Algorithme de branch-and-price-and-cut pour le problème de conception de réseaux avec coûts fixes, capacités et un seul produit

De nombreux problèmes liés aux domaines du transport, des télécommunications et de la logistique peuvent être modélisés comme des problèmes de conception de réseaux. Le problème classique consiste à transporter un flot (données, personnes, produits, etc.) sur un réseau sous un certain nombre de contraintes dans le but de satisfaire la demande, tout en minimisant les coûts. Dans ce mémoire, on se propose d'étudier le problème de conception de réseaux avec coûts fixes, capacités et un seul produit, qu'on transforme en un problème équivalent à plusieurs produits de façon à améliorer la valeur de la borne inférieure provenant de la relaxation continue du modèle. La méthode que nous présentons pour la résolution de ce problème est une méthode exacte de branch-and-price-and-cut avec une condition d'arrêt, dans laquelle nous exploitons à la fois la méthode de génération de colonnes, la méthode de génération de coupes et l'algorithme de branch-and-bound. Ces méthodes figurent parmi les techniques les plus utilisées en programmation linéaire en nombres entiers. Nous testons notre méthode sur deux groupes d'instances de tailles différentes (gran-des et très grandes), et nous la comparons avec les résultats donnés par CPLEX, un des meilleurs logiciels permettant de résoudre des problèmes d'optimisation mathématique, ainsi qu’avec une méthode de branch-and-cut. Il s'est avéré que notre méthode est prometteuse et peut donner de bons résultats, en particulier pour les instances de très grandes tailles.

Cut-first branch-and-price-second for the capacitated arc-routing problem

This paper presents the first full-fledged branch-and-price (bap) algorithm for the capacitated arc-routing problem (CARP). Prior exact solution techniques either rely on cutting planes or the transformation of the CARP into a node-routing problem. The drawbacks are either models with inherent symmetry, dense underlying networks, or a formulation where edge flows in a potential solution do not allow the reconstruction of unique CARP tours. The proposed algorithm circumvents all these drawbacks by taking the beneficial ingredients from existing CARP methods and combining them in a new way. The first step is the solution of the one-index formulation of the CARP in order to produce strong cuts and an excellent lower bound. It is known that this bound is typically stronger than relaxations of a pure set-partitioning CARP model.rnSuch a set-partitioning master program results from a Dantzig-Wolfe decomposition. In the second phase, the master program is initialized with the strong cuts, CARP tours are iteratively generated by a pricing procedure, and branching is required to produce integer solutions. This is a cut-first bap-second algorithm and its main function is, in fact, the splitting of edge flows into unique CARP tours.

Efficient articulated trajectory reconstruction using dynamic programming and filters

This paper considers the problem of reconstructing the motion of a 3D articulated tree from 2D point correspondences subject to some temporal prior. Hitherto, smooth motion has been encouraged using a trajectory basis, yielding a hard combinatorial problem with time complexity growing exponentially in the number of frames. Branch and bound strategies have previously attempted to curb this complexity whilst maintaining global optimality. However, they provide no guarantee of being more efficient than exhaustive search. Inspired by recent work which reconstructs general trajectories using compact high-pass filters, we develop a dynamic programming approach which scales linearly in the number of frames, leveraging the intrinsically local nature of filter interactions. Extension to affine projection enables reconstruction without estimating cameras.

Phosphorus nutrition and tolerance of cotton to water stress: II. Water relations, free and bound water and leaf expansion rate

In previous experiments, increased leaf-Phosphorus (P) content with increasing P supply enhanced the individual leaf expansion and water content of fresh cotton leaves in a severely drying soil. In this paper, we report on the bulk water content of leaves and its components, free and bound water, along with other measures of plant water status, in expanding cotton leaves of various ages in a drying soil with different P concentrations. The bound water in living tissue is more likely to play a major role in tolerance to abiotic stresses by maintaining the structural integrity and/or cell wall extensibility of the leaves, whilst an increased amount of free water might be able to enhance solute accumulation, leading to better osmotic adjustment and tolerance to water stress, and maintenance of the volumes of sub-cellular compartments for expansive leaf growth. There were strong correlations between leaf-P%, leaf water (total, free and bound water) and leaf expansion rate (LER) under water stress conditions in a severely drying soil. Increased soil-P enhanced the uptake of P from a drying soil, leading to increased supply of osmotically active inorganic solutes to the cells in growing leaves. This appears to have led to the accumulation of free water and more bound water, ultimately leading to increased leaf expansion rates as compared to plants in low P soil under similar water stress conditions. The greater amount of bound and free water in the high-P plants was not necessarily associated with changes in cell turgor, and appears to have maintained the cell-wall properties and extensibility under water stressed conditions in soils that are nutritionally P-deficient.

Open-pit block sequencing optimization: A mathematical model and solution technique

This study presents a comprehensive mathematical formulation model for a short-term open-pit mine block sequencing problem, which considers nearly all relevant technical aspects in open-pit mining. The proposed model aims to obtain the optimum extraction sequences of the original-size (smallest) blocks over short time intervals and in the presence of real-life constraints, including precedence relationship, machine capacity, grade requirements, processing demands and stockpile management. A hybrid branch-and-bound and simulated annealing algorithm is developed to solve the problem. Computational experiments show that the proposed methodology is a promising way to provide quantitative recommendations for mine planning and scheduling engineers.

Free-to-bound and bound exciton transitions at isoelectronic impurities: GaP(Zn,O)

We show, for sufficiently high temperatures and sufficiently weak majority-carrier binding energies, that the dominant radiative transition at an isoelectronic acceptor (donor) in p-type (n-type) material consists of the recombination of singly trapped minority carriers (bound by central-cell forces) with free majority carriers attracted by a Coulomb interaction. There are two reasons why the radiative recombination rate of the free-to-bound process is greater than the bound exciton process, which dominates at lower temperatures: (i) The population of free majority-carrier states greatly exceeds that of exciton states at higher temperatures, and (ii) the oscillator strength of the free-to-bound transition is greatly enhanced by the Coulomb attraction between the free carrier and the charged isoelectronic impurity. This enhancement is important for isoelectronic centers and is easily calculable from existing exciton models. We show that the free carrier attracted by a Coulomb interaction can be viewed as a continuum excited state of the bound exciton. When we apply the results of our calculations to the GaP(Zn, O) system, we find that the major part of the room-temperature luminescence from nearest-neighbor isoelectronic Zn-O complexes results from free-to-bound recombination and not exciton recombination as has been thought previously. Recent experiments on impulse excitation of luminescence in GaP(Zn, O) are reevaluated in the light of our calculations and are shown to be consistent with a strong free-to-bound transition. For deep isoelectronic centers with weakly bound majority carriers, we predict an overwhelming dominance of the free-to-bound process at 300°K.

Reasoning with imprecise trade-offs in decision making under certainty and uncertainty

In many real world situations, we make decisions in the presence of multiple, often conflicting and non-commensurate objectives. The process of optimizing systematically and simultaneously over a set of objective functions is known as multi-objective optimization. In multi-objective optimization, we have a (possibly exponentially large) set of decisions and each decision has a set of alternatives. Each alternative depends on the state of the world, and is evaluated with respect to a number of criteria. In this thesis, we consider the decision making problems in two scenarios. In the first scenario, the current state of the world, under which the decisions are to be made, is known in advance. In the second scenario, the current state of the world is unknown at the time of making decisions. For decision making under certainty, we consider the framework of multiobjective constraint optimization and focus on extending the algorithms to solve these models to the case where there are additional trade-offs. We focus especially on branch-and-bound algorithms that use a mini-buckets algorithm for generating the upper bound at each node of the search tree (in the context of maximizing values of objectives). Since the size of the guiding upper bound sets can become very large during the search, we introduce efficient methods for reducing these sets, yet still maintaining the upper bound property. We define a formalism for imprecise trade-offs, which allows the decision maker during the elicitation stage, to specify a preference for one multi-objective utility vector over another, and use such preferences to infer other preferences. The induced preference relation then is used to eliminate the dominated utility vectors during the computation. For testing the dominance between multi-objective utility vectors, we present three different approaches. The first is based on a linear programming approach, the second is by use of distance-based algorithm (which uses a measure of the distance between a point and a convex cone); the third approach makes use of a matrix multiplication, which results in much faster dominance checks with respect to the preference relation induced by the trade-offs. Furthermore, we show that our trade-offs approach, which is based on a preference inference technique, can also be given an alternative semantics based on the well known Multi-Attribute Utility Theory. Our comprehensive experimental results on common multi-objective constraint optimization benchmarks demonstrate that the proposed enhancements allow the algorithms to scale up to much larger problems than before. For decision making problems under uncertainty, we describe multi-objective influence diagrams, based on a set of p objectives, where utility values are vectors in Rp, and are typically only partially ordered. These can be solved by a variable elimination algorithm, leading to a set of maximal values of expected utility. If the Pareto ordering is used this set can often be prohibitively large. We consider approximate representations of the Pareto set based on ϵ-coverings, allowing much larger problems to be solved. In addition, we define a method for incorporating user trade-offs, which also greatly improves the efficiency.

Positron-molecule interactions: Resonant attachment, annihilation, and bound states

This article presents an overview of current understanding of the interaction of low-energy positrons with molecules with emphasis on resonances, positron attachment, and annihilation. Measurements of annihilation rates resolved as a function of positron energy reveal the presence of vibrational Feshbach resonances (VFRs) for many polyatomic molecules. These resonances lead to strong enhancement of the annihilation rates. They also provide evidence that positrons bind to many molecular species. A quantitative theory of VFR-mediated attachment to small molecules is presented. It is tested successfully for selected molecule (e.g., methyl halides and methanol) where all modes couple to the positron continuum. Combination and overtone resonances are observed and their role is elucidated. Molecules that do not bind positrons and hence do not exhibit such resonances are discussed. In larger molecules, annihilation rates from VFR far exceed those explicable on the basis of single-mode resonances. These enhancements increase rapidly with the number of vibrational degrees of freedom, approximately as the fourth power of the number of atoms in the molecule. While the details are as yet unclear, intramolecular vibrational energy redistributio (IVR) to states that do not couple directly to the positron continuum appears to be responsible for these enhanced annihilation rates. In connection with IVR, experimental evidence indicates that inelastic positron escape channels are relatively rare. Downshifts of the VFR from the vibrational mode energies, obtained by measuring annihilate rates as a function of incident positron energy, have provided binding energies for 30 species. Their dependence upon molecular parameters and their relationship to positron-atom and positron-molecule binding-energy calculations are discussed. Feshbach resonances and positron binding to molecules are compared with the analogous electron-molecul (negative-ion) cases. The relationship of VFR-mediated annihilation to other phenomena such as Doppler broadening of the gamma-ray annihilation spectra, annihilation of thermalized positrons in gases, and annihilation-induced fragmentation of molecules is discussed. Possible areas for future theoretical and experimental investigation are also discussed.

Optimised search heuristics: combining metaheuristics and exact methods to solve scheduling problems

Tese dout., Matemática, Investigação Operacional, Universidade do Algarve, 2009

Intelligent predictive control for thermal comfort and energy savings in public buildings

This talk addresses the problem of controlling a heating ventilating and air conditioning system with the purpose of achieving a desired thermal comfort level and energy savings. The formulation uses the thermal comfort, assessed using the predicted mean vote (PMV) index, as a restriction and minimises the energy spent to comply with it. This results in the maintenance of thermal comfort and on the minimisation of energy, which in most operating conditions are conflicting goals requiring some sort of optimisation method to find appropriate solutions over time. In this work a discrete model based predictive control methodology is applied to the problem. It consists of three major components: the predictive models, implemented by radial basis function neural networks identifed by means of a multi-objective genetic algorithm [1]; the cost function that will be optimised to minimise energy consumption and provide adequate thermal comfort; and finally the optimisation method, in this case a discrete branch and bound approach. Each component will be described, with a special emphasis on a fast and accurate computation of the PMV indices [2]. Experimental results obtained within different rooms in a building of the University of Algarve will be presented, both in summer [3] and winter [4] conditions, demonstrating the feasibility and performance of the approach. Energy savings resulting from the application of the method are estimated to be greater than 50%.

The constrained compartmentalized knapsack problem: mathematical models and solution methods

The constrained compartmentalized knapsack problem can be seen as an extension of the constrained knapsack problem. However, the items are grouped into different classes so that the overall knapsack has to be divided into compartments, and each compartment is loaded with items from the same class. Moreover, building a compartment incurs a fixed cost and a fixed loss of the capacity in the original knapsack, and the compartments are lower and upper bounded. The objective is to maximize the total value of the items loaded in the overall knapsack minus the cost of the compartments. This problem has been formulated as an integer non-linear program, and in this paper, we reformulate the non-linear model as an integer linear master problem with a large number of variables. Some heuristics based on the solution of the restricted master problem are investigated. A new and more compact integer linear model is also presented, which can be solved by a branch-and-bound commercial solver that found most of the optimal solutions for the constrained compartmentalized knapsack problem. On the other hand, heuristics provide good solutions with low computational effort. (C) 2011 Elsevier BM. All rights reserved.

Scattering and bound states of spinless particles in a mixed vector-scalar smooth step potential

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Scattering and bound states of spin-0 particles in a nonminimal vector double-step potential

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)