Network Interdiction under Uncertainty

We consider variants to one of the most common network interdiction formulations: the shortest path interdiction problem. This problem involves leader and a follower playing a zero-sum game over a directed network. The leader interdicts a set of arcs, and arc costs increase each time they are interdicted. The follower observes the leader\u27s actions and selects a shortest path in response. The leader\u27s optimal interdiction strategy maximizes the follower\u27s minimum-cost path. Our first variant allows the follower to improve the network after the interdiction by lowering the costs of some arcs, and the leader is uncertain regarding the follower\u27s cardinality budget restricting the arc improvements. We propose a multiobjective approach for this problem, with each objective corresponding to a different possible improvement budget value. To this end, we also present the modified augmented weighted Tchebychev norm, which can be used to generate a complete efficient set of solutions to a discrete multi-objective optimization problem, and which tends to scale better than competing methods as the number of objectives grows. In our second variant, the leader selects a policy of randomized interdiction actions, and the follower uses the probability of where interdictions are deployed on the network to select a path having the minimum expected cost. We show that this continuous non-convex problem becomes strongly NP-hard when the cost functions are convex or when they are concave. After formally describing each variant, we present various algorithms for solving them, and we examine the efficacy of all our algorithms on test beds of randomly generated instances

A linear fractional optimization over an integer efficient set

Mathematical optimization problems with a goal function, have many applications in various fields like financial sectors, management sciences and economic applications. Therefore, it is very important to have a powerful tool to solve such problems when the main criterion is not linear, particularly fractional, a ratio of two affine functions. In this paper, we propose an exact algorithm for optimizing a linear fractional function over the efficient set of a Multiple Objective Integer Linear Programming (MOILP) problem without having to enumerate all the efficient solutions. We iteratively add some constraints, that eliminate the undesirable (not interested) points and reduce, progressively, the admissible region. At each iteration, the solution is being evaluated at the reduced gradient cost vector and a new direction that improves the objective function is then defined. The algorithm was coded in MATLAB environment and tested over different instances randomly generated

Techniques for Multiobjective Optimization with Discrete Variables: Boxed Line Method and Tchebychev Weight Set Decomposition

Many real-world applications involve multiple competing objectives, but due to conflict between the objectives, it is generally impossible to find a feasible solution that optimizes all, simultaneously. In contrast to single objective optimization, the goal in multiobjective optimization is to generate a set of solutions that induces the nondominated (ND) frontier. This thesis presents two techniques for multiobjective optimization problems with discrete decision variables. First, the Boxed Line Method is an exact, criterion space search algorithm for biobjective mixed integer programs (Chapter 2). A basic version of the algorithm is presented with a recursive variant and other enhancements. The basic and recursive variants permit complexity analysis, which yields the first complexity results for this class of algorithms. Additionally, a new instance generation method is presented, and a rigorous computational study is conducted. Second, a novel weight space decomposition method for integer programs with three (or more) objectives is presented with unique geometric properties (Chapter 3). The weighted Tchebychev scalarization used for this weight space decomposition provides the benefit of including unsupported ND images but at the cost of convexity of weight set components. This work proves convexity-related properties of the weight space components, including star-shapedness. Further, a polytopal decomposition is used to properly define dimension for these nonconvex components. The weighted Tchebychev weight set decomposition is then applied as a “dual” perspective on the class of multiobjective “primal” algorithms (Chapter 4). It is shown that existing algorithms do not yield enough information for a complete decomposition, and the necessary modifications required to yield the missing information is proven. Modifications for primal algorithms to compute inner and outer approximations of the weight space components are presented. Lastly, a primal algorithm is restricted to solving for a subset of the ND frontier, where this subset represents the compromise between multiple decision makers’ weight vectors.Ph.D

Approches de résolution exacte et approchée en optimisation combinatoire multi-objectif, application au problème de l'arbre couvrant de poids minimal

This thesis deals with several aspects related to solving multi-objective problems, without restriction to the bi-objective case. We consider exact solving, which generates the nondominated set, and approximate solving, which computes an approximation of the nondominated set with a priori guarantee on the quality.We first consider the determination of an explicit representation of the search region. The search region, defined with respect to a set of known feasible points, excludes from the objective space the part which is dominated by these points. Future efforts to find all nondominated points should therefore be concentrated on the search region.Then we review branch and bound and ranking algorithms and we propose a new hybrid approach for the determination of the nondominated set. We show how the proposed method can be adapted to generate an approximation of the nondominated set. This approach is instantiated on the minimum spanning tree problem. We review several properties of this problem which enable us to specialize some procedures of the proposed approach and integrate specific preprocessing rules. This approach is finally supported through experimental results.On s'attache dans cette thèse à plusieurs aspects liés à la résolution de problèmes multi-objectifs, sans se limiter au cas biobjectif. Nous considérons la résolution exacte, dans le sens de la détermination de l'ensemble des points non dominés, ainsi que la résolution approchée dans laquelle on cherche une approximation de cet ensemble dont la qualité est garantie a priori.Nous nous intéressons d'abord au problème de la détermination d'une représentation explicite de la région de recherche. La région de recherche, étant donné un ensemble de points réalisables connus, exclut la partie de l'espace des objectifs que dominent ces points et constitue donc la partie de l'espace des objectifs où les efforts futurs doivent être concentrés dans la perspective de déterminer tous les points non dominés.Puis nous considérons le recours aux algorithmes de séparation et évaluation ainsi qu'aux algorithmes de ranking afin de proposer une nouvelle méthode hybride de détermination de l'ensemble des points non dominés. Nous montrons que celle-ci peut également servir à obtenir une approximation de l'ensemble des points non dominés. Cette méthode est implantée pour le problème de l'arbre couvrant de poids minimal. Les quelques propriétés de ce problème que nous passons en revue nous permettent de spécialiser certaines procédures et d'intégrer des prétraitements spécifiques. L'intérêt de cette approche est alors soutenu à l'aide de résultats expérimentaux

Operational Research: Methods and Applications

Throughout its history, Operational Research has evolved to include a variety of methods, models and algorithms that have been applied to a diverse and wide range of contexts. This encyclopedic article consists of two main sections: methods and applications. The first aims to summarise the up-to-date knowledge and provide an overview of the state-of-the-art methods and key developments in the various subdomains of the field. The second offers a wide-ranging list of areas where Operational Research has been applied. The article is meant to be read in a nonlinear fashion. It should be used as a point of reference or first-port-of-call for a diverse pool of readers: academics, researchers, students, and practitioners. The entries within the methods and applications sections are presented in alphabetical order. The authors dedicate this paper to the 2023 Turkey/Syria earthquake victims. We sincerely hope that advances in OR will play a role towards minimising the pain and suffering caused by this and future catastrophes

Operational Research: Methods and Applications

Throughout its history, Operational Research has evolved to include a variety of methods, models and algorithms that have been applied to a diverse and wide range of contexts. This encyclopedic article consists of two main sections: methods and applications. The first aims to summarise the up-to-date knowledge and provide an overview of the state-of-the-art methods and key developments in the various subdomains of the field. The second offers a wide-ranging list of areas where Operational Research has been applied. The article is meant to be read in a nonlinear fashion. It should be used as a point of reference or first-port-of-call for a diverse pool of readers: academics, researchers, students, and practitioners. The entries within the methods and applications sections are presented in alphabetical order

Fuelling the zero-emissions road freight of the future: routing of mobile fuellers

The future of zero-emissions road freight is closely tied to the sufficient availability of new and clean fuel options such as electricity and Hydrogen. In goods distribution using Electric Commercial Vehicles (ECVs) and Hydrogen Fuel Cell Vehicles (HFCVs) a major challenge in the transition period would pertain to their limited autonomy and scarce and unevenly distributed refuelling stations. One viable solution to facilitate and speed up the adoption of ECVs/HFCVs by logistics, however, is to get the fuel to the point where it is needed (instead of diverting the route of delivery vehicles to refuelling stations) using "Mobile Fuellers (MFs)". These are mobile battery swapping/recharging vans or mobile Hydrogen fuellers that can travel to a running ECV/HFCV to provide the fuel they require to complete their delivery routes at a rendezvous time and space. In this presentation, new vehicle routing models will be presented for a third party company that provides MF services. In the proposed problem variant, the MF provider company receives routing plans of multiple customer companies and has to design routes for a fleet of capacitated MFs that have to synchronise their routes with the running vehicles to deliver the required amount of fuel on-the-fly. This presentation will discuss and compare several mathematical models based on different business models and collaborative logistics scenarios

Operational research:methods and applications

Throughout its history, Operational Research has evolved to include a variety of methods, models and algorithms that have been applied to a diverse and wide range of contexts. This encyclopedic article consists of two main sections: methods and applications. The first aims to summarise the up-to-date knowledge and provide an overview of the state-of-the-art methods and key developments in the various subdomains of the field. The second offers a wide-ranging list of areas where Operational Research has been applied. The article is meant to be read in a nonlinear fashion. It should be used as a point of reference or first-port-of-call for a diverse pool of readers: academics, researchers, students, and practitioners. The entries within the methods and applications sections are presented in alphabetical order

Operational Research: methods and applications

This is the final version. Available on open access from Taylor & Francis via the DOI in this recordThroughout its history, Operational Research has evolved to include methods, models and algorithms that have been applied to a wide range of contexts. This encyclopedic article consists of two main sections: methods and applications. The first summarises the up-to-date knowledge and provides an overview of the state-of-the-art methods and key developments in the various subdomains of the field. The second offers a wide-ranging list of areas where Operational Research has been applied. The article is meant to be read in a nonlinear fashion and used as a point of reference by a diverse pool of readers: academics, researchers, students, and practitioners. The entries within the methods and applications sections are presented in alphabetical order. The authors dedicate this paper to the 2023 Turkey/Syria earthquake victims. We sincerely hope that advances in OR will play a role towards minimising the pain and suffering caused by this and future catastrophes