A contribution to the evaluation and optimization of networks reliability

L’évaluation de la fiabilité des réseaux est un problème combinatoire très complexe qui nécessite des moyens de calcul très puissants. Plusieurs méthodes ont été proposées dans la littérature pour apporter des solutions. Certaines ont été programmées dont notamment les méthodes d’énumération des ensembles minimaux et la factorisation, et d’autres sont restées à l’état de simples théories. Cette thèse traite le cas de l’évaluation et l’optimisation de la fiabilité des réseaux. Plusieurs problèmes ont été abordés dont notamment la mise au point d’une méthodologie pour la modélisation des réseaux en vue de l’évaluation de leur fiabilités. Cette méthodologie a été validée dans le cadre d’un réseau de radio communication étendu implanté récemment pour couvrir les besoins de toute la province québécoise. Plusieurs algorithmes ont aussi été établis pour générer les chemins et les coupes minimales pour un réseau donné. La génération des chemins et des coupes constitue une contribution importante dans le processus d’évaluation et d’optimisation de la fiabilité. Ces algorithmes ont permis de traiter de manière rapide et efficace plusieurs réseaux tests ainsi que le réseau de radio communication provincial. Ils ont été par la suite exploités pour évaluer la fiabilité grâce à une méthode basée sur les diagrammes de décision binaire. Plusieurs contributions théoriques ont aussi permis de mettre en place une solution exacte de la fiabilité des réseaux stochastiques imparfaits dans le cadre des méthodes de factorisation. A partir de cette recherche plusieurs outils ont été programmés pour évaluer et optimiser la fiabilité des réseaux. Les résultats obtenus montrent clairement un gain significatif en temps d’exécution et en espace de mémoire utilisé par rapport à beaucoup d’autres implémentations. Mots-clés: Fiabilité, réseaux, optimisation, diagrammes de décision binaire, ensembles des chemins et coupes minimales, algorithmes, indicateur de Birnbaum, systèmes de radio télécommunication, programmes.Efficient computation of systems reliability is required in many sensitive networks. Despite the increased efficiency of computers and the proliferation of algorithms, the problem of finding good and quickly solutions in the case of large systems remains open. Recently, efficient computation techniques have been recognized as significant advances to solve the problem during a reasonable period of time. However, they are applicable to a special category of networks and more efforts still necessary to generalize a unified method giving exact solution. Assessing the reliability of networks is a very complex combinatorial problem which requires powerful computing resources. Several methods have been proposed in the literature. Some have been implemented including minimal sets enumeration and factoring methods, and others remained as simple theories. This thesis treats the case of networks reliability evaluation and optimization. Several issues were discussed including the development of a methodology for modeling networks and evaluating their reliabilities. This methodology was validated as part of a radio communication network project. In this work, some algorithms have been developed to generate minimal paths and cuts for a given network. The generation of paths and cuts is an important contribution in the process of networks reliability and optimization. These algorithms have been subsequently used to assess reliability by a method based on binary decision diagrams. Several theoretical contributions have been proposed and helped to establish an exact solution of the stochastic networks reliability in which edges and nodes are subject to failure using factoring decomposition theorem. From this research activity, several tools have been implemented and results clearly show a significant gain in time execution and memory space used by comparison to many other implementations. Key-words: Reliability, Networks, optimization, binary decision diagrams, minimal paths set and cuts set, algorithms, Birnbaum performance index, Networks, radio-telecommunication systems, programs

Resource-constrained project scheduling.

Abstract: Resource-constrained project scheduling involves the scheduling of project activities subject to precedence and resource constraints in order to meet the objective(s) in the best possible way. The area covers a wide variety of problem types. The objective of this paper is to provide a survey of what we believe are important recent in the area . Our main focus will be on the recent progress made in and the encouraging computational experience gained with the use of optimal solution procedures for the basic resource-constrained project scheduling problem (RCPSP) and important extensions. The RCPSP involves the scheduling of a project its duration subject to zero-lag finish-start precedence constraints of the PERT/CPM type and constant availability constraints on the required set of renewable resources. We discuss recent striking advances in dealing with this problem using a new depth-first branch-and-bound procedure, elaborating on the effective and efficient branching scheme, bounding calculations and dominance rules, and discuss the potential of using truncated branch-and-bound. We derive a set of conclusions from the research on optimal solution procedures for the basis RCPSP and subsequently illustrate how effective and efficient branching rules and several of the strong dominance and bounding arguments can be extended to a rich and realistic variety of related problems. The preemptive resource-constrained project scheduling problem (PRCPSP) relaxes the nonpreemption condition of the RCPSP, thus allowing activities to be interrupted at integer points in time and resumed later without additional penalty cost. The generalized resource-constrained project scheduling (GRCPSP) extends the RCPSP to the case of precedence diagramming type of precedence constraints (minimal finish-start, start-start, start-finish, finish-finish precedence relations), activity ready times, deadlines and variable resource availability's. The resource-constrained project scheduling problem with generalized precedence relations (RCPSP-GPR) allows for start-start, finish-start and finish-finish constraints with minimal and maximal time lags. The MAX-NPV problem aims at scheduling project activities in order to maximize the net present value of the project in the absence of resource constraints. The resource-constrained project scheduling problem with discounted cash flows (RCPSP-DC) aims at the same non-regular objective in the presence of resource constraints. The resource availability cost problem (RACP) aims at determining the cheapest resource availability amounts for which a feasible solution exists that does not violate the project deadline. In the discrete time/cost trade-off problem (DTCTP) the duration of an activity is a discrete, non-increasing function of the amount of a single nonrenewable resource committed to it. In the discrete time/resource trade-off problem (DTRTP) the duration of an activity is a discrete, non-increasing function of the amount of a single renewable resource. Each activity must then be scheduled in one of its possible execution modes. In addition to time/resource trade-offs, the multi-mode project scheduling problem (MRCPSP) allows for resource/resource trade-offs and constraints on renewable, nonrenewable and doubly-constrained resources. We report on recent computational results and end with overall conclusions and suggestions for future research.Scheduling; Optimal;

Robust Branch-Cut-and-Price for the Capacitated Minimum Spanning Tree Problem over a Large Extended Formulation

This paper presents a robust branch-cut-and-price algorithm for the Capacitated Minimum Spanning Tree Problem (CMST). The variables are associated to q-arbs, a structure that arises from a relaxation of the capacitated prize-collecting arbores- cence problem in order to make it solvable in pseudo-polynomial time. Traditional inequalities over the arc formulation, like Capacity Cuts, are also used. Moreover, a novel feature is introduced in such kind of algorithms. Powerful new cuts expressed over a very large set of variables could be added, without increasing the complexity of the pricing subproblem or the size of the LPs that are actually solved. Computational results on benchmark instances from the OR-Library show very signi¯cant improvements over previous algorithms. Several open instances could be solved to optimalityNo keywords;

Contributions to the solution of the symmetric travelling salesman problem

Imperial Users onl

Algorithms for scheduling projects with generalized precedence relations.

Project scheduling under the assumption of renewable resource constraints and generalized precedence relations, i.e. arbitrary minimal and maximal time lags between the starting and completion times of the activities of the project, constitutes an important and challenging problem. Over the past few years considerable progress has been made in the use of exact solution procedure for this problem type and its variants. We review the fundamental logic and report new computational experience with a branch-and-bound procedure for optimally solving resource-constrained project scheduling problems with generalized precedence relations of the precedence diagramming type, i.e. start-start, start-finish, finish-start and finish-finish relations with minimal time lags for minimizing the project makespan. Subsequently, we review and report new results for several branch-and -bound procedures for the case of generalized precedence relations, including both minimal and maximal time lags, and demonstrate how the solution methodology can be expected to cope with other regular and nonregular objective functions such a smaximizing the net present value of a project.Networks; Problems; Scheduling; Algorithms; Functions; Net present value;

Solving the optimum communication spanning tree problem

This paper presents an algorithm based on Benders decomposition to solve the optimum communication spanning tree problem. The algorithm integrates within a branch-and-cut framework a stronger reformulation of the problem, combinatorial lower bounds, in-tree heuristics, fast separation algorithms, and a tailored branching rule. Computational experiments show solution time savings of up to three orders of magnitude compared to state-of-the-art exact algorithms. In addition, our algorithm is able to prove optimality for five unsolved instances in the literature and four from a new set of larger instances.Peer ReviewedPostprint (author's final draft

NEW METHODS AND NEW PARADIGM TO DESIGN SENSOR NETWORKS FOR PROCESS PLANTS

Due to economic reason, not every process variable can be measured by a sensor. The problem of optimum selection of sensor location is referred to as sensor network design problem (SNDP).Being a combinatorial optimization problem, the SNDP poses significant computational challenges for researchers, especially for large scale problems. The methods to solve the SNDP can be divided into two three classes: mathematical programming, graph-theoretic methods and stochastic methods (e.g. genetic algorithm)The SNDP problem itself can be divided into two big classes: designing sensor network intended for process monitoring purpose (to obtain accurate process data) and designing sensor network for process fault diagnosis and resolution. The former can be solved by many methods while the latter is usually solved by graph-theoretic methodsAlthough extensive researches have been done on this problem, efficient methods to design sensor networks for large scale nonlinear problems have not yet been found. Moreover, all the published models are developed from technical point of view, which requires knowledge / expertise of the users to use appropriate constraints / specifications in the model. A model that bases solely on an economic viewpoint has not yet been proposed.Addressing the mentioned drawbacks is the objective of this work. More specifically, in this work:i)Efficient computational methods to solve SNDP for large scale nonlinear problems are proposed.ii)A value-optimal SNDP is proposed and solved by using appropriate methods