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- Frejinger, Emma, 1979-, et al.
(författare)
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Capturing correlation with subnetworks in route choice models
- 2007
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Ingår i: Transportation Research Part B. - : Elsevier BV. - 0191-2615 .- 1879-2367. ; 41:3, s. 363-378
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Tidskriftsartikel (refereegranskat)abstract
- When using random utility models for a route choice problem, a critical issue is the significant correlation among alternatives. There are basically two types of models proposed in the literature to address it: (i) a deterministic correction of the path utilities in a Multinomial Logit model (Such as the Path Size Logit or the C-Logit models) and (ii) an explicit modeling of the correlation through assumptions about the error terms, and the use of advanced discrete choice models such as the Cross-Nested Logit or the Error Component models. The first is simple, easy to handle and often used in practice. Unfortunately, it does not correctly capture the correlation structure, as we discuss in details in the paper. The second is more consistent with the modeling objectives, but very complicated to specify and estimate. The modeling framework proposed in this paper allows the analyst to control the trade-off between the simplicity of the model and the level of realism. Within this framework, the key concept capturing the correlation structure is called subnetwork. A subnetwork is a simplification of the road network only containing easy identifiable and behaviorally relevant roads. In practice, the subnetwork can easily be defined based oil the route network hierarchy. The importance and the originality of our approach lie in the possibility to capture the most important correlation without considerably increasing the model complexity. This makes it suitable for a wide spectrum of application,.;, namely involving realistic large-scale networks. As an illustration, we present estimation results of a factor analytic specification of a mixture of Multinomial Logit model, where the correlation among paths is captured by error components. The estimation is based on a GPS dataset collected in the Swedish city of Borlange. The results show a significant increase in model fit and forecasting performance for the Error Component model compared to a Path Size Logit model. Moreover, the correlation parameters are significant.
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- Frejinger, Emma, et al.
(författare)
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Sampling of alternatives for route choice modeling
- 2009
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Ingår i: Transportation Research Part B. - : Elsevier BV. - 0191-2615 .- 1879-2367. ; 43:10, s. 984-994
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Tidskriftsartikel (refereegranskat)abstract
- This paper presents a new paradigm for choice set generation in the context of route choice model estimation. We assume that the choice sets contain all paths connecting each origin-destination pair. Although this is behaviorally questionable, we make this assumption in order to avoid bias in the econometric model. These sets are in general impossible to generate explicitly. Therefore, we propose an importance sampling approach to generate subsets of paths suitable for model estimation. Using only a subset of alternatives requires the path utilities to be corrected according to the sampling protocol in order to obtain unbiased parameter estimates. We derive such a sampling correction for the proposed algorithm. Estimating models based on samples of alternatives is straightforward for some types of models, in particular the multinomial logit (MNL) model. In order to apply MNL for route choice, the utilities should also be corrected to account for the correlation using, for instance, a path size (PS) formulation. We argue that the PS attribute should be computed based on the full choice set. Again, this is not feasible in general, and we propose a new version of the PS attribute derived from the sampling protocol, called Expanded PS. Numerical results based on synthetic data show that models including a sampling correction are remarkably better than the ones that do not. Moreover, the Expanded PS shows good results and outperforms models with the original PS formulation.
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| 5. |
- Lundgren, Jan, et al.
(författare)
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A Heuristic for the Bilevel Origin–Destination Matrix Estimation Problem
- 2008
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Ingår i: Transportation Research Part B. - : Institutionen för teknik och naturvetenskap. - 0191-2615 .- 1879-2367. ; 42:4, s. 339-354
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we consider the estimation of an origin–destination (OD) matrix, given a target OD-matrix and traffic counts on a subset of the links in the network. We use a general nonlinear bilevel minimization formulation of the problem, where the lower level problem is to assign a given OD-matrix onto the network according to the user equilibrium principle. After reformulating the problem to a single level problem, the objective function includes implicitly given link flow variables, corresponding to the given OD-matrix. We propose a descent heuristic to solve the problem, which is an adaptation of the wellknown projected gradient method. In order to compute a search direction we have to approximate the Jacobian matrix representing the derivatives of the link flows with respect to a change in the OD-flows, and we propose to do this by solving a set of quadratic programs with linear constraints only. If the objective function is differentiable at the current point, the Jacobian is exact and we obtain a gradient. Numerical experiments are presented which indicate that the solution approach can be applied in practice to medium to large size networks.
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| 7. |
- Patriksson, Michael, 1964
(författare)
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On the applicability and solution of bilevel optimization models in transportation science: A study on the existence, stability and computation of optimal solutions to stochastic mathematical programs with equilibrium constraints
- 2008
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Ingår i: Transportation Research Part B. - : Elsevier BV. - 0191-2615. ; 42:10, s. 843-860
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Tidskriftsartikel (refereegranskat)abstract
- Bilevel optimization models, and more generally MPEC (mathematical program with equilibrium constraints) models, constitute important modelling tools in transportation science and network games, as they place the classic ``what-if'' analysis in a proper mathematical framework. The MPEC model is also becoming a standard for the computation of optimal design solutions, where ``design'' may include either or both of network infrastructure investments and various types of tolls. At the same time, it does normally not sufficiently well take into account possible uncertainties and/or perturbations in problem data (travel costs and demands), and thus may not a priori guarantee robust designs under varying conditions. We consider natural stochastic extensions to a class of MPEC traffic models which explicitly incorporate data uncertainty. In stochastic programming terminology, we consider ``here-and-now'' models where decisions on the design must be made before observing the uncertain parameter values and the responses of the network users, and the design is chosen to minimize the expectation of the upper-level objective function. Such a model could, for example, be used to derive a fixed link pricing scheme that provides the best revenue for a given network over a given time period, where the varying traffic conditions are described by distributions of parameters in the link travel time and OD demand functions. For a general such SMPEC network model we establish not only the existence of optimal solutions, but in particular their stability to perturbations in the probability distribution. We also provide convergence results for general algorithmic schemes based on the penalization of the equilibrium conditions or possible joint upper-level constraints, as well as for algorithms based on the discretization of the probability distribution, the latter enabling the utilization of standard MPEC algorithms. Especially the latter part utilizes relations between the traffic application of SMPEC and stochastic structural topology optimization problems.
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