Rozprawy doktorskie na temat „Localisation discrète”
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Posta, Marius. "" Resolution Search " et problèmes d'optimisation discrète". Phd thesis, Université d'Avignon, 2012. http://tel.archives-ouvertes.fr/tel-00968201.
Pełny tekst źródłaPosta, Marius. "« Resolution Search » et problèmes d’optimisation discrète". Thèse, Avignon, 2012. http://hdl.handle.net/1866/8393.
Pełny tekst źródłaThe combinatorial nature of discrete optimization problems often makes them diffi- cult to solve. Consider for instance integer linear programming problems, which are commonly solved using a Branch-and-Bound approach. An alternative approach, Resolution Search, was proposed by Chvátal in 1997 for solving 0-1 optimization problems, but remains little known to this day and as such has seen few practical applications. This thesis attempts to remedy this state of affairs, with partial success. Its first contribution consists in the generalization of Resolution Search to any discrete optimization problem, while introducing new definitions and concepts. Next, we tried to validate this approach by attempting to solve well-known problems efficiently with it. Although our research did not succeed in this respect, it lead us to new methods for solving the generalized assignment and uncapacitated facility location problems. After presenting these methods, this thesis concludes with a summary of our attempts at practical application of Resolution Search, along with further perspectives on this matter.
Thèse réalisée en cotutelle avec l'Université d'Avignon.
Papin, Morgane. "Apport de la bioacoustique pour le suivi d’une espèce discrète : le Loup gris (Canis lupus)". Thesis, Université de Lorraine, 2018. http://www.theses.fr/2018LORR0258/document.
Pełny tekst źródłaThe growing number of studies carried out in recent years has shown that bioacoustics is particularly interesting for the monitoring of secretive species. The emergence of autonomous recording devices, combined with new methods of analysis, have recently contributed to the increase of studies in this field. Over the last 30 years, many bioacoustic studies have been developed for the Grey wolf (Canis lupus), a secretive large carnivore known for its howls spreading over distances up to several kilometers. These researches notably aimed to improve its monitoring, which is complex because of the strong wolf dispersal capacities over long distances, the large extent of their territories and the various natural contexts in which they live. In this context, this PhD thesis was organized around three research axes. The first two axes focused on the contribution of passive bioacoustics for the Grey wolf monitoring in the field. By combining acoustic, statistical and cartographic analysis, the first objective was to develop a spatial sampling method adapted to large study areas for the detection of wolf howls by using autonomous recorders. Then, the same protocol was used to investigate the possibility to localize wolves thanks to their howls. Field experimentations, conducted in mid-mountain (Massif des Vosges) and lowland (Côtes de Meuse) environments, in two study areas of 30 km² and with an array of 20 autonomous recorders, demonstrated the high potential of passive bioacoustics for the Grey wolf monitoring. Indeed, nearly 70% of broadcasts (synthetic sound with similar acoustic properties to howls) were detected by at least one autonomous recorder in mid-mountain environment and more than 80% in lowland environment, for sound source-recorders distances of up to 2.7 km and 3.5 km respectively. By using statistical model and Geographic Information System, the detection probability of wolf howls was modeled in both study areas. In the mid-mountain environment, this detection probability was high or very high (greater than 0.5) in 5.72 km² of the study area, compared with 21.43 km² in lowland environment. The broadcast sites were localized with an overall mean accuracy of 315 ± 617 (SD) m, reducing until 167 ± 308 (SD) m after setting a temporal error threshold defined from the data distribution. The third axe focused on the application of acoustic diversity indices to estimate the number of howling wolves in choruses and thus to contribute to pack size monitoring. Index values of the six indices (H, Ht, Hf, AR, M, and ACI) were positively correlated with the number of howling wolves in the artificial tested choruses. Interesting size predictions based on real choruses were obtained with one of the indices (ACI). The effects of several biases on the reference values for the acoustic indices were then explored, showing that three of them were relatively insensitive (Hf, AR and, ACI). Finally, results obtained with autonomous recorders confirm the real potential of passive acoustic methods for detecting the presence of wolves but also for localizing individuals with high precision, in contrasting natural environments, at large spatial and temporal scales. The use of acoustic diversity indices also opens new perspectives for estimating pack sizes. All of the promising methods emerging from this thesis require now further investigations before considering a concrete application for monitoring the Grey wolf in its natural environment
Durán, Mateluna Cristian. "Exact solution methods for large-scale discrete p-facility location problems". Electronic Thesis or Diss., Institut polytechnique de Paris, 2024. http://www.theses.fr/2024IPPAE001.
Pełny tekst źródłaThis thesis focuses on the exact solution of the NP-hard problems p-median and p-center, combinatorial optimization problems that quickly become difficult to solve as the instance size increases. These discrete location problems involve opening a defined number p of facilities and then allocating to them a set of clients according to an objective function to be minimized.First, we study the p-median problem, which seeks to minimize the sum of distances between clients and the open facilities to which they are allocated. We develop an algorithm based on Benders decomposition that outperforms state-of-the-art exact methods. The algorithm considers a two-stage approach and an efficient algorithm for separating Benders cuts. The method has been evaluated on over 230 benchmark instances with up to 238025 clients and sites. Many instances are solved to optimality for the first time or have their best known solution improved.Secondly, we explore the p-center problem, which seeks to minimize the largest distance between a client and its nearest open facility. We first compare the five main MILP formulations in the literature. We study the Benders decomposition and also propose an exact algorithm based on a client clustering procedure based on the structure of the problem. All the proposed methods are compared with the state-of-the-art on benchmark instances. The results obtained are analyzed, highlighting the advantages and disadvantages of each method.Finally, we study a robust two-stage p-center problem with uncertainty on node demands and distances. We introduce the robust reformulation of the problem based on the five main deterministic MILP formulations in the literature. We prove that only a finite subset of scenarios from the infinite uncertainty set can be considered without losing optimality. We also propose a column and constraint generation algorithm and a branch-and-cut algorithm to efficiently solve this problem. We show how these algorithms can also be adapted to solve the robust single-stage problem. The different proposed formulations are tested on randomly generated instances and on a case study drawn from the literature
Inoa-Peña, Ignacio. "Sur l’interdépendance entre localisation résidentielle et localisationprofessionnelle : modèles de choix discrets". Thesis, Cergy-Pontoise, 2015. http://www.theses.fr/2015CERG0792.
Pełny tekst źródłaThis thesis studies the interdependency between the choices of residential and workplace location. Issues such as the decision-making process, the accessibility to jobs, the geographical distribution of job types, and the spouses collective decision process, among others, are analyzed with discrete choice models. In this setting, we study the location decisions from two complementary points of view. (1) First, we study the interdependency between the two location choices without any within-household consideration. We develop a three-level nested logit model of residential and workplace location and study the effect of individual-specific attractiveness and accessibility (log-sum) measures. Results presented in the first chapter show that the individual-specific accessibility measure is an important determinant of the choice of residential location and its effect differs along the household life cycle. Additionally, the attractiveness of the types of employment is a better predictor of the workplace location than the usual total number of jobs. We analyze the evolution of the attractiveness and attractivity measures in the second chapter. (2) Second, we study the interdependency of residential location and workplaces within the household. This thesis contributes with a within-household bargaining process model of location decisions. As such, it applies the collectiveapproach à la Chiappori of household behavior to describe residential location choice of two-worker households. The last chapter develops and estimates a two-step structural model to disentangle bargaining powers from spouses' values of time. Results show that the nationalities of the couple, their education level, as well as the age difference between spouses play a crucial role in determining bargaining power
Giacometti, Romain. "Détection et localisation des signaux radar (systèmes passifs ou discrets)". Thesis, Brest, 2017. http://www.theses.fr/2017BRES0083.
Pełny tekst źródłaThe purpose of this work is to develop new methods for the detection and the location of radar sources. The developed approach exploits the direct and indirect signals received at the receiving point. In our study, we first develop a model of these signals that takes into account the characteristics of the transmitters and the reflectors. We evaluate this model by simulating a particular case of reflectors detection and location, defined in the literature. Our goal is to use the multipaths to locate emission sources. Most existing methods are based on specular reflections. Methods based on non-specular reflections, to locate emission sources in an unknown environment, are rarely studied in the literature. In our study, we propose a new location method that uses a fixed receiver measuring the Angle of Arrival (AOA) and Time Difference of Arrival (TDOA). In practice, an assignment problem must be solved before locating the emitters and reflectors. The problem is to assign each pair of TDOA-AOA measurements to a given reflector, assuming that each pair has already been assigned to a transmitter. The method developed has been tested and evaluated by using simulated data and real measurements
Hounwanou, Sonagnon. "Pour une approche territoriale de la logistique urbaine : choix individuels de déplacement, localisation commerciale et impact sur l’environnement des flux de transport de marchandises en ville". Thesis, Lyon, 2019. http://www.theses.fr/2019LYSEM013.
Pełny tekst źródłaThe significance of shopping trips for a city is at least twofold. They are essential to supply households as they are critical for the retail sector viability. Despite, shopping trip flows are rarely taken into account while evaluating urban goods flows. Actually, urban goods flows are more often addressed in a transport operating perspective only. We noticed during these PhD works that there is another approach for urban logistics in the scientific literature. We call it the territorial approach because it introduces warehouses location and urban planning matters into urban logistics. But there still are several operating issues to address about this approach. That’s what we targeted during our reflections, investigating the before and the after of a relocation project of an important retail store from Saint-Etienne ‘city centre. The key contributions of our works are twofold. The data we collected first allowed us to develop and test a discrete choice modelling methodology making the link between retail location and individual shopping trips behaviours. Second, we suggest to link both upstream and downstream transport flows generated by a retail store and assess their environmental impacts. Then another question is emerging. Having the possibility to model the retail location choice of consumers, is it easier to compare the environmental impacts of both upstream and downstream flows generated by different commercial areas in the city?
Zhou, Chong. "Investigation of micro- and macro-phenomena in densely packed granular media using the discrete element method". Thesis, University of Edinburgh, 2011. http://hdl.handle.net/1842/4899.
Pełny tekst źródłaBolting, Jan. "Contributions au vol en formation serrée de petits drones". Thesis, Toulouse, ISAE, 2017. http://www.theses.fr/2017ESAE0013.
Pełny tekst źródłaSmall, electrically driven unmanned aircraft are likely to suffer from inferior endurance compared to their larger counterparts. Upwash exploitation by tight formation flight, as well as aerial recharging are the most promising control-driven approaches to mitigate this disadvantage. Continuous time higher order sliding mode control (CTHOSM) has been considered as a candidate for this challenging open problem and was successfully applied to simple kinematic models in simulation, where excellent relative position tracking performance can be demonstrated. In this work we study the implications of the presence of inner loop dynamics and discrete implementation at moderate sampling rates and we find that it precludes the application of CTHOSM control to fixed-wing UAS. We propose a predictive discrete sliding mode guidance scheme to approximate the performance of CTHOSM control assuming realistic fixed-wing UAS dynamics. We show that the proposed guidance scheme in combination with inner load factor tracking loops and a disturbance observer allows for relative position tracking performance compatible with the requirements of upwash exploitation. We propose as well an openly accessible benchmark problem. Existing probabilistic localization algorithms cannot provide guaranteed confidence regions of the relative position between UAS. We present a set membership filter that provides ellipsoidal regions guaranteed to contain the relative positions of the other UAS. It is compatible with the hardware constraints of small low-cost UAS. Simulations suggest computational efforts compatible with the computational resources typically available onboard small UAS
Brancherie, Delphine. "Modèles continus et "discrets" pour les problèmes de localisation et de rupture fragile et/ou ductile". Phd thesis, École normale supérieure de Cachan - ENS Cachan, 2003. http://tel.archives-ouvertes.fr/tel-00132116.
Pełny tekst źródłaGodbout, Claudia. "Étude du choix de localisation des immigrants au Canada". Thesis, Université Laval, 2008. http://www.theses.ulaval.ca/2008/25861/25861.pdf.
Pełny tekst źródłaRazafindrazaka, Mialy. "Simulation par dynamique 2,5D des dislocations discrètes de la localisation de la déformation dans le 316L irradié : application à la rupture intergranulaire". Saint-Etienne, EMSE, 2008. http://www.theses.fr/2008EMSE0029.
Pełny tekst źródłaIrradiated austenitic stainless steel display a localization of deformation in “clear channels”, which may contribute to Irradiation-Assisted Stress Corrosion Cracking (IASCC). We assess this contribution using a bi-dimensional discrete dislocation dynamics simulation of plasticity. We first identify a plastic model that includes 3-dimensional plasticity mechanisms such as the line tension, junction formation and destruction, sweeping of irradiation defects by mobile dislocations. We reproduce the strain-softening associated to the formation of clear bands. We then apply this model to the case of a cracked bi-crystal. A high density of point obstacles induces the formation of an intense primary slip band ahead of the crack-tip. Dislocation pile-ups are relaxed by the activation of a secondary slip system, which in turn interacts with the grain boundary ahead of the crack. By amplifying these effects, the sweeping of irradiation defects favours intergranular brittle fracture
Joste, Baptiste. "Simulation of plastic strain localization by Discrete Dislocation Dynamics and crystal plasticity". Electronic Thesis or Diss., Université Paris sciences et lettres, 2023. http://www.theses.fr/2023UPSLM077.
Pełny tekst źródłaUnderstanding the deformation processes leading to the failure of polycrystalline materials is one of the major challenges in materials science. To date, the mechanisms of plastic strain localization into slip bands and the propagation of deformation through a polycrystalline aggregate are not fully understood. Investigating such phenomena is the aim of the 3DiPolyPlast ANR project. In the proposed multi-scale simulation approach, Discrete Dislocation Dynamics (DDD) simulations will be used to better model the individual and collective behavior of dislocations at the mesoscopic scale. The majority of the simulations carried out are based on a so-called weak coupling between DDD and the Finite Element Method (FEM), in which the stress field resulting from a FEM calculation in elasticity is used as the initial intragranular loading condition. This assumption enables a more systematic and physically justified study of the various mechanisms taking place during plastic deformation within the dislocation microstructure. The simulations carried out show the role played by the polycrystalline microstructure on the localization of plastic deformation, notably through elastic deformation incompatibilities leading to the appearance of intragranular stress concentrations. Using these simulations, we show that during plastic deformation, certain mechanisms such as cross-slip or collinear annihilation allow plastic deformation to initiate in certain regions of the grain. Meticulous observation of this dislocation microstructure has enabled us to reconsider one of the initial assumptions of our DDD simulations, the impenetrability of grain boundaries. In fact, the number of dislocations stacking up at grain boundaries is significant, and the stresses calculated at the head of these stacks are of the order of the GPa. Part of the work presented in this manuscript has therefore been dedicated to the implementation of a local rule to model the reaction mechanisms between dislocations and grain boundaries during plastic deformation. In addition, we have shown that these reaction mechanisms are responsible for a sharp decrease in kinematic strain hardening, leading to intense plastic slip in local regions of the grain. Further calculations were carried out within the framework of the discrete-continuous model (DCM), which couples crystal plasticity finite element calculations carried out on the complete polycrystalline aggregate with DDD simulations. This modeling provides a more precise description of plastic deformation mechanisms, and represents a major asset in the study of the role of interactions between grains, particularly during their plastic deformation. These simulations are also proving to be a source of information for better understanding the diffraction contrasts observed experimentally in X-ray topo-tomography
Aissaoui, Hind. "Choix de localisation résidentielle des ménages en milieu urbain : les apports récents des modèles de choix discrets en présence d'un nombre élevé d'alternatives". Thesis, Lyon, 2016. http://www.theses.fr/2016LYSE2093/document.
Pełny tekst źródłaThis thesis, focusing on the choice of residential location, is based on the theoretical framework of urban micro-economy and random utility. Though discrete choice modelling is the most appropriate in this field, the difficulty lies in choosing the appropriate model to the spatial context of residential location choice (spatial autocorrelation, large number of alternatives), on the one hand, and in the way of defining the spatial scale, on the other hand. For this purpose, we proceeded in two stages. We estimated a multinomial logit with random sampling of alternatives to understand the process of residential location choice before taking into account the spatial autocorrelation, and estimating a nested logit model. It also allowed to investigate the feasibility of applying a new method to correct biases of sampling alternatives in the case of nested logit model. In terms of results, we have shown that social environment are the most important determinants of residential location choice. Though job accessibility still weigh on household choice decision. In terms of methodology, we were able to test the feasibility of estimating a nested logit model with sampling of alternatives to analyze the choice of location of Lyon urban area. However, we could not overcome the difficulty of distinguishing spatial autocorrelation from nesting. The use of 1999 and 2007 databases to model residential location choice also helped to provide answers on the temporal transferability of location choice models and discuss in future work the predictive power of a location choice model
Homocianu, George Marius. "Modélisation de l’interaction transport-urbanisme : choix résidentiels des ménages dans l’aire urbaine de Lyon". Thesis, Lyon 2, 2009. http://www.theses.fr/2009LYO22001/document.
Pełny tekst źródłaThe objective of the thesis is to propose a modeling of the residential behaviors of the households: the choice of change of residence (or removal), and the choice of the new location. This type of models aims at envisaging the probability that a household changes residence and its choice of new location, according to a certain number of explanatory variables. In our case, modeling is founded on the discrete choice theory (random utility approach). Research is based on the Lyons case, the model being built on the urban area of Lyon, on data of the year 1999. In terms of results, side of residential mobility, it should be retained that the variables which explain the variation of the degree of mobility (of the rate of removal) of the households are the age of head, the number of children and the statute of occupation of housing. With regard to the households location, the preferences of the households for a zone are related on the characteristics of those and particularly to accessibility on various opportunities and services, which confirms that among the factors which influence the location behavior of the households one finds accessibilities, and thus, the assumption of the existence of a relation between transport and land use. It was also found that the characteristics of the households like age of head, income or household size have an influence on their location choices. The study and the results of the models suggest that improvements and new directions of research are possible. Thus, on the side of residential mobility, there could be other variables which justify the housing change, like characteristics of the residence, residential environment or other characteristics of the households not observed. It would be also interesting to estimate the location model at a finer geographical level (îlot). Other alternatives of modeling of the residential decisions of the households would be to model a hierarchical structure of the choices, by a hierarchical or nested logit, or to model the life cycle, whit its components family, residential and professional, which are in interdependence (in condition of availability of necessary data)
Soldani, Siegfried. "Vers le diagnostic embarqué de défaillances dans les systèmes à événements discrets : application au domaine automobile". Toulouse 3, 2008. https://hal.laas.fr/tel-01591892.
Pełny tekst źródłaThis thesis deals with the diagnosis of behavior functions in the embedded network systems and especially in the automotive systems. It is focused on the localization of intermittent faults in discrete events systems. The proposed methods are based on a discrete events model representing the normal functioning of the observable behavior of the monitored system. The detection step consists of a comparison between the flow of observable events emitted by the monitored system and the flow foreseen by the model. A localization mechanism, based on the diagnoser approach (Sampath et al. , 1998), points out the set of events potentially responsible for the faults. The aim of this approach is to get the diagnosis information into a data structure (off-line) which efficiently joins the observations with the faults during the on-line diagnosis. This thesis have lead to the building of many applications for the intermittent fault diagnosis. This works have been validated on a test bench representing the network used in the city transports (bus, subways. . . )
Baraklianos, Ioannis. "The accessibility in Land-Use Transport Interaction models : four essays on location choice models". Thesis, Lyon, 2019. http://www.theses.fr/2019LYSE2037/document.
Pełny tekst źródłaThis PhD thesis has as objective to examine the place and the importance of accessibility in location choice models of households and firms, two key construction elements of Land-Use Transport Interaction models. More specifically, the aim is to analyse the effect of various methodological choices from a theoretical and empirical point of view in order to give some answers to theoretical, methodological, empirical and policy issues. Having as a case study the urban area of Lyon and using discrete models to explain the location choices of households and firms, four research papers comprise the main work of this dissertation.In the first paper, the objective was to analyse the effect of the accessibility measure on the results of residential location choice model. While accessibility has always been important at theoretical level, at empirical level, some works questioned its importance, considering other location characteristics as more influential. This paper examines whether different accessibility measurement methods can lead to divergent results. The conclusion is that accessibility is an indispensable variable for residential location choice models and the conclusion remains the same whatever is the measure. Without accessibility, the model gives inconsistent results. Complex accessibility measures give better results, especially for predictions, but simple measures are also relevant for residential location choices modelling.In the second paper, the objective was to analyse the differences of accessibility preferences between new and relocating firms. Accessibility is one of the most important attributes of a location choice of an economic establishment. However, even if it seems intuitive, works analysing any differences between creations and relocations are scarce. Using data from eighteconomic sectors and comparing creations to relocations, the results demonstrate that the effect of accessibility differs between in the same economic sector.In the third paper, the objective was to evaluate the difference of the accessibility impact on the location choices of firms of the business services sector. Distinguishing between Front Office and Back Office business services in a location choice model, the results demonstrate that the effect of accessibility differs between economic subsectors.In the fourth paper, the objective was to analyse the temporal evolution of the preferences for accessibility for residential choices. More and more people choose to buy a residence at the suburbs taking advantage of the accessibility increase. At the same time, young households, the so called millennials, choose to rent in central areas. Distinguishing between renters andowners, the analysis of the elasticities for 1999, 2006 and 2013 confirm the initial intuition. Renters were always more sensitive to accessibility to employment. More importantly, renters show an increasing preference for accessibility during the analysis period, while the owners the opposite. We suggest that planners and model developers should integrate temporal dynamics into their models in order to anticipate better future tendencies
Claude, Christophe. "Extensions et applications de la méthode spectrale aux systèmes discrets et aux systèmes couplés". Montpellier 2, 1993. http://www.theses.fr/1993MON20084.
Pełny tekst źródłaVermaut, Alexis. "Concentration spatiale des activités économiques at spécialisation des territoires : approche théorique et application aux régions et zones d'emploi françaises". Lille 1, 2003. https://pepite-depot.univ-lille.fr/LIBRE/Th_Num/2003/50374-2003-15.pdf.
Pełny tekst źródłaHeusch, Michaël. "Modélisation et résolution d'une application d'aide au déploiement d'antennes radio en programmation par contraintes sur le discret et le continu". Phd thesis, Université de Nantes, 2006. http://tel.archives-ouvertes.fr/tel-00481598.
Pełny tekst źródłaHomocianu, Marius. "Modélisation de l'intéraction transport-urbanisme - Choix résidentiels des ménages dans l'aire urbaine de Lyon". Phd thesis, Université Lumière - Lyon II, 2009. http://tel.archives-ouvertes.fr/tel-00359302.
Pełny tekst źródłaEn termes de résultats, du côté de la mobilité résidentielle, il faut retenir que les variables qui expliquent la variation du degré de mobilité (du taux de déménagement) des ménages sont l'âge de la personne de référence du ménage, le nombre d'enfants et le statut d'occupation du logement. En ce qui concerne la localisation des ménages, les préférences des ménages pour une zone ou autre sont liées aux caractéristiques de celles-ci et notamment à l'accessibilité aux différentes opportunités et services, ce qui confirme que parmi les facteurs qui influencent le comportement de localisation des ménages on retrouve les accessibilités, et donc, l'hypothèse de l'existence d'un lien entre transports et urbanisme. On a également trouvé que les caractéristiques des ménages comme l'âge de la personne de référence, le revenu ou le nombre de personnes ont une influence sur leurs choix de localisation.
L'étude et les résultats des modèles suggèrent que des améliorations et nouvelles pistes de recherche sont possibles. Ainsi, du côté de la mobilité résidentielle, il pourrait y avoir d'autres variables qui motivent les ménages à changer de logement, comme des caractéristiques des logements, de l'environnement résidentiel ou d'autres caractéristiques des ménages non observées. Il serait aussi intéressant d'estimer le modèle de localisation a un niveau géographique encore plus fin (à l'îlot). D'autres alternatives de modélisation des décisions résidentielles des ménages seraient de modéliser une structure hiérarchisée des choix, par un modèle logit hiérarchique ou emboîté, ou bien de modéliser la trajectoire de vie, avec ses composantes familiale, résidentielle et professionnelle, qui sont en interdépendance (à condition de la disponibilité des données nécessaires).
Gland, Nicolas. "Etude numérique des propriétés mécaniques et des processus de déformation et d'endommagement des matériaux granulaires". Phd thesis, Université Paris Sud - Paris XI, 2003. http://tel.archives-ouvertes.fr/tel-00006671.
Pełny tekst źródłaPehlivan, Canan. "Design and flow control of stochastic health care networks without waiting rooms : A perinatal application". Phd thesis, Ecole Nationale Supérieure des Mines de Saint-Etienne, 2014. http://tel.archives-ouvertes.fr/tel-00994291.
Pełny tekst źródłaKhuong, Paul Virak. "Lagrangian-informed mixed integer programming reformulations". Thèse, 2013. http://hdl.handle.net/1866/10538.
Pełny tekst źródłaInteger linear programming is a robust and efficient approach to solve large-scale instances of combinatorial problems. However, problems constantly gain in complexity and sometimes impose strong constraints on computation times. We must then develop specialised methods to compute heuristic primal solutions to the problem and derive lower bounds on the optimal value, and thus prove the quality of our primal solutions. We propose to guide a reformulation approach for mixed integer programs with Lagrangian relaxations. After the identification of a strong relaxation, a mechanical process leads to a second integer formulation. This reformulation is equivalent to the initial one, but its linear relaxation is equivalent to the strong Lagrangian dual. We will show that the reformulation approach unifies and generalises prior formulations and lower bounding approaches, and that it exposes a simple mechanism to reduce the size of reformulations in return for weaker bounds. Nevertheless, our reformulations are large. We address this issue by solving their linear relaxations with specialised methods. Finally, we apply the reformulation approach to two location problems. This yields novel formulations for both problems; some are very large but, thanks to the aforementioned specialised methods, still practical.
Bouix, Rémy. "Caractérisation mécanique et modélisation numérique du comportement des mousses polymériques sous sollicitations statiques et dynamiques". Phd thesis, 2008. http://pastel.archives-ouvertes.fr/pastel-00005433.
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