model, an equivalent mathematical programming formulation is proposed. For the congestion-based C-logit SUE model, we provide two equivalent variational inequality formulations. To solve the proposed formulations, a new self-adaptive gradient projection algorithm is developed. The proposed formulations and new solution algorithm are tested in two well-known networks. Numerical results demonstrate the validity of the formulations and solution algorithm. [ABSTRACT FROM PUBLISHER]

The traffic equilibrium problem plays an important role in urban transportation planning and management. It predicts vehicular flows on the transportation network by assigning travel demands given in terms of an origin-destination trip table to routes in a network according to some behavioral route choice rules. In this paper, we enhance the realism of the traffic equilibrium problem by explicit modeling various physical and environment restrictions as side constraints. These side constraints are a useful means for describing queuing and congestion effects, restraining traffic flows to limit the amount of emissions, and modeling different traffic control policies. A generalized side-constrained traffic equilibrium (GSCTE) model is presented and some characterizations of the equilibrium solutions are discussed. The model is formulated as a variational inequality problem and solved by a predictor-corrector decomposition algorithm. Two numerical experiments are conducted to demonstrate some properties of the GSCTE model and the convergence properties of the decomposition algorithm. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we present an algorithm for solving the bicriteria traffic equilibrium problem with variable demand and nonlinear path costs. The path cost function considered is comprised of two attributes, travel time and toll, that are combined into a nonlinear generalized cost. Travel demand is determined endogenously according to a travel disutility function. Travelers choose routes with the minimum overall generalized costs. The algorithm involves two components: a bicriteria shortest path routine to implicitly generate the set of non-dominated paths and a projection and contraction method to solve the nonlinear complementarity problem (NCP) describing the traffic equilibrium problem. Numerical experiments are conducted to demonstrate the feasibility of the algorithm to this class of traffic equilibrium problems. [Copyright &y& Elsevier]

Path flow estimator (PFE) is a single-level network observer proposed to estimate path flows and origin-destination flows from traffic counts in a transportation network. The PFE model handles the traffic count inconsistency problem by allowing user to specify appropriate error bounds (or confidence interval) on the traffic counts. This approach, although flexible, introduces a systematic bias in underestimating the total demand when improper error bounds are specified. This paper presents an L∞-norm PFE model that minimizes the systematic bias of the total demand estimate encountered in the PFE model by determining the least maximum absolute error needed to accommodate measurement errors and traffic count inconsistencies within the estimation process. A solution algorithm based on the dual formulation combined with a column generation procedure is developed for solving the proposed L∞-norm PFE model. Numerical results are presented to illustrate the features and applicability of the proposed L∞-norm PFE model and solution algorithm. [ABSTRACT FROM AUTHOR]

Abstract: Path flow estimator (PFE) is a one-stage network observer proposed to estimate path flows and hence origin–destination (O–D) flows from traffic counts in a transportation network. Although PFE does not require traffic counts to be collected on all network links when inferring unmeasured traffic conditions, it does require all available counts to be reasonably consistent. This requirement is difficult to fulfill in practice due to errors inherited in data collection and processing. The original PFE model handles this issue by relaxing the requirement of perfect replication of traffic counts through the specification of error bounds. This method enhances the flexibility of PFE by allowing the incorporation of local knowledge, regarding the traffic conditions and the nature of traffic data, into the estimation process. However, specifying appropriate error bounds for all observed links in real networks turns out to be a difficult and time-consuming task. In addition, improper specification of the error bounds could lead to a biased estimation of total travel demand in the network. This paper therefore proposes the norm approximation method capable of internally handling inconsistent traffic counts in PFE. Specifically, three norm approximation criteria are adopted to formulate three L p-PFE models for estimating consistent path flows and O–D flows that simultaneously minimize the deviation between the estimated and observed link volumes. A partial linearization algorithm embedded with an iterative balancing scheme and a column generation procedure is developed to solve the three L p-PFE models. In addition, the proposed L p-PFE models are illustrated with numerical examples and the characteristics of solutions obtained by these models are discussed. [Copyright &y& Elsevier]

In recent years, researchers have shown interests in adopting path-based algorithms to the traffic assignment problem (TAP). The gradient projection (GP) algorithm demonstrates promising computational efficiency and convergence performance over state-of-the-practice link-based algorithms such as the widely accepted and used Frank-Wolfe (FW) algorithm. Note that GP still retains a linear convergence rate. GP thus could be slow as it is approaching the optimal solution. As a remedy, the Newton type approach becomes an intuitive candidate to improve GP''s performance. In this paper, we introduce an additional projection along the conjugate gradient direction besides the ordinary gradient projection in every iteration, by which the Hessian matrix is approximated more accurately. According to our computational results, the conjugate gradient projection (CGP) improves the convergence performance greatly. The results indicate that CGP can deliver better and more reliable convergence than GP and remains its computational tractability even when large-scale networks are being considered. © 2003 Elsevier Science Ltd. All rights reserved. [Copyright &y& Elsevier]