Network assimilation methodology and sectorization of water distribution systems by graph mining and optimization algorithm

Water Distribution Networks (WDNs) play a vital importance rule in communities, ensuring well-being band supporting economic growth and productivity. The need for greater investment requires design choices will impact on the efficiency of management in the coming decades. This thesis proposes an algorithmic approach to address two related problems:(i) identify the fundamental asset of large WDNs in terms of main infrastructure;(ii) sectorize large WDNs into isolated sectors in order to respect the minimum service to be guaranteed to users. Two methodologies have been developed to meet these objectives and subsequently they were integrated to guarantee an overall process which allows to optimize the sectorized configuration of WDN taking into account the needs to integrated in a global vision the two problems (i) and (ii). With regards to the problem (i), the methodology developed introduces the concept of primary network to give an answer with a dual approach, of connecting main nodes of WDN in terms of hydraulic infrastructures (reservoirs, tanks, pumps stations) and identifying hypothetical paths with the minimal energy losses. This primary network thus identified can be used as an initial basis to design the sectors. The sectorization problem (ii) has been faced using optimization techniques by the development of a new dedicated Tabu Search algorithm able to deal with real case studies of WDNs. For this reason, three new large WDNs models have been developed in order to test the capabilities of the algorithm on different and complex real cases. The developed methodology also allows to automatically identify the deficient parts of the primary network and dynamically includes new edges in order to support a sectorized configuration of the WDN. The application of the overall algorithm to the new real case studies and to others from literature has given applicable solutions even in specific complex situations.

Constraint solving over multi-valued logics - application to digital circuits

Due to usage conditions, hazardous environments or intentional causes, physical and virtual systems are subject to faults in their components, which may affect their overall behaviour. In a ‘black-box’ agent modelled by a set of propositional logic rules, in which just a subset of components is externally visible, such faults may only be recognised by examining some output function of the agent. A (fault-free) model of the agent’s system provides the expected output given some input. If the real output differs from that predicted output, then the system is faulty. However, some faults may only become apparent in the system output when appropriate inputs are given. A number of problems regarding both testing and diagnosis thus arise, such as testing a fault, testing the whole system, finding possible faults and differentiating them to locate the correct one. The corresponding optimisation problems of finding solutions that require minimum resources are also very relevant in industry, as is minimal diagnosis. In this dissertation we use a well established set of benchmark circuits to address such diagnostic related problems and propose and develop models with different logics that we formalise and generalise as much as possible. We also prove that all techniques generalise to agents and to multiple faults. The developed multi-valued logics extend the usual Boolean logic (suitable for faultfree models) by encoding values with some dependency (usually on faults). Such logics thus allow modelling an arbitrary number of diagnostic theories. Each problem is subsequently solved with CLP solvers that we implement and discuss, together with a new efficient search technique that we present. We compare our results with other approaches such as SAT (that require substantial duplication of circuits), showing the effectiveness of constraints over multi-valued logics, and also the adequacy of a general set constraint solver (with special inferences over set functions such as cardinality) on other problems. In addition, for an optimisation problem, we integrate local search with a constructive approach (branch-and-bound) using a variety of logics to improve an existing efficient tool based on SAT and ILP.

Solução de problemas de planejamento florestal com restrições de inteireza utilizando busca tabu

Este trabalho teve como objetivos desenvolver e testar um algoritmo com base na metaheurística busca tabu (BT), para a solução de problemas de gerenciamento florestal com restrições de inteireza. Os problemas avaliados tinham entre 93 e 423 variáveis de decisão, sujeitos às restrições de singularidade, produção mínima e produção máxima periódicas. Todos os problemas tiveram como objetivo a maximização do valor presente líquido. O algoritmo para implementação da BT foi codificado em ambiente delphi 5.0 e os testes foram efetuados em um microcomputador AMD K6II 500 MHZ, com memória RAM de 64 MB e disco rígido de 15GB. O desempenho da BT foi avaliado de acordo com as medidas de eficácia e eficiência. Os diferentes valores ou categorias dos parâmetros da BT foram testados e comparados quanto aos seus efeitos na eficácia do algoritmo. A seleção da melhor configuração de parâmetros foi feita com o teste L&O, a 1% de probabilidade, e as análises através de estatísticas descritivas. A melhor configuração de parâmetros propiciou à BT eficácia média de 95,97%, valor mínimo igual a 90,39% e valor máximo igual a 98,84%, com um coeficiente de variação de 2,48% do ótimo matemático. Para o problema de maior porte, a eficiência da BT foi duas vezes superior à eficiência do algoritmo exato branch and bound, apresentando-se como uma abordagem muito atrativa para solução de importantes problemas de gerenciamento florestal.

Metaheurística algoritmo genético para solução de problemas de planejamento florestal com restrições de integridade

Os objetivos deste trabalho foram desenvolver e testar um algoritmo genético (AG) para a solução de problemas de gerenciamento florestal com restrições de integridade. O AG foi testado em quatro problemas, contendo entre 93 e 423 variáveis de decisão, sujeitos às restrições de singularidade, produção mínima e produção máxima, periodicamente. Todos os problemas tiveram como objetivo a maximização do valor presente líquido. O AG foi codificado em ambiente delphi 5.0 e os testes foram realizados em um microcomputador AMD K6II 500 MHZ, com memória RAM de 64 MB e disco rígido de 15GB. O desempenho do AG foi avaliado de acordo com as medidas de eficácia e eficiência. Os valores ou categorias dos parâmetros do AG foram testados e comparados quanto aos seus efeitos na eficácia do algoritmo. A seleção da melhor configuração de parâmetros foi feita com o teste L&O, a 1% de probabilidade, e as análises foram realizadas através de estatísticas descritivas. A melhor configuração de parâmetros propiciou ao AG eficácia média de 94,28%, valor mínimo de 90,01%, valor máximo de 98,48%, com coeficiente de variação de 2,08% do ótimo matemático, obtido pelo algoritmo exato branch and bound. Para o problema de maior porte, a eficiência do AG foi cinco vezes superior à eficiência do algoritmo exato branch and bound. O AG apresentou-se como uma abordagem bastante atrativa para solução de importantes problemas de gerenciamento florestal.

Metaheurística Simulated Annealing para solução de problemas de planejamento florestal com restrições de integridade

Os objetivos deste trabalho foram desenvolver e testar a metaheurística SA para solução de problemas de gerenciamento florestal com restrições de integridade. O algoritmo SA desenvolvido foi testado em quatro problemas, contendo entre 93 e 423 variáveis de decisão, sujeitos às restrições de singularidade, produção mínima e produção máxima, periodicamente. Todos os problemas tiveram como objetivo a maximização do valor presente líquido. O algoritmo SA foi codificado em liguagem delphi 5.0 e os testes foram efetuados em um microcomputador AMD K6II 500 MHZ, com memória RAM de 64 MB e disco rígido de 15GB. O desempenho da SA foi avaliado de acordo com as medidas de eficácia e eficiência. Os diferentes valores ou categorias dos parâmetros da SA foram testados e comparados quanto aos seus efeitos na eficácia do algoritmo. A seleção da melhor configuração de parâmetros foi feita com o teste L&O, a 1% de probabilidade, e as análises foram realizadas através de estatísticas descritivas. A melhor configuração de parâmetros propiciou à SA eficácia média de 95,36%, valor mínimo de 83,66%, valor máximo de 100% e coeficiente de variação igual a 3,18% do ótimo matemático obtido pelo algoritmo exato branch and bound. Para o problema de maior porte, a eficiência da SA foi dez vezes superior à eficiência do algoritmo exato branch and bound. O bom desempenho desta heurística reforçou as conclusões, tiradas em outros trabalhos, do seu enorme potencial para resolver importantes problemas de gerenciamento florestal de difícil solução pelos instrumentos computacionais da atualidade.

On the use of convex underestimators in global optimization

Många kvantitativa problem från vitt skilda områden kan beskrivas som optimeringsproblem. Ett mått på lösningens kvalitet bör optimeras samtidigt som vissa villkor på lösningen uppfylls. Kvalitetsmåttet kallas vanligen objektfunktion och kan beskriva kostnader (exempelvis produktion, logistik), potentialenergi (molekylmodellering, proteinveckning), risk (finans, försäkring) eller något annat relevant mått. I min doktorsavhandling diskuteras speciellt icke-linjär programmering, NLP, i ändliga dimensioner. Problem med enkel struktur, till exempel någon form av konvexitet, kan lösas effektivt. Tyvärr kan inte alla kvantitativa samband modelleras på ett konvext vis. Icke-konvexa problem kan angripas med heuristiska metoder, algoritmer som söker lösningar med hjälp av deterministiska eller stokastiska tumregler. Ibland fungerar det här väl, men heuristikerna kan sällan garantera kvaliteten på lösningen eller ens att en lösning påträffas. För vissa tillämpningar är det här oacceptabelt. Istället kan man tillämpa så kallad global optimering. Genom att successivt dela variabeldomänen i mindre delar och beräkna starkare gränser på det optimala värdet hittas en lösning inom feltoleransen. Den här metoden kallas branch-and-bound, ungefär dela-och-begränsa. För att ge undre gränser (vid minimering) approximeras problemet med enklare problem, till exempel konvexa, som kan lösas effektivt. I avhandlingen studeras tillvägagångssätt för att approximera differentierbara funktioner med konvexa underskattningar, speciellt den så kallade alphaBB-metoden. Denna metod adderar störningar av en viss form och garanterar konvexitet genom att sätta villkor på den perturberade Hessematrisen. Min forskning har lyft fram en naturlig utvidgning av de perturbationer som används i alphaBB. Nya metoder för att bestämma underskattningsparametrar har beskrivits och jämförts. I sammanfattningsdelen diskuteras global optimering ur bredare perspektiv på optimering och beräkningsalgoritmer.

Planification de la récolte et allocation des produits aux usines

L’industrie forestière est un secteur qui, même s’il est en déclin, se trouve au cœur du débat sur la mondialisation et le développement durable. Pour de nombreux pays tels que le Canada, la Suède et le Chili, les objectifs sont de maintenir un secteur florissant sans nuire à l’environnement et en réalisant le caractère fini des ressources. Il devient important d’être compétitif et d’exploiter de manière efficace les territoires forestiers, de la récolte jusqu’à la fabrication des produits aux usines, en passant par le transport, dont les coûts augmentent rapidement. L’objectif de ce mémoire est de développer un modèle de planification tactique/opérationnelle qui permet d’ordonnancer les activités pour une année de récolte de façon à satisfaire les demandes des usines, sans perdre de vue le transport des quantités récoltées et la gestion des inventaires en usine. L’année se divise en 26 périodes de deux semaines. Nous cherchons à obtenir les horaires et l’affectation des équipes de récolte aux blocs de coupe pour une année. Le modèle mathématique développé est un problème linéaire mixte en nombres entiers dont la structure est basée sur chaque étape de la chaine d’approvisionnement forestière. Nous choisissons de le résoudre par une méthode exacte, le branch-and-bound. Nous avons pu évaluer combien la résolution directe de notre problème de planification était difficile pour les instances avec un grand nombre de périodes. Cependant l’approche des horizons roulants s’est avérée fructueuse. Grâce à elle en une journée, il est possible de planifier les activités de récolte des blocs pour l’année entière (26 périodes).

« Resolution Search » et problèmes d’optimisation discrète

Thèse réalisée en cotutelle avec l'Université d'Avignon.

Problèmes de tournées de véhicules avec contraintes de chargement

Cette thèse s’intéresse aux problèmes de tournées de véhicules où l’on retrouve des contraintes de chargement ayant un impact sur les séquences de livraisons permises. Plus particulièrement, les items placés dans l’espace de chargement d’un véhicule doivent être directement accessibles lors de leur livraison sans qu’il soit nécessaire de déplacer d’autres items. Ces problèmes sont rencontrés dans plusieurs entreprises de transport qui livrent de gros objets (meubles, électroménagers). Le premier article de cette thèse porte sur une méthode exacte pour un problème de confection d’une seule tournée où un véhicule, dont l’aire de chargement est divisée en un certain nombre de piles, doit effectuer des cueillettes et des livraisons respectant une contrainte de type dernier entré, premier sorti. Lors d’une collecte, les items recueillis doivent nécessairement être déposés sur le dessus de l’une des piles. Par ailleurs, lors d’une livraison, les items doivent nécessairement se trouver sur le dessus de l’une des piles. Une méthode de séparation et évaluation avec plans sécants est proposée pour résoudre ce problème. Le second article présente une méthode de résolution exacte, également de type séparation et évaluation avec plans sécants, pour un problème de tournées de véhicules avec chargement d’items rectangulaires en deux dimensions. L’aire de chargement des véhicules correspond aussi à un espace rectangulaire avec une orientation, puisque les items doivent être chargés et déchargés par l’un des côtés. Une contrainte impose que les items d’un client soient directement accessibles au moment de leur livraison. Le dernier article aborde une problème de tournées de véhicules avec chargement d’items rectangulaires, mais où les dimensions de certains items ne sont pas connus avec certitude lors de la planification des tournées. Il est toutefois possible d’associer une distribution de probabilités discrète sur les dimensions possibles de ces items. Le problème est résolu de manière exacte avec la méthode L-Shape en nombres entiers.

Two-level network design with intermediate facilities: An application to electrical distribution systems

We consider the two-level network design problem with intermediate facilities. This problem consists of designing a minimum cost network respecting some requirements, usually described in terms of the network topology or in terms of a desired flow of commodities between source and destination vertices. Each selected link must receive one of two types of edge facilities and the connection of different edge facilities requires a costly and capacitated vertex facility. We propose a hybrid decomposition approach which heuristically obtains tentative solutions for the vertex facilities number and location and use these solutions to limit the computational burden of a branch-and-cut algorithm. We test our method on instances of the power system secondary distribution network design problem. The results show that the method is efficient both in terms of solution quality and computational times. (C) 2010 Elsevier Ltd. All rights reserved.

Orthogonal packing of identical rectangles within isotropic convex regions

A mixed integer continuous nonlinear model and a solution method for the problem of orthogonally packing identical rectangles within an arbitrary convex region are introduced in the present work. The convex region is assumed to be made of an isotropic material in such a way that arbitrary rotations of the items, preserving the orthogonality constraint, are allowed. The solution method is based on a combination of branch and bound and active-set strategies for bound-constrained minimization of smooth functions. Numerical results show the reliability of the presented approach. (C) 2010 Elsevier Ltd. All rights reserved.

Uma análise experimental de algoritmos exatos aplicados ao problema da árvore geradora multiobjetivo

The Multiobjective Spanning Tree Problem is NP-hard and models applications in several areas. This research presents an experimental analysis of different strategies used in the literature to develop exact algorithms to solve the problem. Initially, the algorithms are classified according to the approaches used to solve the problem. Features of two or more approaches can be found in some of those algorithms. The approaches investigated here are: the two-stage method, branch-and-bound, k-best and the preference-based approach. The main contribution of this research lies in the fact that no research was presented to date reporting a systematic experimental analysis of exact algorithms for the Multiobjective Spanning Tree Problem. Therefore, this work can be a basis for other research that deal with the same problem. The computational experiments compare the performance of algorithms regarding processing time, efficiency based on the number of objectives and number of solutions found in a controlled time interval. The analysis of the algorithms was performed for known instances of the problem, as well as instances obtained from a generator commonly used in the literature

O problema de corte de placas defeituosas

O problema tratado neste trabalho consiste em cortar uma placa retangular em peças menores retangulares, de modo que a perda seja minimizada. A placa, entretanto, contém defeitos bem localizados. Propomos uma abordagem em grafo E/OU para representação das soluções possíveis e um método de enumeração implícita para determinar a solução ótima. Resultados computacionais demonstram a efetividade da abordagem.

Two-level network design with intermediate facilities: An application to electrical distribution systems

We consider the two-level network design problem with intermediate facilities. This problem consists of designing a minimum cost network respecting some requirements, usually described in terms of the network topology or in terms of a desired flow of commodities between source and destination vertices. Each selected link must receive one of two types of edge facilities and the connection of different edge facilities requires a costly and capacitated vertex facility. We propose a hybrid decomposition approach which heuristically obtains tentative solutions for the vertex facilities number and location and use these solutions to limit the computational burden of a branch-and-cut algorithm. We test our method on instances of the power system secondary distribution network design problem. The results show that the method is efficient both in terms of solution quality and computational times. © 2010 Elsevier Ltd.

Optimal energy generation with biomass of sugarcane harvest

The aim of this work is the application of the Interior Point and Branch and Bound methods in multiobjective optimization models related to sugarcane harvest residual biomass. These methods showed their viability to help on choosing the sugarcane planting varieties, searching to optimize cost and energy balance of harvest residual biomass, which have conflitant objectives. These methods provide satisfactory results, with fair computing performance and reliable and consistent solutions to the analyzed models. © 2011 IEEE.