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Evgenia Gasnikova

Publications and source records attributed to Evgenia Gasnikova.

14 recordsLinked to original sources
arXiv2023

Sufficient conditions for multi-stages traffic assignment model to be the convex optimization problem

In this paper we consider multi-stages traffic assignment with several demand layers, user types and network types. We consider two stages: demand matrix calculation (Entropy Wilson's model) and traffic assignment models (Beckmann or Nesterov--de Palma). For the traffic assignment stage we use dual reformulation and combine these stages as a saddle-point problem (convex-concave). Then we discuss how one can solve this problem numerically.

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arXiv2023

An evolutionary view on equilibrium models of transport flows

In this short paper we describe natural logit population games dynamics that explain equilibrium models of origin-destination matrix estimation and (stochastic) traffic assignment models (Beckmann, Nesterov--de Palma). Composition of the proposed dynamics allows to explain two-stages traffic assignment models.

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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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arXiv2020

Traffic assignment models. Numerical aspects

In this book we describe BMW traffic assignment model and Nesterov-dePalma model. We consider Entropy model for demand matrix. Based on this models we build multi-stage traffic assignment models. The equilibrium in such models can be found from convex-concave saddle-point problem. We show how to solve this problem by using special combination of universal gradient method and Sinkhorn's algorithm.

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arXiv2020

Evolutionary interpretations of entropy model for correspondence matrix calculation

In the work two ways of evolutionary interpretation of entropy model for correspondence matrix calculation are proposed. Both approaches based on the stochastic chemical kinetic evolution under the detailed balance condition. The first approach is based on the binary reactions, and the second one is based on the population games theory. Both approaches allow one to understand better possible physical interpretations of the classic model and to obtain the answers for some open questions in neighborhoods branches. For example, one can propose a selection rule to the unique equilibrium among the set of equilibriums.

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arXiv2018

Primal-dual method for searching equillibriums in mixed traffic assignment problems

We consider mixed model of traffic flow distribution in large networks (BMW model, 1954 & Stable Dynamic model, 1999). We build dual problem and consider primal-dual mirror descent method for the dual problem. There are two ways to recover the solution of the primal problem. First technique is based on "models" approach and second one is based on Lagrange multiplyers technique. Both approaches have its own advantages and drawbacks. We discuss them.

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arXiv2018

About universality of entropy in stochastic chemical kinetic models

This paper studies the relationship between the Lyapunov function of a macrosystem whose dynamics is governed by the laws of stochastic chemical kinetics and the invariant measure of this macrosystem arising at large times. A necessary and sufficient condition for the reduction of the search problem for the equilibrium of the macrosystem (the most probable macrostate of the invariant measure of this macrosystem) to an entropy-linear programming problem is given.

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arXiv2017

Universal similar triangulars method for searching equilibriums in traffic flow distribution models

We describe how primal-dual version of Nesterov's Universal Method (with one projection) can be applied to solve the dual problem for the problem of searching equilibrium traffic flow distribution in transport networks (BMW-model, Stable Dynamic model). We observe that although the dual problem isn't smooth Universal Methods works as it is Mirror Prox method and we consider saddle-point type problem.

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arXiv2016

Primal-Dual Method for Searching Equilibrium in Hierarchical Congestion Population Games

In this paper, we consider a large class of hierarchical congestion population games. One can show that the equilibrium in a game of such type can be described as a minimum point in a properly constructed multi-level convex optimization problem. We propose a fast primal-dual composite gradient method and apply it to the problem, which is dual to the problem describing the equilibrium in the considered class of games. We prove that this method allows to find an approximate solution of the initial problem without increasing the complexity.

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arXiv2016

Efficient calculation of stochastic equilibriums in the Beckmann's and stable dynamic models

We propose composite approache to the special sum-type convex optimization problem with affine restriction and special entropy type regularization. Since the fuctional has a penalty type form, we reformulate initial conditional optimization problem in a special unconstrained form that allows us to put the penalty type functional into the composite term. We also describe the characteristic functions on graphs technique (Yu. Nesterov, 2007) in application to the dual problem.

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arXiv2016

Searching of equilibriums in hierarchical congestion population games

An universal primal-dual approach of description equilibriums in large class of hierarchical congestion population games is proposed. At the very core of the approach is hierarchy of enclosed to each other transport networks. In different time-scales corresponding logit dynamics on this networks is considered. This dynamics reflect restricted rationality of the agents. Searching of equilibrium configuration to the multi-level convex optimization problem is reduced (in other words variational principle for these class of the games/models is formulated). Then the dual problem is formulated. This problem has natural interpretation in turn and it is more computationally attractive then the primal one. So an effective primal-dual method for this problem is proposed. This method is based on the composite fast gradient method. Due to primal-duality the solution of the primal problem from the dual iterative process is recovered. To fulfil one iteration of this method the rather complex problem of calculation characteristic function on graph is solved. A special technique (smooth version of Bellman--Ford approach to the shortest path problem) is proposed (based on some ideas of Yu. Nesterov) that allows to do it in a cheap manner. It also should be mentioned that different tricks of small parameters methods are actively used.

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arXiv2016

Entropy linear programming

We propose an efficient dual algorithm for ELP based on Fast Gradient Method. The basic idea - to solve properly regularized dual problem.

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arXiv2011

About new dynamical interpretations of entropic model of correspondence matrix calculation and Nash-Wardrop's equilibrium in Beckmann's traffic flow distribution model

In this work we widespread statistical physics (chemical kinetic stochastic) approach to the investigation of macrosystems, arise in economic, sociology and traffic flow theory. The main line is a definition of equilibrium of macrosystem as most probable macrostate of invariant measure of Markov dynamic (corresponds to the macrosystem). We demonstrate new dynamical interpretations for the well known static model of correspondence matrix calculation. Based on this model we propose a best response dynamics for the Beckmann's traffic flow distribution model. We prove that this "natural" dynamic under quite general conditions converges to the Nash-Wardrop's equilibrium. After that we consider two interesting demonstration examples.

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