arXiv subjects

Ekaterina Kotliarova

Publications and source records attributed to Ekaterina Kotliarova.

3 recordsLinked to original sources

arXiv2023

Primal-Dual Gradient Methods for Searching Network Equilibria in Combined Models with Nested Choice Structure and Capacity Constraints

We consider a network equilibrium model (i.e. a combined model), which was proposed as an alternative to the classic four-step approach for travel forecasting in transportation networks. This model can be formulated as a convex minimization program. We extend the combined model to the case of the stable dynamics (SD) model in the traffic assignment stage, which imposes strict capacity constraints in the network. We propose a way to solve corresponding dual optimization problems with accelerated gradient methods and give theoretical guarantees of their convergence. We conducted numerical experiments with considered optimization methods on Moscow and Berlin networks.

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arXiv2021

The recovery model for the calculation of correspondence matrix for Moscow

In this paper, we consider the problem of restoring the correspondence matrix based on the observations of real correspondences in Moscow. Following the conventional approach, the transport network is considered as a directed graph whose edges correspond to road sections and the graph vertices correspond to areas that the traffic participants leave or enter. The number of city residents is considered constant. The problem of restoring the correspondence matrix is to calculate all the correspondence from the $i$ area to the $j$ area. To restore the matrix, we propose to use one of the most popular methods of calculating the correspondence matrix in urban studies -- the entropy model. In our work, we describe the evolutionary justification of the entropy model and the main idea of the transition to solving the problem of entropy-linear programming (ELP) in calculating the correspondence matrix. To solve the ELP problem, it is proposed to pass to the dual problem. In this paper, we describe several numerical optimization methods for solving this problem: the Sinkhorn method and the Accelerated Sinkhorn method. We provide numerical experiments for the following variants of cost functions: a linear cost function and a superposition of the power and logarithmic cost functions. In these functions, the cost is a combination of average time and distance between areas, which depends on the parameters. The correspondence matrix is calculated for multiple sets of parameters and then we calculate the quality of the restored matrix relative to the known correspondence matrix. We assume that the noise in the restored correspondence matrix is Gaussian, as a result, we use the standard deviation as a quality metric.

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arXiv2020

Finding equilibrium in two-stage traffic assignment model

Authors describe a two-stage traffic assignment model. It contains of two blocks. The first block consists of model for calculating correspondence (demand) matrix, whereas the second block is a traffic assignment model. The first model calculates a matrix of correspondences using a matrix of transport costs. It characterizes the required volumes of movement from one area to another. The second model describes how exactly the needs for displacement, specified by the correspondence matrix, are distributed along the possible paths. It works on the basis of the Nash--Wardrop equilibrium (each driver chooses the shortest path). Knowing the ways of distribute flows along the paths, it is possible to calculate the cost matrix. Equilibrium in a two-stage model is a fixed point in the sequence of these two models. The article proposes a method of reducing the problem of finding the equilibrium to the problem of the convex non-smooth optimization. Also a numerical method for solving the obtained optimization problem is proposed. Numerical experiments were carried out for the small towns.

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