A self-adaptive gradient projection algorithm for the nonadditive traffic equilibrium problem

Chen, Anthony; Zhong, Zhang; Xu, Xiangdong

doi:10.1016/j.cor.2011.02.018

Cited by 65 publications

(29 citation statements)

References 46 publications

(63 reference statements)

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“…However, we did not adjust α specifically for every instance, but rather fixed it to a value that allows all tested instances to converge. Chen et al [42] and Chen et al [43] also suggest a self-adaptive step size strategy for GP and other algorithms that we did not implement in our study. Another modification of GP based on conjugate directions is presented in Lee et al [44].…”

Section: Gradient Projectionmentioning

confidence: 98%

A framework for and empirical study of algorithms for traffic assignment

Perederieieva

Ehrgott

Raith

et al. 2015

Computers & Operations Research

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Traffic congestion is an issue in most cities worldwide. Transportation engineers and urban planners develop various traffic management projects in order to solve this issue. One way to evaluate such projects is traffic assignment (TA). The goal of TA is to predict the behaviour of road users for a given period of time (morning and evening peaks, for example). Once such a model is created, it can be used to analyse the usage of a road network and to predict the impact of implementing a potential project. The most commonly used TA model is known as user equilibrium, which is based on the assumption that all drivers minimise their travel time or generalised cost. In this study, we consider the static deterministic user equilibrium TA model.The constant growth of road networks and the need of highly precise solutions (required for select link analysis, network design, etc) motivate researchers to propose numerous methods to solve this problem. Our study aims to provide a recommendation on what methods are more suitable depending on available computational resources, time and requirements on the solution. In order to achieve this goal, we implement a flexible software framework that maximises usage of common code and, hence, ensures comparison of algorithms on common ground. In order to identify similarities and differences of the methods, we analyse groups of algorithms that are based on common principles. In addition, we implement and compare several different methods for solving sub-problems and discuss issues related to accumulated numerical errors that might occur when highly accurate solutions are required.

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Section: Gradient Projectionmentioning

confidence: 98%

A framework for and empirical study of algorithms for traffic assignment

Perederieieva

Ehrgott

Raith

et al. 2015

Computers & Operations Research

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“…The unknown state variables x 1 (t − i) of the information vector ϕ(t) are replaced by their estimated statesx 1 …”

Section: The Observer-based Multi-innovation Stochastic Gradient Algomentioning

confidence: 99%

“…The stochastic gradient (SG) algorithms include the conjugate gradient algorithms [2], the alternative gradient algorithms [41], the gradient projection algorithms [1], and the steepest descent algorithms [20]. Two typical algorithms are the multi-innovation SG algorithm and the gradient-based iterative algorithm [8,10].…”

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confidence: 99%

Gradient-Based Parameter Identification Algorithms for Observer Canonical State Space Systems Using State Estimates

Ding

2014

Circuits Syst Signal Process

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This paper considers the parameter identification problem of the state space observer canonical model for linear stochastic systems, and proposes a Kalman filterbased gradient iterative algorithm and an observer-based multi-innovation stochastic gradient algorithm. The fundamental idea is to replace the unmeasurable states in the information vector with the estimated states and to compute the states of the systems through the Kalman filter or the state observer using the previous parameter estimates. Examples are provided to confirm the effectiveness of the proposed algorithms.

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“…Jayakrishnan et al (1994) recommend setting α to 1. Chen et al (2012) and Chen et al (2013) also suggest a self-adaptive step size strategy for GP that we did not implement in our study. Another path-based algorithm is proposed in Florian et al (2009).…”

Section: Path-based Algorithmsmentioning

confidence: 99%

Numerical stability of path-based algorithms for traffic assignment

Perederieieva

Ehrgott

Raith

et al. 2015

Optimization Methods and Software

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In this paper we study numerical stability of path-based algorithms for the traffic assignment problem. These algorithms are based on decomposition of the original problem into smaller sub-problems which are optimised sequentially. Previously, path-based algorithms were numerically tested only in the setting of moderate requirements to the level of solution precision. In this study we analyse convergence of these methods when the convergence measure approaches machine epsilon of IEEE double precision format. In particular, we demonstrate that the straightforward implementation of one of the algorithms of this group (projected gradient) suffers from loss of precision and is not able to converge to highly precise solution. We propose a way to solve this problem and test the proposed adjusted version of the algorithm on various benchmark instances.

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A self-adaptive gradient projection algorithm for the nonadditive traffic equilibrium problem

Cited by 65 publications

References 46 publications

A framework for and empirical study of algorithms for traffic assignment

A framework for and empirical study of algorithms for traffic assignment

Gradient-Based Parameter Identification Algorithms for Observer Canonical State Space Systems Using State Estimates

Numerical stability of path-based algorithms for traffic assignment

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