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Equilibria in the multi-criteria traffic networks
| Content Provider | Semantic Scholar |
|---|---|
| Author | Truong, Thi Thanh Phuong |
| Copyright Year | 2015 |
| Abstract | The purpose of this thesis is to study equilibria in multi-criteria trafficnetworks and develop numerical methods to find the set of all equilibria oronly one representative part of this set. The thesis is structured as follows.In the first chapter we present an introduction of the thesis. Chapter 2is of preliminary character. We recall the concept of Pareto minimal pointsand some notions related to set-valued maps and variational inequality pro-blem. We introduce some scalarizing functions, in particular the so-calledaugmented biggest/smallest monotone functions and augmented signed distance functions, and establish some properties we shall use later.Chapter 3 describes the traffic network models to be studied in this thesis.We define equilibrium for each model and determine a relationship betweenthem. We also give some counter examples for some existing results in therecent literature on this topic.In Chapter 4 we develop a new solution method for multi-criteria net-work equilibrium problems without capacity constraints. To this end we shallconstruct two optimization problems the solutions of which are exactly theset of equilibria of the model, and establish some important generic conti-nuity and differentiability properties of the objective functions. Then we givethe formula to calculate the gradient of the objective functions which enablesus to modify Frank-Wolfe's reduced gradient method to get descent directiontoward an optimal solution. We prove the convergence of the method whichgenerates a nice representative set of equilibria. Since the objective functionsof our optimization problems are not continuous, a method of smoothingthem is also considered in order to see how global optimization algorithmsmay help.We shall also introduce the concept of robust equilibrium, establishcriteria for robustness and a formula to compute the radius of robustness.In Chapter 5 we consider vector equilibrium in the multi-criteria single-product traffic network with capacity constraints.We propose an equivalent optimization problem and establish some im-portant generic continuity and differentiability properties of the objectivefunction. Then we give a formula which allows us to calculate the gradientof the objective function. After that we apply the approach of Chapter 4 toobtain an algorithm for generating equilibria of this network. We also givesome numerical examples to illustrate our approach.In the last chapter we consider strong vector equilibrium in the multi-criteria multi-product traffic network with capacity constraints.We establish conditions for existence of strong vector equilibrium.We alsoestablish relations between equilibrium and efficient points of the value set ofthe cost function and with equilibrium with respect to a family of functions.Moreover we exploit particular increasing functions discussed in Chapter 2 toconstruct variational inequality problems, solutions of which are equilibriumflows. The final part of this chapter is devoted to an algorithm for findingequilibrium flows of a multi-criteria network with capacity constraints. Somenumerical examples are given to illustrate our method and its applicability.A list of references and appendices containing the code Matlab of ouralgorithms follow. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | https://tel.archives-ouvertes.fr/tel-01264132/document |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
