La norme 3G/UMTS a permis de développer les premières applications multimédia pour téléphones et tablettes mobiles. Le nouveau standard 4G/LTE (Long Term Evolution) a pour objectif le très haut débit mobile. Dans ce standard, beaucoup d’efforts ont portés sur la reconfiguration automatique des réseaux en fonction de la demande des clients dans un processus appelé Self-Organizing Network (SON). Le travail de cette thèse s’inscrit dans cette direction. La reconfiguration de réseaux est comprise principalement dans le sens des modèles, des méthodes et des outils pour analyser les indicateurs remontés du réseau et configurer automatiquement les paramètres. Nous avons essentiellement travaillé sur les paramètres des aériens, l’allocation des fréquences, des puissances d’émission et des inclinaisons verticales.Dans cette optique, étant donné la forte variabilité des données d’entrée de l’optimisation issues des remontées de réseau, cette thèse porte sur les modèles et algorithmes d’optimisation robuste dans le contexte de l’optimisation sous contraintes. L’optimisation robuste fait référence à un ensemble de procédés pour proposer des solutions à des problèmes combinatoires dans un contexte de données incertaines et de scénarios variables dans le temps. Une première partie est dédiée à l’état de l’art et présente les principes des Self-Organizing Network (SON). La deuxième partie est consacrée à l’état de l’art des méthodes en optimisation robuste. En troisième partie nous présentons la modélisation mathématique du problème d’optimisation pour lequel les données de trafic (répartitions des clients sur la zone de service et leurs demandes respectives) prennent des valeurs variables dans le temps. Une phase de diagnostic sur le fonctionnement du réseau à partir des données, et une étude de sensibilité des solutions vis-à-vis des variations dans la réalisation des données ont été faites en quatrième partie avec des algorithmes de recherche locale. La cinquième partie présente le travail de conception, développement et test sur scénarios, d’une Recherche Tabou ainsi qu’une analyse approfondie sur les méthodes de pilotage envisagées pour les SON en 4G. / The standard 3G/UMTS has launched the first multimedia applications for mobile phones and tablets. The new standard 4G/LTE (Long Term Evolution) has mobile broadband objective. In this standard a huge effort has been done on automatic network reconfiguration based on customer demand variation in a process called Self-Organizing Network (SON). The work of this thesis lies in this direction. Reconfiguration of networks lies mainly in the direction of models, methods and tools to analyze network Key Performance Indicators and automatically configure its settings. We mainly worked on the air interface parameters such that frequency assignment, emitted power and pattern vertical inclination.In this context, given the high variability of optimization input data issued from the network, this thesis focuses on robust optimization under constraints. The robust optimization refers to a set of processes to provide solutions to combinatorial problems with uncertain and variable scenarios of data over time. The first Section presents the principles of Self-Organizing Network (SON). The second Section concerns the state of the art on robust optimization. The third Section defines the mathematical model to optimize for which traffic data (distribution of customers and throughput requirements on the service area) take variable values over time. A data diagnostic phase on the network operation and a sensitivity analysis of the solutions were made in the fourth Section with several local search algorithms. The fifth Section presents the work of design, development and test of a Tabu Search method and a thorough analysis of SON control methodology proposed for 4G.

Combinatorial optimisation problems (COPs) pervade human society: scheduling, design, layout, distribution, timetabling, resource allocation and project management all feature problems where the solution is some combination of elements, the overall value of which needs to be either maximised or minimised (i.e., optimised), typically subject to a number of constraints. Thus, techniques to efficiently solve such problems are an important area of research. A popular group of optimisation algorithms are the metaheuristics, approaches that specify how to search the space of solutions in a problem independent way so that high quality solutions are likely to result in a reasonable amount of computational time. Although metaheuristic algorithms are specified in a problem independent manner, they must be tailored to suit each particular problem to which they are applied. This thesis investigates a number of aspects of the application of the relatively new Ant Colony Optimisation (ACO) metaheuristic to different COPs.The standard ACO metaheuristic is a constructive algorithm loosely based on the foraging behaviour of ant colonies, which are able to find the shortest path to a food source by indirect communication through pheromones. ACO’s artificial pheromone represents a model of the solution components that its artificial ants use to construct solutions. Developing an appropriate pheromone representation is a key aspect of the application of ACO to a problem. An examination of existing ACO applications and the constructive approach more generally reveals how the metaheuristic can be applied more systematically across a range of COPs. The two main issues addressed in this thesis are biases inherent in the constructive process and the systematic selection of pheromone representations.The systematisation of ACO should lead to more consistently high performance of the algorithm across different problems. Additionally, it supports the creation of a generalised ACO system, capable of adapting itself to suit many different combinatorial problems without the need for manual intervention.

There are many real world assignment, scheduling and planning tasks which can be classified as combinatorial optimisation problems (COPs). These are usually formulated as a mathematical problem of minimising or maximising some cost function subject to a number of constraints. Usually, such problems are NP hard, and thus, whilst it is possible to find exact solutions to specific problems, in general only approximate solutions can be found. There are many algorithms that have been proposed for finding approximate solutions to COPs, ranging from special purpose heuristics to general search meta-heuristics such as simulated annealing and tabu search. General meta-heuristic algorithms like simulated annealing have been applied to a wide range of problems. In most cases, the designer must choose an appropriate data structure and a set of local operators that define a search neighbourhood. The variability in representation techniques, and suitable neighbourhood transition operators, has meant that it is usually necessary to develop new code for each problem. Toolkits like the one developed by Ingber's Adaptive Simulated Annealing (Ingber 1993, 1996) have been applied to assist rapid prototyping of simulated annealing codes, however, these still require the development of new programs for each type of problem. There have been very few attempts to develop a general meta-heuristic solver, with the notable exception being Connolly's General Purpose Simulated Annealing (Connolly 1992). In this research, a general meta-heuristic based system is presented that is suitable for a wide range of COPs. The main goal of this work is to build an environment in which it is possible to specify a range of COPs using an algebraic formulation, and to produce a tailored solver automatically. This removes the need for the development of specific software, allowing very rapid prototyping. Similar techniques have been available for linear programming based solvers for some years in the form of the GAMS (General Algebraic Modelling System) (Brooke, Kendrick, Meeraus and Raman 1997) and AMPL (Fourer, Gay and Kernighan 1993) interfaces. The new system is based on a novel linked list data structure rather than the more conventional vector notation due to the natural mapping between COPS and lists. In addition, the modelling system is found to be very suitable for processing by meta-heuristic search algorithms as it allows the direct application of common local search operators. A general solver is built that is based on the linked list modelling system. This system is capable of using meta-heuristic search engines such as greedy search, tabu search and simulated annealing. A number of implementation issues such as generating initial solutions, choosing and invoking appropriate local search transition operators and producing suitable incremental cost expressions, are considered. As such, the system can been seen as a good test-bench for model prototypers and those who wish to test various meta-heuristic implementations in a standard way. However, it is not meant as a replacement or substitute for efficient special purpose search algorithms. The solver shows good performance on a wide range of problems, frequently reaching the optimal and best-known solutions. Where this is not the case, solutions within a few percent deviation are produced. Performance is dependent on the chosen transition operators and the frequency with which each is applied. To a lesser extent, the performance of this implementation is influenced by runtime parameters of the meta-heuristic search engine.

Combinatorial optimisation problems (COPs) pervade human society: scheduling, design, layout, distribution, timetabling, resource allocation and project management all feature problems where the solution is some combination of elements, the overall value of which needs to be either maximised or minimised (i.e., optimised), typically subject to a number of constraints. Thus, techniques to efficiently solve such problems are an important area of research. A popular group of optimisation algorithms are the metaheuristics, approaches that specify how to search the space of solutions in a problem independent way so that high quality solutions are likely to result in a reasonable amount of computational time. Although metaheuristic algorithms are specified in a problem independent manner, they must be tailored to suit each particular problem to which they are applied. This thesis investigates a number of aspects of the application of the relatively new Ant Colony Optimisation (ACO) metaheuristic to different COPs.The standard ACO metaheuristic is a constructive algorithm loosely based on the foraging behaviour of ant colonies, which are able to find the shortest path to a food source by indirect communication through pheromones. ACO’s artificial pheromone represents a model of the solution components that its artificial ants use to construct solutions. Developing an appropriate pheromone representation is a key aspect of the application of ACO to a problem. An examination of existing ACO applications and the constructive approach more generally reveals how the metaheuristic can be applied more systematically across a range of COPs. The two main issues addressed in this thesis are biases inherent in the constructive process and the systematic selection of pheromone representations.The systematisation of ACO should lead to more consistently high performance of the algorithm across different problems. Additionally, it supports the creation of a generalised ACO system, capable of adapting itself to suit many different combinatorial problems without the need for manual intervention.

La gestion de chaîne d’approvisionnement est un élément essentiel à la performance des entreprises et fait l’objet d’une attention particulière depuis plusieurs décennies. Dans le domaine des télécommunications, cette gestion inclût généralement des activités de réparation et prend alors place sur une chaîne d’approvisionnement en boucle fermée. Dans ce contexte, la gestion de la chaîne d’approvisionnement vise à la planification optimale des mouvements de pièces saines et défaillantes basée sur une prévision des défaillances futures et fait face à différents objectifs conflictuels (rupture de stock, stockage, réparation,transfert). Le travail présenté dans cette thèse s’intéresse à ce problème d’optimisation et s’appuie sur un cas réel. Spécifiquement nous proposons un système d’aide à la planification tactique. Ce système est centré sur une modélisation générique du problème d’optimisation applicable à une grande variété de chaînes d’approvisionnement. Nous présentons particulièrement une approche exacte et une méta-heuristique pour résoudre ce problème et évaluons ces approches sur une variété d’instances de différentes tailles avec plusieurs niveaux et distributions du stock initial dans la chaîne d’approvisionnement. Nous étudions également la possibilité de mener des politiques de gestion particulières (e.g., juste-à-temps, réparations minimales) en pondérant les différents objectifs étudiés. Nous nous intéressons également à l’application de plans successifs produits par le système et, particulièrement, nous étudions la capacité du système à faire face aux incertitudes pouvant apparaître dans les prévisions. / Supply chains are ubiquitous across industries and a considerable effort has been invested in supply chain management techniques over the last decades. In Telecommunications service industries, it often involves repair operations and consequently takes place in a closed-loop supply chain. In this context, supply chain management is concerned with optimally planning movements of faulty parts and spare parts based on a demand forecast and in the face of conflicting objectifs (stock out, storage, repair, transfer). This thesis describes this optimisation problem and based on a case study. Specifically, we consider a tactical planning decision support system. This system depends on a generic modeling of the problem that can be applied on a wide range of supply chains. We present an exact method and a metaheuristic to solve this problem and evaluate our approaches against a variety of instances of different sizes. We also study the ability to emulate specific management policies (e.g., just-in-time replenishment, minimal repair) by weighting the objectives. Finally, we investigate how to apply successive plans generated by the system and study the capability to face forecast uncertainties.

La programmation par contraintes est une approche régulièrement utilisée pour traiter des problèmes d’ordonnancement variés. Les problèmes d’ordonnancement cumulatifs représentent une classe de problèmes dans laquelle des tâches non morcelable peuvent être effectuées en parallèle. Ces problèmes apparaissent dans de nombreux contextes réels, tels que par exemple l’allocation de machines virtuelles ou l’ordonnancement de processus dans le "cloud", la gestion de personnel ou encore d’un port. De nombreux mécanismes ont été adaptés et proposés en programmation par contraintes pour résoudre les problèmes d’ordonnancement. Les différentes adaptations ont abouti à des raisonnements qui semblent à priori significativement distincts. Dans cette thèse nous avons effectué une analyse détaillée des différents raisonnements, proposant à la fois une notation unifiée purement théorique mais aussi des règles de dominance, permettant une amélioration significative du temps d’exécution d’algorithmes issus de l’état de l’art, pouvant aller jusqu’à un facteur sept. Nous proposons aussi un nouveau cadre de travail pour l’ordonnancement cumulatif robuste, permettant de trouver des solutions supportant qu’à tout moment une ou plusieurs tâches soit retardées, sans remise en cause de l’ordonnancement généré et en gardant une date de fin de projet satisfaisante. Dans ce cadre, nous proposons une adaptation d’un algorithme de l’état de l’art, Dynamic Sweep. / Constraint programming is an approach regularly used to treat a variety of scheduling problems. Cumulative scheduling problems represent a class of problems in which non-preemptive tasks can be performed in parallel. These problems appear in many contexts, such as for example the allocation of virtual machines, the ordering process in the "cloud", personnel management or a port. Many mechanisms have been adapted and offered in constraint programming to solve scheduling problems. The various adaptations have resulted in reasoning that appear a priori significantly different. In this thesis we performed a detailed analysis of the various arguments, offering both a theoretical unified caracterization but also dominance rules, allowing a significant improvement in execution time of algorithms from the state of the art, up to a factor of seven. we also propose a new framework for robust cumulative scheduling, to find solutions that support at any time one or more tasks to be delayed while keeping a satisfactory end date of the project and without calling into question the generated scheduling. In this context, we propose an adaptation of an algorithm of the state of the art, Dynamic Sweep.

MiniZinc is a modelling language for constraint satisfaction and optimisation problems. It can be used to solve difficult problems by declaratively modelling them and giving them to a generic solver. A linter, a tool for static analysis, is implemented for MiniZinc to provide analysis for improving models. Suggesting rewrites that will speed up solving, removing unnecessary constructs, and pointing out potential problems are examples of the analysis this tool provides. A method for finding points of interest in abstract syntax trees (parsed models) is designed and implemented. The linter is tested and evaluated against models in the MiniZinc Benchmarks, a collection of models used to benchmark solvers. The result from running the linter on one of the models from the benchmarks is more closely inspected and evaluated. The suggestions were correct and made the model simpler, but, unfortunately, there was no noticeable impact on the solving speed.

Constraint-Based Local Search (CBLS) is a technology used to solve computationally hard optimisation problems. A model written in a solver-independent modelling language needs to be processed before it can be solved by a CBLS solver. In this processing step, it is necessary to identify invariants and create an invariant structure. How to best obtain such a structure, or even how to identify a good structure, is not clear. The purpose of this project is to develop a framework for evaluating invariant structures and structure identification schemes. To do this, we introduce a set of metrics, which are also evaluated. The evaluation shows that these metrics are useful for evaluating invariant structures and structure identification schemes. We introduce a notion of optimal invariant structures and show that these can in many cases be produced by simple structure identification schemes. Finally, we present a strategy that improves on these schemes and yields optimal invariant structures in even more cases.

The main goal of a scheduling process is to decide when and how to execute each of the project’s activities. Despite large variety of researched scheduling problems, the majority of them can be described as generalisations of the resource-constrained project scheduling problem (RCPSP). Because of wide applicability and challenging difficulty, RCPSP has attracted vast amount of attention in the research community and great variety of heuristics have been adapted for solving it. Even though these heuristics are structurally different and operate according to diverse principles, they are designed to obtain only one solution at a time. In the recent researches on RCPSPs, it was proven that these kind of problems have complex multimodal fitness landscapes, which are characterised by a wide solution search spaces and presence of multiple local and global optima. The main goal of this thesis is twofold. Firstly, it presents a variation of the RCPSP that considers optimisation of projects in an uncertain environment where resources are modelled to adapt to their environment and, as the result of this, improve their efficiency. Secondly, modification of a novel evolutionary computation method Cuckoo Search (CS) is proposed, which has been adapted for solving combinatorial optimisation problems and modified to obtain multiple solutions. To test the proposed methodology, two sets of experiments are carried out. Firstly, the developed algorithm is applied to a real-life software development project. Secondly, the performance of the algorithm is tested on universal benchmark instances for scheduling problems which were modified to take into account specifics of the proposed optimisation model. The results of both experiments demonstrate that the proposed methodology achieves competitive level of performance and is capable of finding multiple global solutions, as well as prove its applicability in real-life projects.

Yes / An Improved Discrete Cuckoo Search (IDCS) is proposed in this paper to solve resource-constrained project scheduling problems (RCPSPs). The original Cuckoo Search (CS) was inspired by the breeding behaviour of some cuckoo species and was designed specifically for application in continuous optimisation problems, in which the algorithm had been demonstrated to be effective. The proposed IDCS aims to improve the original CS for solving discrete scheduling problems by reinterpreting its key elements: solution representation scheme, Lévy flight and solution improvement operators. An event list solution representation scheme has been used to present projects and a novel event movement and an event recombination operator has been developed to ensure better quality of received results and improve the efficiency of the algorithm. Numerical results have demonstrated that the proposed IDCS can achieve a competitive level of performance compared to other state-of-the-art metaheuristics in solving a set of benchmark instances from a well-known PSPLIB library, especially in solving complex benchmark instances. / Partially funded by the Innovate UK project HARNET – Harmonised Antennas, Radios and Networks under contract no. 100004607.