L'optimisation des tournées de livraison est souvent modélisée par un problème de voyageur de commerce (Traveling Salesman Problem / TSP). Pour ce problème, il est fréquent d’avoir des contraintes additionnelles telles que, par exemple, des fenêtres horaires limitant les heures de livraison chez le client ou des pauses obligatoires pour les conducteurs des camions. Le temps est une dimension importante à prendre en compte pour respecter ces contraintes. Cependant, les durées des trajets ne sont généralement pas constantes mais varient en fonction des congestions, et cette variabilité doit être intégrée au moment de l’optimisation des tournées. Ainsi, le problème du voyageur de commerce dépendant du temps (Time Dependent TSP / TD-TSP) est la version étendue du TSP où le coût d'un arc dépend de l'heure à laquelle cet arc est emprunté. Dans cet thèse nous proposons un nouveau benchmark pour le TD-TSP basé sur des données réelles de trafic (fournies par la Métropole de Lyon) et nous montrons l'intérêt de prendre en compte la variabilité des durées dans ce problème. Nous étudions comment mieux modéliser les fonctions de durée de trajet dépendantes du temps. Nous introduisons et comparons différents modèles pour résoudre le TD-TSP avec la programmation par contraintes (Constraint Programming / CP). Un premier modèle est directement dérivé du modèle CP classique pour le TSP. Nous montrons que ce modèle ne permet pas de raisonner avec des relations de précédence indirectes, ce qui pénalise sa performance sur notre benchmark. Nous introduisons une nouvelle contrainte globale qui est capable d'exploiter des relations de précédence indirectes sur des données dépendantes du temps et nous introduisons un nouveau modèle CP basé sur notre nouvelle contrainte. Nous comparons expérimentalement les deux modèles sur notre benchmark, et nous montrons que notre nouvelle contrainte permet de résoudre le TD-TSP plus efficacement. / In the context of urban deliveries, the optimization of delivery tours is usually modeled as a Traveling Salesman Problem (TSP). Side constraints like time-windows constraining the delivery times at the client or breaks for the drivers are also common in this kind of problem and time is an important dimension to take into account to respect these constraints. With travel times' variability in big cities time also tends to have a greater influence in costs and therefore it should be included in the optimization of delivery routes. The Time-Dependent Traveling Salesman Problem (TDTSP) is the extended version of the Traveling Salesman Problem (TSP) where arc costs depend on the time when the arc is traveled. In this thesis we propose a set of benchmarks for the TDTSP based on real traffic data (obtained from the city of Lyon) and show the interest of handling time dependency in the problem. A study of how to better model time-dependent travel functions in general and specifically for our approach is performed. We introduce and compare different models to solve the TDTSP with Constraint Programming (CP). A first model is derived in a straightforward way from the classical CP model for the TSP. We show that this model is not able to reason on indirect precedence relations, so that it has poor performance on our benchmark. We introduce a new global constraint which is able to exploit indirect precedence relations on time-dependent data, and we introduce a second model which is based on our new constraint. We experimentally compare the two models on our benchmark.

O objetivo dessa dissertação é apresentar um problema de otimização do uso de recursos críticos no desenvolvimento de poços de petróleo marítimos e a técnica empregada para a abordagem proposta ao problema. A revisão da técnica de Programação por Restrições é feita analisando aspectos relevantes de modelagem, propagação, busca e paradigmas de programação. A especialização da técnica para problemas de escalonamento, o Escalonamento Baseado em Restrições, é descrita com ênfase nos paradigmas descritivos e nos mecanismos de propagação de restrições. Como subsídio ao uso da técnica em outros problemas, a linguagem comercial de modelagem OPL é apresentada no Apêndice. O objetivo da abordagem ao problema é obter um escalonador para maximizar a produção de óleo obtida no curto prazo. O escalonador proposto baseia-se na declaração de um modelo empregando variáveis de intervalo. Um algoritmo e um modelo de Programação Linear Inteira abordando relaxações do problema são apresentados para que se obtenha um limitante superior ao valor de produção ótimo. Para o cenário real no qual a análise experimental foi feita, foram obtidas soluções a menos de 16% do ótimo após uma hora de execução; e os testes em instâncias de tamanhos variados evidenciaram a robustez do escalonador. Direções para trabalhos futuros são apresentadas ponderando os resultados obtidos. / The aim of this work is to present a problem of optimizing the use of critical resources to develop offshore oil wells and the technique used to approach the problem. The review of the Constraint Programming technique is made by analyzing relevant aspects of modeling, propagation, search and programming paradigms. The specialization of the technique to scheduling problems, known as Constraint-Based Scheduling, is described with emphasis on descriptive paradigms and constraint propagation mechanisms. In order to support the use of the technique to tackle other problems, the commercial modeling language OPL is presented in the appendix. The aim of the approach to the problem is to obtain a scheduler that maximizes the short-term production of oil. The scheduler presented relies on the description of a model using interval variables. An algorithm and an Integer Linear Programming model approaching relaxations of the problem are presented in order to obtain an upper bound for the optimal production value. For the real scenario upon which the experimental analysis was done, there were found solutions within 16% of the optimal after one hour of execution; and the tests on instances of varied sizes gave evidence of the robustness of the scheduler. Directions for future work are presented based on the results achieved.

Cette thèse traite de l'adaptation du niveau de cohérence locale au cours de la résolution d'un problème de satisfaction de contraintes (CSP). En particulier, nous nous intéressons à l'utilisation des propriétés de cohérence locale plus fortes que la cohérence d'arc (AC) pour gagner en efficacité de résolution d'un CSP. Les cohérences plus fortes que AC sont généralement coûteuses à maintenir dans un réseau de contraintes. Par conséquent, elles sont rarement utilisées en pratique. Cette thèse apporte plusieurs contributions qui permettent de bénéficier de la puissance de filtrage de ces cohérences fortes tout en évitant le coût élevé de les maintenir dans tout le réseau de contraintes. Premièrement, nous introduisons la cohérence locale paramétrée (p-LC), une approche originale qui permet de définir des niveaux de cohérence intermédiaires entre AC et une de cohérence locale LC, plus forte que AC. Puis, nous présentons l'instanciation de cette approche à maxRPC et SAC, deux cohérences plus fortes que AC. Il en découle deux cohérences paramétrées, à savoir p-maxRPC et p-SAC. Ensuite, nous présentons l'algorithme p-maxRPC3, qui réalise p-maxRPC et l'algorithme p-SAC1, pour réaliser p-SAC dans un réseau de contraintes. Deuxièmement, nous montrons expérimentalement que maintenir un niveau de cohérence intermédiaire p-LC, peut donner un bon compromis entre puissance de filtrage et coût de calcul nécessaire pour maintenir ce niveau de cohérence. En outre, nous montrons que pour chaque instance de CSP il est possible de trouver un paramètre adéquat qui donne ce bon compromis. L'approche de cohérence paramétrée ne précise pas comment le paramètre peut être choisi a priori. Nous proposons donc deux techniques qui permettent d'ajuster automatiquement le niveau de cohérence paramétrée p-LC. Ces deux techniques utilisent plusieurs paramètres à la fois. Chaque paramètre est associé à une partie du problème et s'adapte automatiquement et localement au cours de la résolution. Finalement, nous proposons POAC1, le premier algorithme pour établir partition-one-AC (POAC) dans un réseau de contraintes. Puis, en comparant POAC à SAC nous constatons que POAC converge au point fixe plus rapidement que SAC. Sur la base de ce constat, nous proposons APOAC, une version adaptative de POAC qui contrôle le nombre de variables sur lesquelles POAC est appliqué. / This thesis deals with adapting the level of consistency during solving a constraint satisfaction problem (CSP). It focuses on the use of local consistency properties stronger than arc consistency (AC) to improve the CSP solving efficiency. Local consistency properties stronger than arc consistency are generally expensive to maintain in a constraint network. Therefore, these local consistencies are seldom used in practice. This thesis gives several contributions to benefit from the filtering power of local consistencies stronger than AC while avoiding the high cost of maintaining them in the whole constraint network and throughout the search. First, we introduce the parameterized local consistency (p-LC), an original approach that allows us to define intermediate levels of consistency between AC and a local consistency LC stronger than AC. Then, we present the instantiation of the parameterized local consistency approach to maxRPC and SAC, two consistencies stronger than AC. This leads to two parameterized consistencies, namely p-maxRPC and p-SAC. After giving the definitions of p-maxRPC and p-SAC, we present the algorithm p-maxRPC3, that achieves p-maxRPC and the algorithm p-SAC1, for achieving p-SAC in a constraint network. We show experimentally that maintaining an intermediate level of consistency p-LC, can give a good compromise between filtering power and the computational cost of maintaining this level of consistency. We also show that for each instance of CSP we can find a parameter that gives this good compromise. The parameterized local consistency approach does not specify how the parameter can be chosen a priori. Hence, we propose two techniques to automatically adjust the parameter p. In fact, both techniques don't use a single parameter, but several parameters. Each parameter is mapped to a part of the problem and it is automatically and locally adjusted during search. Finally, we propose POAC1, the first algorithm achieving partition-one-AC (POAC) in a constraint network. We compare POAC to SAC and we found that POAC converges faster than SAC to the fixed point due to its ability to prune values from all variable domains when being enforced on a given variable. Based on this observation, we proposed APOAC, an adaptive version of POAC, that monitors the number of variables on which to enforce POAC.

A área do petróleo é uma das que mais podem se beneficiar da melhoria de eficiência da gestão da cadeia de suprimentos. Entretanto, o comportamento dinâmico de tais cadeias é muito complexo para ser modelado de forma analítica. Por outro lado, estas cadeias mostram várias características intrínsecas em comum com sistemas multiagentes, que oferecem a flexibilidade necessária para modelar as complexidades e a dinâmica das cadeias de suprimentos reais sem a necessidade de premissas muito simplificadoras. Como o problema de gerenciamento da cadeia de suprimentos apresenta uma estrutura recursiva, torna-se ainda mais conveniente usar um modelo baseado em agentes holônicos, que mostram uma estrutura do tipo fractal. Além disso, o tipo de relacionamento entre as entidades da cadeia e a necessidade de uma otimização global sugerem modelar suas interações na forma de restrições. Por esta razão, esta tese propõe um modelo distribuído de otimização através da definição de um novo problema denominado Problema de Satisfação de Restrições Holônico com Otimização (HCOP), que é baseado nos conceitos do Problema de Satisfação de Restrições Distribuído com Otimização (DCOP) e agentes holônicos. Além disso, foi desenvolvido um meta-algoritmo baseado no algoritmo DTREE para solucionar este tipo de problema, onde vários algoritmos disponíveis de otimização centralizados podem ser embutidos e integrados de tal forma a obter a configuração mais adequada para cada caso. Assim, uma típica cadeia de suprimentos da indústria do petróleo foi modelada como um HCOP, e foi desenvolvido um protótipo que implementa o meta-algoritmo proposto em um ambiente que integra sistemas de otimização de produção e logística, que são representativos em relação a situações reais. Finalmente foram realizados experimentos sobre um estudo de caso da empresa PETROBRAS, que permitiram a verificação da viabilidade deste modelo e a comprovação de suas vantagens em relação às abordagens convencionais. / The oil area is one of those that may most benefit from the improved efficiency of supply chain management. However, the dynamic behavior of such chains is too complex to be modeled analytically. Moreover, these chains show several intrinsic characteristics in common with multiagent systems, which offer the required flexibility to model the complexities and dynamics of real supply chains without rather simplifying assumptions. As the problem of managing the supply chain has a recursive structure, it becomes more convenient to use a model based on holonic agents, which show a fractal-type structure. Furthermore, the type of relationship between entities in the chain and the need for global optimization suggest to model their interactions in the form of constraints. For this reason, this thesis proposes an optimization distributed model by defining a new problem called Holonic Constraint Optimization Problem (HCOP), which is based on concepts from Distributed Constraint Satisfaction Optimization Problem (DCOP) and holonic agents. In addition we developed a meta-algorithm based on DTREE algorithm for solving this type of problem, where several algorithms available for centralized optimization algorithms can be embedded and integrated so as to obtain the most suitable configuration for each case. Thus, a typical supply chain of the petroleum industry was modeled as a HCOP, and we developed a prototype that implements the meta-algorithm in an environment that integrates the optimization systems for production and logistics, which are representative in relation to actual situations. Finally experiments were performed on a case study of the company PETROBRAS, which allowed the verification of the feasibility of this model and the proof of their advantages over conventional approaches.

Optimization of time and cost in construction projects has been subject to extensive research since the development of the Critical Path Method (CPM). Many researchers have investigated various versions of the well-known Time-Cost Trade-off (TCT) problem including linear, convex, concave, and also the discrete (DTCT) version. Traditional methods in the literature for optimizing time and cost of construction projects range from mathematical methods to evolutionary-based ones, such as genetic algorithms, particle swarm, ant-colony, and leap frog optimization. However, none of the existing research studies has dealt with the optimization of large-scale projects in which any small saving would be significant. Traditional approaches have all been applied to projects of less than 100 activities which are far less than what exists in real-world construction projects. The objective of this study is to utilize recent developments in computation technology and novel optimization techniques such as Constraint Programming (CP) to improve the current limitations in solving large-scale DTCT problems. Throughout the first part of this research, an Excel-based TCT model has been developed to investigate the performance of traditional optimization methods, such as mathematical programming and genetic algorithms, for solving large TCT problems. The result of several experimentations confirms the inefficiency of traditional methods for optimizing large TCT problems. Subsequently, a TCT model has been developed using Optimization Programming Language (OPL) to implement the Constraint Programming (CP) technique. CP Optimizer of IBM ILOG Optimization Studio has been used to solve the model and to successfully optimize several projects ranging from a small project of 18 activities to very large projects consisting of more than 10,000 activities. Constraint programming proved to be very efficient in solving large-scale TCT problems, generating substantially better results in terms of solution quality and processing speed. While traditional optimization methods have been used to optimize projects consisting of less than one hundred activities, constraint programming demonstrated its capability of solving TCT problems comprising of thousands of activities. As such, the developed model represents a significant improvement in optimization of time and cost of large-scale construction projects and can greatly enhance the level of planning and control in such projects.

We define an order cutoff for a retailer as a time in the day such that orders sent to the depot before this point will be delivered by tomorrow, and orders submitted after will be delivered by the day after tomorrow. The later a retailer’s cutoff, the sooner it receives its orders which helps it to maintain ideal inventory levels. Generally, not all retailers in a supply chain can have the latest cutoff since transportation takes a significant amount of time. This thesis tries to assign optimal order cutoffs to retailers. We call this an order cutoff assignment problem and we solve it using three different mathematical programming approaches. The approaches are exhaustive route generation and selection, a series of mixed integer programs, and branch-and-price. 60 sample problems were solved and results showed that branch-and-price is often the most effective method.

We define an order cutoff for a retailer as a time in the day such that orders sent to the depot before this point will be delivered by tomorrow, and orders submitted after will be delivered by the day after tomorrow. The later a retailer’s cutoff, the sooner it receives its orders which helps it to maintain ideal inventory levels. Generally, not all retailers in a supply chain can have the latest cutoff since transportation takes a significant amount of time. This thesis tries to assign optimal order cutoffs to retailers. We call this an order cutoff assignment problem and we solve it using three different mathematical programming approaches. The approaches are exhaustive route generation and selection, a series of mixed integer programs, and branch-and-price. 60 sample problems were solved and results showed that branch-and-price is often the most effective method.

We study in this thesis three well known global constraints. The All-Different constraint restricts a set of variables to be assigned to distinct values. The <em>global cardinality constraint</em> (GCC) ensures that a value <em>v</em> is assigned to at least <em>l_v</em> variables and to at most <em>u_v</em> variables among a set of given variables where <em>l_v</em> and <em>u_v</em> are non-negative integers such that <em>l_v</em> &le; <em>u_v</em>. The Inter-Distance constraint ensures that all variables, among a set of variables <em>x</em>₁, . . . , <em>x_n</em>, are pairwise distant from <em>p</em>, i. e. |<em>x_i</em> - <em>x_j</em>| &ge; <em>p</em> for all <em>i</em> &ne; <em>j</em>. The All-Different constraint, the GCC, and the Inter-Distance constraint are largely used in scheduling problems. For instance, in scheduling problems where tasks with unit processing time compete for a single resource, we have an All-Different constraint on the starting time variables. When there are <em>k</em> resources, we have a GCC with <em>l_v</em> = 0 and <em>u_v</em> = <em>k</em> over all starting time variables. Finally, if tasks have processing time <em>t</em> and compete for a single resource, we have an Inter-Distance constraint with <em>p</em> = <em>t</em> over all starting time variables. We present new propagators for the All-Different constraint, the GCC, and the Inter-Distance constraint i. e. , new filtering algorithms that reduce the search space according to these constraints. For a given consistency, our propagators outperform previous propagators both in practice and in theory. The gains in performance are achieved through judicious use of advanced data structures combined with novel results on the structural properties of the constraints.

We study in this thesis three well known global constraints. The All-Different constraint restricts a set of variables to be assigned to distinct values. The <em>global cardinality constraint</em> (GCC) ensures that a value <em>v</em> is assigned to at least <em>l_v</em> variables and to at most <em>u_v</em> variables among a set of given variables where <em>l_v</em> and <em>u_v</em> are non-negative integers such that <em>l_v</em> &le; <em>u_v</em>. The Inter-Distance constraint ensures that all variables, among a set of variables <em>x</em>₁, . . . , <em>x_n</em>, are pairwise distant from <em>p</em>, i. e. |<em>x_i</em> - <em>x_j</em>| &ge; <em>p</em> for all <em>i</em> &ne; <em>j</em>. The All-Different constraint, the GCC, and the Inter-Distance constraint are largely used in scheduling problems. For instance, in scheduling problems where tasks with unit processing time compete for a single resource, we have an All-Different constraint on the starting time variables. When there are <em>k</em> resources, we have a GCC with <em>l_v</em> = 0 and <em>u_v</em> = <em>k</em> over all starting time variables. Finally, if tasks have processing time <em>t</em> and compete for a single resource, we have an Inter-Distance constraint with <em>p</em> = <em>t</em> over all starting time variables. We present new propagators for the All-Different constraint, the GCC, and the Inter-Distance constraint i. e. , new filtering algorithms that reduce the search space according to these constraints. For a given consistency, our propagators outperform previous propagators both in practice and in theory. The gains in performance are achieved through judicious use of advanced data structures combined with novel results on the structural properties of the constraints.

Diese Arbeit befasst sich mit der Entwicklung einer Applikation, welche Infrastrukturdaten über Eisenbahnnetze generiert. Dabei bildet die Erzeugung der topologischen Informationen den Schwerpunkt dieser Arbeit. Der Anwender charakterisiert hierfür vorab das gewünschte Eisenbahnnetz, wobei die geforderten Eigenschaften die Randbedingungen darstellen, die bei der Synthese zu beachten sind. Zur Einhaltung dieser Bedingungen wird die Constraint-Programmierung eingesetzt, welche durch ihr spezielles Programmierparadigma konsistente Lösungen effizient erzeugt. Dies wird u.a. durch die Nachnutzung so genannter globaler Constraints erreicht. Aus diesem Grund wird insbesondere auf den Einsatz der Constraint-Programmierung bei der Modellierung und Implementierung der Applikation eingegangen. / This work deals with the development of an application, which generates infrastructure data of railway networks. The focus of this work concentrates on the generation process of topological information. As input for the application a characterization of the intended railway network is given as attributes, which are handled as constraints in the generation process. To satisfy these restrictions constraint programming, a special programming paradigm, which is able to search efficently consistent solutions, is applied. In particular, the use of so-called global constraints improves the computation. For that reason the role of constraint-programming in modelling and implementing these application is discussed in more detail.