A methodology for solving the network toll design problem

Congestion pricing has been regarded as an efficient method to reduce network-wide travel cost. In this dissertation, a methodology for toll design is developed to provide policy-makers with suggestions on both where to charge tolls and how much the tolls should be. As opposed to the traditional approach of marginal social cost pricing, this methodology is capable of dealing with the more realistic case, in which only a small number of links can be tolled. Furthermore, this methodology is expanded to accommodate multiple user groups. The toll design problem can be formulated using both deterministic and stochastic route choice models. The most natural formulation of this problem in both cases is a bilevel formulation. Such formulations are very difficult to solve because of the nonconvexity and nondifferentiability of the constraint set. In this dissertation, the problem is converted into a single level, standard nonlinear optimization problem by making certain simplifying assumption. This single-level version of the toll design problem can be solved using a variety of well-developed algorithms. Tests show that this approach can be used to generate reasonable results and provide valuable decision support to policy-makers

Reserve Capacity Model for Optimizing Traffic Signal Timings with an Equity Constraint

This paper represents a solution algorithm for optimizing traffic signal timings in urban road networks by considering reserve capacity with an equity constraint. It is well known that the variation of signal timings in a road network may cause an inequity issue with regard to the travel costs of road users travelling between origin-destination (O-D) pairs. That is, the users may be influenced differently by changing traffic signal timings. In this context, the bilevel programming model is proposed for finding reserve capacity for signalized road networks by taking into account the equity issue. In the upper level, the reserve capacity is maximized with an equity constraint, whereas deterministic user equilibrium problem is dealt in the lower level. In order to solve the proposed model, a heuristic solution algorithm based on harmony search combined with a penalty function approach is developed. The application of the proposed model is illustrated for an example road network taken from a literature

Integer Bilevel Linear Programming Problems: New Results and Applications

Integer Bilevel Linear Programming Problems: New Results and Application

Integer Bilevel Linear Programming Problems: New Results and Applications

Integer Bilevel Linear Programming Problems: New Results and Application

A Metaheuristic Framework for Bi-level Programming Problems with Multi-disciplinary Applications

Bi-level programming problems arise in situations when the decision maker has to take into account the responses of the users to his decisions. Several problems arising in engineering and economics can be cast within the bi-level programming framework. The bi-level programming model is also known as a Stackleberg or leader-follower game in which the leader chooses his variables so as to optimise his objective function, taking into account the response of the follower(s) who separately optimise their own objectives, treating the leader’s decisions as exogenous. In this chapter, we present a unified framework fully consistent with the Stackleberg paradigm of bi-level programming that allows for the integration of meta-heuristic algorithms with traditional gradient based optimisation algorithms for the solution of bi-level programming problems. In particular we employ Differential Evolution as the main meta-heuristic in our proposal.We subsequently apply the proposed method (DEBLP) to a range of problems from many fields such as transportation systems management, parameter estimation and game theory. It is demonstrated that DEBLP is a robust and powerful search heuristic for this class of problems characterised by non smoothness and non convexity

Bi-level optimisation and machine learning in the management of large service-oriented field workforces.

The tactical planning problem for members of the service industry with large multi-skilled workforces is an important process that is often underlooked. It sits between the operational plan - which involves the actual allocation of members of the workforce to tasks - and the strategic plan where long term visions are set. An accurate tactical plan can have great benefits to service organisations and this is something we demonstrate in this work. Sitting where it does, it is made up of a mix of forecast and actual data, which can make effectively solving the problem difficult. In members of the service industry with large multi-skilled workforces it can often become a very large problem very quickly, as the number of decisions scale quickly with the number of elements within the plan. In this study, we first update and define the tactical planning problem to fit the process currently undertaken manually in practice. We then identify properties within the problem that identify it as a new candidate for the application of bi-level optimisation techniques. The tactical plan is defined in the context of a pair of leader-follower linked sub-models, which we show to be solvable to produce automated solutions to the tactical plan. We further identify the need for the use of machine learning techniques to effectively find solutions in practical applications, where limited detail is available in the data due to its forecast nature. We develop neural network models to solve this issue and show that they provide more accurate results than the current planners. Finally, we utilise them as a surrogate for the follower in the bi-level framework to provide real world applicable solutions to the tactical planning problem. The models developed in this work have already begun to be deployed in practice and are providing significant impact. This is along with identifying a new application area for bi-level modelling techniques

Line planning with user-optimal route choice

We consider the problem of designing lines in a public transport system, where we include user-optimal route choice. The model we develop ensures that there is enough capacity present for every passenger to travel on a shortest route. We present two different integer programming formulations for this problem, and discuss exact solution approaches. To solve large-scale line planning instances, we also implemented a genetic solution algorithms. We test our algorithms in computational experiments using randomly generated instances along realistic data, as well as a realistic instance modeling the German long-distance network. We examine the advantages and disadvantages of using such user-optimal solutions, and show that our algorithms sufficiently scale with instance size to be used for practical purposes

Traffic prediction and bilevel network design

Cette thèse porte sur la modélisation du trafic dans les réseaux routiers et comment celle-ci est intégrée dans des modèles d'optimisation. Ces deux sujets ont évolué de manière plutôt disjointe: le trafic est prédit par des modèles mathématiques de plus en plus complexes, mais ce progrès n'a pas été incorporé dans les modèles de design de réseau dans lesquels les usagers de la route jouent un rôle crucial. Le but de cet ouvrage est d'intégrer des modèles d'utilités aléatoires calibrés avec de vraies données dans certains modèles biniveaux d'optimisation et ce, par une décomposition de Benders efficace. Cette décomposition particulière s'avère être généralisable par rapport à une grande classe de problèmes communs dans la litérature et permet d'en résoudre des exemples de grande taille. Le premier article présente une méthodologie générale pour utiliser des données GPS d'une flotte de véhicules afin d'estimer les paramètres d'un modèle de demande dit recursive logit. Les traces GPS sont d'abord associées aux liens d'un réseau à l'aide d'un algorithme tenant compte de plusieurs facteurs. Les chemins formés par ces suites de liens et leurs caractéristiques sont utilisés afin d'estimer les paramètres d'un modèle de choix. Ces paramètres représentent la perception qu'ont les usagers de chacune de ces caractéristiques par rapport au choix de leur chemin. Les données utilisées dans cet article proviennent des véhicules appartenant à plusieurs compagnies de transport opérant principalement dans la région de Montréal. Le deuxième article aborde l'intégration d'un modèle de choix de chemin avec utilités aléatoires dans une nouvelle formulation biniveau pour le problème de capture de flot de trafic. Le modèle proposé permet de représenter différents comportements des usagers par rapport à leur choix de chemin en définissant les utilités d'arcs appropriées. Ces utilités sont stochastiques ce qui contribue d'autant plus à capturer un comportement réaliste des usagers. Le modèle biniveau est rendu linéaire à travers l'ajout d'un terme lagrangien basé sur la dualité forte et ceci mène à une décomposition de Benders particulièrement efficace. Les expériences numériques sont principalement menés sur un réseau représentant la ville de Winnipeg ce qui démontre la possibilité de résoudre des problèmes de taille relativement grande. Le troisième article démontre que l'approche du second article peut s'appliquer à une forme particulière de modèles biniveaux qui comprennent plusieurs problèmes différents. La décomposition est d'abord présentée dans un cadre général, puis dans un contexte où le second niveau du modèle biniveau est un problème de plus courts chemins. Afin d'établir que ce contexte inclut plusieurs applications, deux applications distinctes sont adaptées à la forme requise: le transport de matières dangeureuses et la capture de flot de trafic déterministe. Une troisième application, la conception et l'établissement de prix de réseau simultanés, est aussi présentée de manière similaire à l'Annexe B de cette thèse.The subject of this thesis is the modeling of traffic in road networks and its integration in optimization models. In the literature, these two topics have to a large extent evolved independently: traffic is predicted more accurately by increasingly complex mathematical models, but this progress has not been incorporated in network design models where road users play a crucial role. The goal of this work is to integrate random utility models calibrated with real data into bilevel optimization models through an efficient Benders decomposition. This particular decomposition generalizes to a wide class of problems commonly found in the literature and can be used to solved large-scale instances. The first article presents a general methodology to use GPS data gathered from a fleet of vehicles to estimate the parameters of a recursive logit demand model. The GPS traces are first matched to the arcs of a network through an algorithm taking into account various factors. The paths resulting from these sequences of arcs, along with their characteristics, are used to estimate parameters of a choice model. The parameters represent users' perception of each of these characteristics in regards to their path choice behaviour. The data used in this article comes from trucks used by a number of transportation companies operating mainly in the Montreal region. The second article addresses the integration of a random utility maximization model in a new bilevel formulation for the general flow capture problem. The proposed model allows for a representation of different user behaviors in regards to their path choice by defining appropriate arc utilities. These arc utilities are stochastic which further contributes in capturing real user behavior. This bilevel model is linearized through the inclusion of a Lagrangian term based on strong duality which paves the way for a particularly efficient Benders decomposition. The numerical experiments are mostly conducted on a network representing the city of Winnipeg which demonstrates the ability to solve problems of a relatively large size. The third article illustrates how the approach used in the second article can be generalized to a particular form of bilevel models which encompasses many different problems. The decomposition is first presented in a general setting and subsequently in a context where the lower level of the bilevel model is a shortest path problem. In order to demonstrate that this form is general, two distinct applications are adapted to fit the required form: hazmat transportation network design and general flow capture. A third application, joint network design and pricing, is also similarly explored in Appendix B of this thesis