Consider the problem of maximizing the revenue generated by tolls set on a subset <p>of arcs of a transportation network, where origin-destination flows (commodities) are assigned to shortest paths with respect to the sum of tolls and initial costs. <p>This thesis is concerned with a particular case of the above problem, in which all toll arcs are connected and constitute a path, as occurs on highways. Further, as toll levels are usually computed using the highway entry and exit points, a complete toll subgraph is considered, where each toll arc corresponds to a toll subpath. Two <p>variants of the problem are studied, with or without specific constraints linking together the tolls on the arcs. <p>The problem is modelled as a linear mixed integer program, and proved to be NP-hard. Next, several classes of valid inequalities are proposed, which strengthen important constraints of the initial model. Their efficiency is first shown theoretically, as these are facet defining for the restricted one and two commodity problems. <p>Also, we prove that some of the valid inequalities proposed, together with several <p>constraints of the linear program, provide a complete description of the convex hull <p>of feasible solutions for a single commodity problem. Numerical tests have also been conducted, and highlight the real efficiency of the valid inequalities for the multi-commodity case. Finally, we point out the links between the problem studied in the thesis and a more classical design and pricing problem in economics. /<p><p><p>Considérons le problème qui consiste à maximiser les profits issus de la tarification d’un sous-ensemble d’arcs d’un réseau de transport, où les flots origine-destination (produits) sont affectés aux plus courts chemins par rapport aux tarifs et aux coûts initiaux. Cette thèse porte sur une structure de réseau particulière du problème ci-dessus, dans laquelle tous les arcs tarifables sont connectés et forment un chemin, <p>comme c’est le cas sur une autoroute. Étant donné que les tarifs sont habituellement déterminés selon les points d’entrée et de sortie sur l’autoroute, nous considérons un sous-graphe tarifable complet, où chaque arc correspond en réalité à un sous-chemin. Deux variantes de ce problème sont étudiées, avec ou sans contraintes <p>spécifiques reliant les niveaux de tarifs sur les arcs. <p>Ce problème peut être modélisé comme un programme linéaire mixte entier. Nous prouvons qu’il est <p>NP-difficile. Plusieurs familles d’inégalités valides sont ensuite proposées, celles-ci renforçant certaines contraintes du modèle initial. Leur efficacité est d’abord démontrée de manière théorique, puisqu’il s’agit de facettes <p>des problèmes restreints à un ou deux produits. Certaines des inégalités valides proposées, ainsi que plusieurs contraintes du modèle initial, permettent aussi de donner une description complète de l’enveloppe convexe des solutions réalisables d’un problème restreint à un seul produit. Des tests numériques ont également <p>été menés, et mettent en évidence l’efficacité réelle des inégalités valides pour le problème général à plusieurs produits. Enfin, nous soulignons les liens entre le problème de tarification de réseau étudié dans cette thèse et un problème plus classique de tarification de produits en gestion. <p> / Doctorat en Sciences / info:eu-repo/semantics/nonPublished

[pt] O Partial Digest Problem (problema de digestão parcial), também conhecido como o Turnpike Problem, consiste na construção de um conjunto de pontos na reta real dadas as distâncias não designadas entre todos os pares de pontos. Uma variante deste problema, chamada Min Distance Superset Problem (problema de superset de distância mínimo), lida com entradas incompletas em que algumas distâncias podem estar faltando. O objetivo deste problema é encontrar um conjunto mínimo de pontos na reta real, tal que as distâncias entre cada par de pontos contenham todas as distâncias de entrada. As principais contribuições deste trabalho são duas formulações de programação matemática diferentes para o Min Distance Superset Problem: uma formulação de programação quadrática e uma formulação de programação inteira. Mostramos como aplicar um método de cálculo direto de limites de valores de variáveis através de uma relaxação Lagrangeana da formulação quadrática. Também introduzimos duas abordagens diferentes para resolver a formulação inteira, ambas baseadas em buscas binárias na cardinalidade de uma solução ótima. A primeira baseia-se num subconjunto de variáveis de decisão, na tentativa de lidar com um problema de viabilidade mais simples, e o segundo é baseado na distribuição de distâncias entre possíveis pontos disponíveis. / [en] The Partial Digest Problem, also known as the Turnpike Problem, consists of building a set of points on the real line given their unlabeled pairwise distances. A variant of this problem, named Min Distance Superset Problem, deals with incomplete input in which distances may be missing. The goal is to find a minimal set of points on the real line such that the multiset of their pairwise distances is a superset of the input. The main contributions of this work are two different mathematical programming formulations for the Min Distance Superset Problem: a quadratic programming formulation and an integer programming formulation.We show how to apply direct computation methods for variable bounds on top of a Lagrangian relaxation of the quadratic formulation. We also introduce two approaches to solve the integer programming formulation, both based on binary searches on the cardinality of an optimal solution. One is based on a subset of decision variables, in an attempt to deal with a simpler feasibility problem, and the other is based on distributing available distances between possible points.

Le problème de dimensionnement et planification d'agents en centre d'appels consiste à déterminer sur une période le nombre d'interlocuteurs requis afin d'atteindre la qualité de service exigée et minimiser les coûts induits. Ce sujet fait l'objet d'un intérêt croissant pour son intérêt théorique mais aussi pour l'impact applicatif qu'il peut avoir. Le but de cette thèse est d'établir des approches en contraintes en probabilités en considérant l'incertitude de la demande.Tout d'abord, la thèse présente un modèle en problème d'optimisation stochastique avec contrainte en probabilité jointe traitant la problématique complète en une étape afin d'obtenir un programme facile à résoudre. Une approche basée sur l'idée de continuité est proposée grâce à des lois de probabilité continues, une nouvelle relation entre les taux d'arrivées et les besoins théoriques et la linéarisation de contraintes. La répartition du risque global est faite pendant le processus d'optimisation, permettant une solution au coût réduit. Ces solutions résultantes respectent le niveau de risque tout en diminuant le coût par rapport à d'autres approches.De plus, le modèle en une étape est étendu pour améliorer sa représentation de la réalité. D'une part, le modèle de file d'attente est amélioré et inclus la patience limitée des clients. D'autre part, une nouvelle expression de l'incertitude est proposée pour prendre la dépendance des périodes en compte.Enfin, une nouvelle représentation de l'incertitude est considérée. L'approche distributionally robust permet de modéliser le problème sous l'hypothèse que la loi de probabilité adéquate est inconnue et fait partie d'un ensemble de lois, défini par une moyenne et une variance données. Le problème est modélisé par une contrainte en probabilité jointe. Le risque à chaque période est définie par une variable à optimiser.Un problème déterministe équivalent est proposé et des approximations linéaires permettent d'obtenir une formulation d'optimisation linéaire. / The staffing and shift-scheduling problems in call centers consist in deciding how many agents handling the calls should be assigned to work during a given period in order to reach the required Quality of Service and minimize the costs. These problems are subject to a growing interest, both for their interesting theoritical formulation and their possible applicative effects. This thesis aims at proposing chance-constrained approaches considering uncertainty on demand forecasts.First, this thesis proposes a model solving the problems in one step through a joint chance-constrained stochastic program, providing a cost-reducing solution. A continuous-based approach leading to an easily-tractable optimization program is formulated with random variables following continuous distributions, a new continuous relation between arrival rates and theoritical real agent numbers and constraint linearizations. The global risk level is dynamically shared among the periods during the optimization process, providing reduced-cost solution. The resulting solutions respect the targeted risk level while reducing the cost compared to other approaches.Moreover, this model is extended so that it provides a better representation of real situations. First, the queuing system model is improved and consider the limited patience of customers. Second, another formulation of uncertainty is proposed so that the period correlation is considered.Finally, another uncertainty representation is proposed. The distributionally robust approach provides a formulation while assuming that the correct probability distribution is unknown and belongs to a set of possible distributions defined by given mean and variance. The problem is formulated with a joint chance constraint. The risk at each period is a decision variable to be optimized. A deterministic equivalent problem is proposed. An easily-tractable mixed-integer linear formulation is obtained through piecewise linearizations.

This dissertation presents a pumping system operation efficiency improvement solution that includes optimal selection and control of the water pump. This solution is formulated based on the performance, operation, equipment and technology (POET) framework. The focus is on the minimization of the operational energy cost. This efficiency improvement solution is divided into three stages in accordance with the operation category of the POET framework. The first stage is to select the optimal pump capacity by considering both energy efficiency and load shifting requirements. The second stage is to develop a flexible pump controlling strategy that combines and balances the contributions from energy efficiency and load shifting. The last stage is to improve the robustness of the control system using the closed-loop model predictive control approach. An optimal pump capacity selection model is formulated. In this model, additional capacity requirements for load shifting are considered along with the traditional energy efficiency requirements. By balancing the contributions from load shifting and energy efficiency, the operational energy cost can be reduced by up to 37%. An optimal pump control is formulated. The objective of this control model is to balance the energy efficiency and load shifting contributions during the operation and minimize the operational energy cost. This control model is tested under different operational conditions and it is compared to other existing control strategies. The simulation and comparison results show that the proposed control strategy achieves the lowest operational energy cost in comparison to other strategies. This optimal pump control model is further modified into the closed-loop model predictive control format to increase the robustness of the control system under operation uncertainties. A mixed integer particle swarm optimization algorithms is employed to solve the optimization problems in this research. AFRIKAANS : Hierdie verhandeling bied ’n verbeterde oplossing vir die operasionele doeltreffendheid van pompstelsels wat die optimale keuse en beheer van die waterpomp insluit. Hierdie oplossing is geformuleer op ’n raamwerk wat werkverrigting, bedryf, toerusting en tegnologie in ag neem. Die oplossing fokus op die vermindering van bedryfsenergie koste. Hierdie oplossing is onderverdeel in drie fases soos bepaal deur die bedryfskategorie gegrond op die bogenoemde raamwerk: Die eerste fase is die keuse van die optimale pompkapasiteit deur beide energiedoeltreffendheid en lasverskuiwing in ag te neem. Die tweede fase is om ’n buigbare pompbeheer strategie te ontwikkel wat ’n goeie balans handhaaf tussen die onderskeie bydraes van energiedoeltreffendheid en lasverskuiwing. Die derde fase is om die stabiliteit van die beheerstelsel te verbeter deur gebruik te maak van ’n geslote-lus beheermodel met voorspellende beheer (Predictive Control). ’n Model vir die keuse van optimale pompkapasiteit is geformuleer. In hierdie model word vereistes vir addisionele pompkapasiteit vir lasverskuiwing sowel as vereistes in terme tradisionele energiedoeltreffendheid in ag geneem. Deur die regte verhouding tussen die onderskeie bydraes van energiedoeltreffendheid en lasverskuiwing te vind kan ’n besparing van tot 37% op die energiekoste verkry word. Optimale pompbeheer is geformuleer. Die doel van die beheermodel is om die bydraes van energiedoeltreffendheid en lasverskuiwing te balanseer en om die bedryfsenergie koste te minimiseer. Hierdie beheermodel is getoets onder verskillende bedryfstoestande en dit is vergelyk met ander bestaande beheerstrategiee. Die simulasie en vergelyking van resultate toon dat die voorgestelde beheerstrategie die laagste bedryfsenergie koste behaal in vergelyking met ander strategiee. Hierdie optimale pomp beheermodel is verder aangepas in ’n geslote beheermodel met voorspellende beheerformaat om die stabiliteit van die beheerstelsel te verbeter onder onsekere bedryfstoestande. ’n Gemende heelgetal partikel swerm optimisasie (Mixed interger particle swarm optimization) algoritme is gebruik om die optimiseringsprobleme op te los tydens hierdie navorsingsoefening. / Dissertation (MEng)--University of Pretoria, 2011. / Electrical, Electronic and Computer Engineering / Unrestricted

Worst Case Execution Time (WCET) is an important metric for programs running on real-time systems, and finding precise estimates of a program’s WCET is crucial to avoid over-allocation and wastage of hardware resources and to improve the schedulability of task sets. Hardware Caches have a major impact on a program’s execution time, and accurate estimation of a program’s cache behavior generally leads to significant reduction of its estimated WCET. However, the cache behavior of an access cannot be determined in isolation, since it depends on the access history, and in multi-path programs, the sequence of accesses made to the cache is not fixed. Hence, the same access can exhibit different cache behavior in different execution instances. This issue is further exacerbated in shared caches in a multi-core architecture, where interfering accesses from co-running programs on other cores can arrive at any time and modify the cache state. Further, cache analysis aimed towards WCET estimation should be provably safe, in that the estimated WCET should always exceed the actual execution time across all execution instances. Faced with such contradicting requirements, previous approaches to cache analysis try to find memory accesses in a program which are guaranteed to hit the cache, irrespective of the program input, or the interferences from other co-running programs in case of a shared cache. To do so, they find the worst-case cache behavior for every individual memory access, analyzing the program (and interferences to a shared cache) to find whether there are execution instances where an access can super a cache miss. However, this approach loses out in making more precise predictions of private cache behavior which can be safely used for WCET estimation, and is significantly imprecise for shared cache analysis, where it is often impossible to guarantee that an access always hits the cache. In this work, we take a fundamentally different approach to cache analysis, by (1) trying to find worst-case behavior of groups of cache accesses, and (2) trying to find the exact cache behavior in the worst-case program execution instance, which is the execution instance with the maximum execution time. For shared caches, we propose the Worst Case Interference Placement (WCIP) technique, which finds the worst-case timing of interfering accesses that would cause the maximum number of cache misses on the worst case execution path of the program. We first use Integer Linear Programming (ILP) to find an exact solution to the WCIP problem. However, this approach does not scale well for large programs, and so we investigate the WCIP problem in detail and prove that it is NP-Hard. In the process, we discover that the source of hardness of the WCIP problem lies in finding the worst case execution path which would exhibit the maximum execution time in the presence of interferences. We use this observation to propose an approximate algorithm for performing WCIP, which bypasses the hard problem of finding the worst case execution path by simply assuming that all cache accesses made by the program occur on a single path. This allows us to use a simple greedy algorithm to distribute the interfering accesses by choosing those cache accesses which could be most affected by interferences. The greedy algorithm also guarantees that the increase in WCET due to interferences is linear in the number of interferences. Experimentally, we show that WCIP provides substantial precision improvement in the final WCET over previous approaches to shared cache analysis, and the approximate algorithm almost matches the precision of the ILP-based approach, while being considerably faster. For private caches, we discover multiple scenarios where hit-miss predictions made by traditional Abstract Interpretation-based approaches are not sufficient to fully capture cache behavior for WCET estimation. We introduce the concept of cache miss paths, which are abstractions of program path along which an access can super a cache miss. We propose an ILP-based approach which uses cache miss paths to find the exact cache behavior in the worst-case execution instance of the program. However, the ILP-based approach needs information about the worst-case execution path to predict the cache behavior, and hence it is difficult to integrate it with other micro-architectural analysis. We then show that most of the precision improvement of the ILP-based approach can be recovered without any knowledge of the worst-case execution path, by a careful analysis of the cache miss paths themselves. In particular, we can use cache miss paths to find the worst-case behavior of groups of cache accesses. Further, we can find upper bounds on the maximum number of times that cache accesses inside loops can exhibit worst-case behavior. This results in a scalable, precise method for performing private cache analysis which can be easily integrated with other micro-architectural analysis.

Les problèmes d’ordonnancement de rendez-vous en tête-à-tête sont des problèmes dans lesquels des personnes souhaitent se rencontrer par deux lors de courts rendez-vous qui se déroulent lors d’une session unique. Dans cette thèse, nous référençons plusieurs applications de ce type de problèmes et proposons des notations qui généralisent les notations standards de problèmes d’ordonnancement α|β|γ. Nous nous intéressons en particulier à un cas dans lequel deux populations distinctes se rencontrent, des participants peuvent arriver en retard et des rencontres sont interdites. L’objectif est de minimiser le nombre maximal d’attentes des participants. Nous étudions dans un premier temps la complexité de ces problèmes : nous démontrons que plusieurs cas sans rencontre interdite sont polynomiaux et que le cas général est NP-complet au sens fort. Nous proposons ensuite des bornes inférieures. Puis nous développons plusieurs méthodes de résolution. Des modèles de programmation linéaire en nombres entiers et un modèle de programmation par contraintes sont tout d’abord proposés. Des règles de dominance permettant de limiter les symétries sont intégrées à ces modèles dans le but de limiter l’espace des solutions. Enfin, nous proposons une recherche à divergence limitée (limited discrepancy search) qui est une méthode approchée basée sur l’exploration d’un arbre de recherche tronqué. Dans cette méthode, nous exploitons le plus possible les propriétés de symétrie du problème pour faciliter la convergence vers une bonne solution. Toutes ces méthodes sont testées et comparées sur un ensemble de 300 instances générées aléatoirement d’après des paramètres réalistes. / One-to-one meeting scheduling problems are problems where a population of actors want to meet each other during short time slots that take place in a single session. In this thesis, we reference several applications of this type of problems found in the literature and introduce a notation extending the well-known scheduling notation α|β|γ. We are particularly interested in a case in which two distinct populations meet, participants may arrive late and some meetings are forbidden. The objective is to minimize the maximum number of participants waiting slots. First, we study the complexity of these problems: we show that several cases with no forbidden meeting are polynomial and that the general case is NP-complete in the strong sense. We then propose lower bounds. After that, we develop several resolution methods. Integer linear programming models and a constraint programming model are developed. To limit the solution space, we add dominance rules based on symmetries to these methods. Finally, we present a limited discrepancy search (i.e. an approximate method based on the exploration of a truncated tree search). In this method, we use as much as possible the symmetry properties of the problem to facilitate the convergence to a good solution. All these methods are tested and compared on a set of 300 randomly generated instances from realistic parameters.

This thesis deals with application of optimisation methods based on linear and mixed-integer linear programming to various problems in the power sector related to electricity production. The thesis goal is to test the applicability of such methods to formulating and solving various instances from the class of real-world electricity production problems, and to find the advantages and disadvantages associated with using these methods. Introductory chapters describe the main characteristics of power markets, including the historical and regulatory context. Fundamental properties of power markets on both demand and supply side are also described, both from a real-world and a modelling point of view. Benefits of optimisation and modelling are discussed, in particular the solution feasibility and optimality as well as insights gained from sensitivity analysis which is often difficult to replicate with the original system. In the core of the thesis, optimisation techniques are applied to three case studies, each of which deals with a specific problem arising during electricity production. In the first problem, the profit of gas-fired power plant in Slovakia from selling power on the day-ahead market is maximised. The model is set up using both technical and commercial constraints. The second problem deals with the problem of representing a two-dimensional production function which primarily arises for a hydro generator with large variations in the level of its reservoir. Several representations of the original function using piecewise linear subsets are presented, compared, and characterised by their computational intensity both theoretically and practically. In the third problem, the prices on the German day-ahead market in 2011 are modelled. Contrary to the previous two models, the model does not capture an optimisation problem faced by a single producer, but incorporates a large subset of the whole market instead. Consequently the model is formed out of generic constraints relevant to all power plants whose parameters are estimated. By combining information about the aggregate availability of power plants with the estimated efficiencies a full supply curve for each day is created. Different scenarios are analysed to test the impact of uncertain inputs such as unknown or estimated constraints. The choice of the investigated problems stems from the attempt to cover electricity production problems from the point of view of multiple criteria. The three investigated electricity production problems span a broad range from the decisions of a single power plant to the modelling a power market as a whole. Formulations of the production function with different level of detail are presented ranging from a simple linear relationship to several bivariate function formulations. While each problem answers a specific question, they all illustrate the ease with which various electricity production problems can solved using optimisation methods based on linear and mixed-integer linear programming. This is mainly due to the ability of these methods to approximate even non-linear functions and constraints over non-convex domains and find global solutions in reasonable time. Moreover, models formulated with these methods allow sensitivity and scenario analyses to be carried out easily as is illustrated in each of the case studies.

Esta Dissertação aborda o Problema de Alocação de Aulas a Salas (PAAS), também conhecido como Problema de Alocação de Salas (PAS). As instituições de ensino superior, no começo de seus calendários letivos, resolvem um PAAS ao determinar os espaços a serem utilizados para as atividades didáticas. Porém, em muitas destas instituições o PAAS é ainda resolvido manualmente, gerando altas cargas de trabalho para os responsáveis. Neste trabalho, o Instituto de Ciências Matemáticas e de Computação (ICMC) da Universidade de São Paulo (USP) foi tomado como caso de estudo para o PAAS. Um modelo de programação matemática inteiro é proposto e abordado por técnicas de resolução exata, metaheurísticas mono-objetivo e uma abordagem multi-objetivo. Uma estrutura de vizinhança proposta obteve resultados comparáveis à da metodologia exata, para um tempo fixo de execução. Demonstra-se que, a abordagem multi-objetivo é uma possibilidade de contornar algumas dificuldades clássicas do problema, como incertezas sobre a escolha dos pesos das métricas. Os métodos de solução propostos para o problema fornecem, aos responsáveis, bons instrumentos de auxílio à tomada de decisão para o PAAS. / This Dissertation addresses the Classroom Assignment Problem (CAP). All Higher Education Institutes, at the schoolyear\'s begin, faces a CAP to define where the classes will be taught. However, many of those still solves this problem manually, demanding high efforts from the responsible staff. In this study, the Universidade de São Paulo\'s (USP) Instituto de Ciências Matemáticas e de Computação (ICMC) was tackled as study case for the CAP. An Integer Programming Model is proposed and tackled by exact methods, meta-heuristics and a multi-objective approach. A novel neighborhood operator is proposed for the local search and obtains good results, even comparable to the exact method. The multi-objective approach is shown to overcome some of the classical adversity of the mono-objective approach, e.g., choosing weights to quality metric. Those CAP\'s proposed solution methods, gives the responsible staff a good decision making support.

Muitas relações min-max em otimização combinatória podem ser demonstradas através de total dual integralidade de sistemas lineares. O conceito algébrico de bases de Hilbert foi originalmente introduzido com o objetivo de melhor compreender a estrutura geral dos sistemas totalmente dual integrais. Resultados apresentados posteriormente mostraram que bases de Hilbert também são relevantes para a otimização combinatória em geral e para a caracterização de certas classes de objetos discretos. Entre tais resultados, foram provadas, a partir dessas bases, versões do teorema de Carathéodory para programação inteira. Nesta dissertação, estudamos aspectos estruturais e computacionais de bases de Hilbert e relações destas com programação inteira e otimização combinatória. Em particular, consideramos versões inteiras do teorema de Carathéodory e conjecturas relacionadas. / There are several min-max relations in combinatorial optimization that can be proved through total dual integrality of linear systems. The algebraic concept of Hilbert basis was originally introduced with the objective of better understanding the general structure of totally dual integral systems. Some results that were proved later have shown that Hilbert basis are also relevant to combinatorial optimization in a general manner and to characterize certain classes of discrete objects. Among such results, there are versions of Carathéodory\'s theorem for integer programming that were proved through those basis. In this dissertation, we study structural and computational aspects of Hilbert basis and their relations to integer programming and combinatorial optimization. In particular, we consider integer versions of Carathéodory\'s theorem and related conjectures.

Over-parameterized networks, where the number of parameters surpass the number of train-ing samples, generalize well on various tasks. However, large networks are computationally expensive in terms of the training and inference time. Furthermore, the lottery ticket hy-pothesis states that a subnetwork of a randomly initialized network can achieve marginal loss after training on a specific task compared to the original network. Therefore, there is a need to optimize the inference and training time, and a potential for more compact neural architectures. We introduce a novel approach “Optimizing ANN Architectures using Mixed-Integer Programming” (OAMIP) to find these subnetworks by identifying critical neurons and re-moving non-critical ones, resulting in a faster inference time. The proposed OAMIP utilizes a Mixed-Integer Program (MIP) for assigning importance scores to each neuron in deep neural network architectures. Our MIP is guided by the impact on the main learning task of the net-work when simultaneously pruning subsets of neurons. In concrete, the optimization of the objective function drives the solver to minimize the number of neurons, to limit the network to critical neurons, i.e., with high importance score, that need to be kept for maintaining the overall accuracy of the trained neural network. Further, the proposed formulation generalizes the recently considered lottery ticket hypothesis by identifying multiple “lucky” subnetworks, resulting in optimized architectures, that not only perform well on a single dataset, but also generalize across multiple ones upon retraining of network weights. Finally, we present a scalable implementation of our method by decoupling the importance scores across layers using auxiliary networks and across di˙erent classes. We demonstrate the ability of OAMIP to prune neural networks with marginal loss in accuracy and generalizability on popular datasets and architectures. / Les réseaux sur-paramétrés, où le nombre de paramètres dépasse le nombre de données, se généralisent bien sur diverses tâches. Cependant, les grands réseaux sont coûteux en termes d’entraînement et de temps d’inférence. De plus, l’hypothèse du billet de loterie indique qu’un sous-réseau d’un réseau initialisé de façon aléatoire peut atteindre une perte marginale après l’entrainement sur une tâche spécifique par rapport au réseau de référence. Par conséquent, il est nécessaire d’optimiser le temps d’inférence et d’entrainement, ce qui est possible pour des architectures neurales plus compactes. Nous introduisons une nouvelle approche “Optimizing ANN Architectures using Mixed-Integer Programming” (OAMIP) pour trouver ces sous-réseaux en identifiant les neurones importants et en supprimant les neurones non importants, ce qui permet d’accélérer le temps d’inférence. L’approche OAMIP proposée fait appel à un programme mixte en nombres entiers (MIP) pour attribuer des scores d’importance à chaque neurone dans les architectures de modèles profonds. Notre MIP est guidé par l’impact sur la principale tâche d’apprentissage du réseau en élaguant simultanément les neurones. En définissant soigneusement la fonction objective du MIP, le solveur aura une tendance à minimiser le nombre de neurones, à limiter le réseau aux neurones critiques, c’est-à-dire avec un score d’importance élevé, qui doivent être conservés pour maintenir la précision globale du réseau neuronal formé. De plus, la formulation proposée généralise l’hypothèse des billets de loterie récemment envisagée en identifiant de multiples sous-réseaux “chanceux”. Cela permet d’obtenir des architectures optimisées qui non seulement fonctionnent bien sur un seul ensemble de données, mais aussi se généralisent sur des di˙érents ensembles de données lors du recyclage des poids des réseaux. Enfin, nous présentons une implémentation évolutive de notre méthode en découplant les scores d’importance entre les couches à l’aide de réseaux auxiliaires et entre les di˙érentes classes. Nous démontrons la capacité de notre formulation à élaguer les réseaux de neurones avec une perte marginale de précision et de généralisabilité sur des ensembles de données et des architectures populaires.