276 research outputs found

    Solving Multiple Timetabling Problems at Danish High Schools

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    Learning-Based Matheuristic Solution Methods for Stochastic Network Design

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    Cette dissertation consiste en trois études, chacune constituant un article de recherche. Dans tous les trois articles, nous considérons le problème de conception de réseaux multiproduits, avec coût fixe, capacité et des demandes stochastiques en tant que programmes stochastiques en deux étapes. Dans un tel contexte, les décisions de conception sont prises dans la première étape avant que la demande réelle ne soit réalisée, tandis que les décisions de flux de la deuxième étape ajustent la solution de la première étape à la réalisation de la demande observée. Nous considérons l’incertitude de la demande comme un nombre fini de scénarios discrets, ce qui est une approche courante dans la littérature. En utilisant l’ensemble de scénarios, le problème mixte en nombre entier (MIP) résultant, appelé formulation étendue (FE), est extrêmement difficile à résoudre, sauf dans des cas triviaux. Cette thèse vise à faire progresser le corpus de connaissances en développant des algorithmes efficaces intégrant des mécanismes d’apprentissage en matheuristique, capables de traiter efficacement des problèmes stochastiques de conception pour des réseaux de grande taille. Le premier article, s’intitulé "A Learning-Based Matheuristc for Stochastic Multicommodity Network Design". Nous introduisons et décrivons formellement un nouveau mécanisme d’apprentissage basé sur l’optimisation pour extraire des informations concernant la structure de la solution du problème stochastique à partir de solutions obtenues avec des combinaisons particulières de scénarios. Nous proposons ensuite une matheuristique "Learn&Optimize", qui utilise les méthodes d’apprentissage pour déduire un ensemble de variables de conception prometteuses, en conjonction avec un solveur MIP de pointe pour résoudre un problème réduit. Le deuxième article, s’intitulé "A Reduced-Cost-Based Restriction and Refinement Matheuristic for Stochastic Network Design". Nous étudions comment concevoir efficacement des mécanismes d’apprentissage basés sur l’information duale afin de guider la détermination des variables dans le contexte de la conception de réseaux stochastiques. Ce travail examine les coûts réduits associés aux variables hors base dans les solutions déterministes pour guider la sélection des variables dans la formulation stochastique. Nous proposons plusieurs stratégies pour extraire des informations sur les coûts réduits afin de fixer un ensemble approprié de variables dans le modèle restreint. Nous proposons ensuite une approche matheuristique utilisant des techniques itératives de réduction des problèmes. Le troisième article, s’intitulé "An Integrated Learning and Progressive Hedging Method to Solve Stochastic Network Design". Ici, notre objectif principal est de concevoir une méthode de résolution capable de gérer un grand nombre de scénarios. Nous nous appuyons sur l’algorithme Progressive Hedging (PHA), ou les scénarios sont regroupés en sous-problèmes. Nous intégrons des methodes d’apprentissage au sein de PHA pour traiter une grand nombre de scénarios. Dans notre approche, les mécanismes d’apprentissage developpés dans le premier article de cette thèse sont adaptés pour résoudre les sous-problèmes multi-scénarios. Nous introduisons une nouvelle solution de référence à chaque étape d’agrégation de notre ILPH en exploitant les informations collectées à partir des sous problèmes et nous utilisons ces informations pour mettre à jour les pénalités dans PHA. Par conséquent, PHA est guidé par les informations locales fournies par la procédure d’apprentissage, résultant en une approche intégrée capable de traiter des instances complexes et de grande taille. Dans les trois articles, nous montrons, au moyen de campagnes expérimentales approfondies, l’intérêt des approches proposées en termes de temps de calcul et de qualité des solutions produites, en particulier pour traiter des cas très difficiles avec un grand nombre de scénarios.This dissertation consists of three studies, each of which constitutes a self-contained research article. In all of the three articles, we consider the multi-commodity capacitated fixed-charge network design problem with uncertain demands as a two-stage stochastic program. In such setting, design decisions are made in the first stage before the actual demand is realized, while second-stage flow-routing decisions adjust the first-stage solution to the observed demand realization. We consider the demand uncertainty as a finite number of discrete scenarios, which is a common approach in the literature. By using the scenario set, the resulting large-scale mixed integer program (MIP) problem, referred to as the extensive form (EF), is extremely hard to solve exactly in all but trivial cases. This dissertation is aimed at advancing the body of knowledge by developing efficient algorithms incorporating learning mechanisms in matheuristics, which are able to handle large scale instances of stochastic network design problems efficiently. In the first article, we propose a novel Learning-Based Matheuristic for Stochastic Network Design Problems. We introduce and formally describe a new optimizationbased learning mechanism to extract information regarding the solution structure of a stochastic problem out of the solutions of particular combinations of scenarios. We subsequently propose the Learn&Optimize matheuristic, which makes use of the learning methods in inferring a set of promising design variables, in conjunction with a state-ofthe- art MIP solver to address a reduced problem. In the second article, we introduce a Reduced-Cost-Based Restriction and Refinement Matheuristic. We study on how to efficiently design learning mechanisms based on dual information as a means of guiding variable fixing in the context of stochastic network design. The present work investigates how the reduced cost associated with non-basic variables in deterministic solutions can be leveraged to guide variable selection within stochastic formulations. We specifically propose several strategies to extract reduced cost information so as to effectively identify an appropriate set of fixed variables within a restricted model. We then propose a matheuristic approach using problem reduction techniques iteratively (i.e., defining and exploring restricted region of global solutions, as guided by applicable dual information). Finally, in the third article, our main goal is to design a solution method that is able to manage a large number of scenarios. We rely on the progressive hedging algorithm (PHA) where the scenarios are grouped in subproblems. We propose a two phase integrated learning and progressive hedging (ILPH) approach to deal with a large number of scenarios. Within our proposed approach, the learning mechanisms from the first study of this dissertation have been adapted as an efficient heuristic method to address the multi-scenario subproblems within each iteration of PHA.We introduce a new reference point within each aggregation step of our proposed ILPH by exploiting the information garnered from subproblems, and using this information to update the penalties. Consequently, the ILPH is governed and guided by the local information provided by the learning procedure, resulting in an integrated approach capable of handling very large and complex instances. In all of the three mentioned articles, we show, by means of extensive experimental campaigns, the interest of the proposed approaches in terms of computation time and solution quality, especially in dealing with very difficult instances with a large number of scenarios

    Integrated machine learning and optimization approaches

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    This dissertation focuses on the integration of machine learning and optimization. Specifically, novel machine learning-based frameworks are proposed to help solve a broad range of well-known operations research problems to reduce the solution times. The first study presents a bidirectional Long Short-Term Memory framework to learn optimal solutions to sequential decision-making problems. Computational results show that the framework significantly reduces the solution time of benchmark capacitated lot-sizing problems without much loss in feasibility and optimality. Also, models trained using shorter planning horizons can successfully predict the optimal solution of the instances with longer planning horizons. For the hardest data set, the predictions at the 25% level reduce the solution time of 70 CPU hours to less than 2 CPU minutes with an optimality gap of 0.8% and without infeasibility. In the second study, an extendable prediction-optimization framework is presented for multi-stage decision-making problems to address the key issues of sequential dependence, infeasibility, and generalization. Specifically, an attention-based encoder-decoder neural network architecture is integrated with an infeasibility-elimination and generalization framework to learn high-quality feasible solutions. The proposed framework is demonstrated to tackle the two well-known dynamic NP-Hard optimization problems: multi-item capacitated lot-sizing and multi-dimensional knapsack. The results show that models trained on shorter and smaller-dimension instances can be successfully used to predict longer and larger-dimension problems with the presented item-wise expansion algorithm. The solution time can be reduced by three orders of magnitude with an average optimality gap below 0.1%. The proposed framework can be advantageous for solving dynamic mixed-integer programming problems that need to be solved instantly and repetitively. In the third study, a deep reinforcement learning-based framework is presented for solving scenario-based two-stage stochastic programming problems, which are computationally challenging to solve. A general two-stage deep reinforcement learning framework is proposed where two learning agents sequentially learn to solve each stage of a general two-stage stochastic multi-dimensional knapsack problem. The results show that solution time can be reduced significantly with a relatively small gap. Additionally, decision-making agents can be trained with a few scenarios and solve problems with a large number of scenarios. In the fourth study, a learning-based prediction-optimization framework is proposed for solving scenario-based multi-stage stochastic programs. The issue of non-anticipativity is addressed with a novel neural network architecture that is based on a neural machine translation system. Furthermore, training the models on deterministic problems is suggested instead of solving hard and time-consuming stochastic programs. In this framework, the level of variables used for the solution is iteratively reduced to eliminate infeasibility, and a heuristic based on a linear relaxation is performed to reduce the solution time. An improved item-wise expansion strategy is introduced to generalize the algorithm to tackle instances with different sizes. The results are presented in solving stochastic multi-item capacitated lot-sizing and stochastic multi-stage multi-dimensional knapsack problems. The results show that the solution time can be reduced by a factor of 599 with an optimality gap of only 0.08%. Moreover, results demonstrate that the models can be used to predict similarly structured stochastic programming problems with a varying number of periods, items, and scenarios. The frameworks presented in this dissertation can be utilized to achieve high-quality and fast solutions to repeatedly-solved problems in various industrial and business settings, such as production and inventory management, capacity planning, scheduling, airline logistics, dynamic pricing, and emergency management

    Timetabling at High Schools

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    An Expandable Machine Learning-Optimization Framework to Sequential Decision-Making

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    We present an integrated prediction-optimization (PredOpt) framework to efficiently solve sequential decision-making problems by predicting the values of binary decision variables in an optimal solution. We address the key issues of sequential dependence, infeasibility, and generalization in machine learning (ML) to make predictions for optimal solutions to combinatorial problems. The sequential nature of the combinatorial optimization problems considered is captured with recurrent neural networks and a sliding-attention window. We integrate an attention-based encoder-decoder neural network architecture with an infeasibility-elimination and generalization framework to learn high-quality feasible solutions to time-dependent optimization problems. In this framework, the required level of predictions is optimized to eliminate the infeasibility of the ML predictions. These predictions are then fixed in mixed-integer programming (MIP) problems to solve them quickly with the aid of a commercial solver. We demonstrate our approach to tackling the two well-known dynamic NP-Hard optimization problems: multi-item capacitated lot-sizing (MCLSP) and multi-dimensional knapsack (MSMK). Our results show that models trained on shorter and smaller-dimensional instances can be successfully used to predict longer and larger-dimensional problems. The solution time can be reduced by three orders of magnitude with an average optimality gap below 0.1%. We compare PredOpt with various specially designed heuristics and show that our framework outperforms them. PredOpt can be advantageous for solving dynamic MIP problems that need to be solved instantly and repetitively

    Operational Research IO2017, Valença, Portugal, June 28-30

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    This proceedings book presents selected contributions from the XVIII Congress of APDIO (the Portuguese Association of Operational Research) held in Valença on June 28–30, 2017. Prepared by leading Portuguese and international researchers in the field of operations research, it covers a wide range of complex real-world applications of operations research methods using recent theoretical techniques, in order to narrow the gap between academic research and practical applications. Of particular interest are the applications of, nonlinear and mixed-integer programming, data envelopment analysis, clustering techniques, hybrid heuristics, supply chain management, and lot sizing and job scheduling problems. In most chapters, the problems, methods and methodologies described are complemented by supporting figures, tables and algorithms. The XVIII Congress of APDIO marked the 18th installment of the regular biannual meetings of APDIO – the Portuguese Association of Operational Research. The meetings bring together researchers, scholars and practitioners, as well as MSc and PhD students, working in the field of operations research to present and discuss their latest works. The main theme of the latest meeting was Operational Research Pro Bono. Given the breadth of topics covered, the book offers a valuable resource for all researchers, students and practitioners interested in the latest trends in this field.info:eu-repo/semantics/publishedVersio
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