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

An efficient algorithm for computing exact system and survival signatures of K-terminal network reliability

An efficient algorithm is presented for computing exact system and survival signatures of K-terminal reliability in undirected networks with unreliable edges. K-terminal reliability is defined as the probability that a subset K of the network nodes can communicate with each other. Signatures have several advantages over direct reliability calculation such as enabling certain stochastic comparisons of reliability between competing network topology designs, extremely fast repeat computation of network reliability for different edge reliabilities and computation of network reliability when failures of edges are exchangeable but not independent. Existing methods for computation of signatures for K-terminal network reliability require derivation of cut-sets or path-sets which is only feasible for small networks due to the computational expense. The new algorithm utilises binary decision diagrams, boundary set partition sets and simple array operations to efficiently compute signatures through a factorisation of the network edges. The performance and advantages of the algorithm are demonstrated through application to a set of benchmark networks and a sensor network from an underground mine

Using multi-valued decision diagram to solve the expected hop count problem

The Expected Hop Count (EHC) of a computer communication network has so far been computed for network models that consider only device or link failure, but not both. We introduce an Augmented Ordered Multi-valued Decision Diagram (OMDD-A) to obtain the EHC of a network in which both devices and links may fail. The OMDD-A approach can compute the EHC of a 2100 grid network with 299 paths, which is unsolvable using existing techniques. We show that OMDD-A generates significantly fewer nodes than the corresponding ordered binary decision diagram, leading to large reductions in processing time

Efficient basic event orderings for binary decision diagrams

Over the last five years significant advances have been made in methodologies to analyse the fault tree diagram. The most successful of these developments has been the Binary Decision Diagram (BDD) approach. The Binary Decision Diagram approach has been shown to improve both the efficiency of determining the minimal cut sets of the fault tree ancl also the accuracy of the calculation procedure used to determine the top event parameters. The BDD technique povides a potential alternative to the traditional approaches based on Kinetic Tree Theory. To utilise the Binary Decision Diagram approach the fault tree structure is first converted to the BDD format. This conversion can be accomplished efficiently but requires the basic events in the fault tree to be placed in an ordering. A poor ordering can result in a Binary Decision Diagram which is not an efficient representation of the fault tree logic structure. The advantages to be gained by utilising the BDD technique rely on the efficiency of the ordering scheme. Alternative ordering schemes have been investigated and no one scheme is appropriate for every tree structure. Research to date has not found any rule based means of determining the best way of ordering basic events for a given fault tree structure. The work presented in this paper takes a machine learning approach based on Genetic Algorithms to select the most appropriate ordering scheme. Features which describe a fault tree structure have been identified and these provide the inputs to the machine learning algorithm. A set of possible ordering schemes has been selected based on previous heuristic work. The objective of the work detailed in the pap:r is to predict the most efficient of the possible ordering alternatives from parameters which describe a fault tree structure

A memory efficient algorithm for network reliability

We combine the Augmented Ordered Binary Decision Diagram (OBDD-A) with the use of boundary sets to create a method for computing the exact K-terminal or all-terminal reliability of an undirected network with failed edges and perfect vertices. We present the results of implementing this algorithm and show that the execution time is comparable with the state of the art and the space requirement is greatly reduced. Indeed the space remains constant when networks increase in size but maintain their structure and maximum boundary set size; with the same amount of memory used for computing a 312 and a 31000 grid network

An Improved Algorithm for Network Reliability Evaluation

Binary Decision Diagram (BDD) is a data structure proved to be compact in representation and efficient in manipulation of Boolean formulas. Using Binary decision diagram in network reliability analysis has already been investigated by some researchers. In this paper we show how an exact algorithm for network reliability can be improved and implemented efficiently by using CUDD - Colorado University Decision Diagram

International Competition on Graph Counting Algorithms 2023

This paper reports on the details of the International Competition on Graph Counting Algorithms (ICGCA) held in 2023. The graph counting problem is to count the subgraphs satisfying specified constraints on a given graph. The problem belongs to #P-complete, a computationally tough class. Since many essential systems in modern society, e.g., infrastructure networks, are often represented as graphs, graph counting algorithms are a key technology to efficiently scan all the subgraphs representing the feasible states of the system. In the ICGCA, contestants were asked to count the paths on a graph under a length constraint. The benchmark set included 150 challenging instances, emphasizing graphs resembling infrastructure networks. Eleven solvers were submitted and ranked by the number of benchmarks correctly solved within a time limit. The winning solver, TLDC, was designed based on three fundamental approaches: backtracking search, dynamic programming, and model counting or #SAT (a counting version of Boolean satisfiability). Detailed analyses show that each approach has its own strengths, and one approach is unlikely to dominate the others. The codes and papers of the participating solvers are available: https://afsa.jp/icgca/.Comment: https://afsa.jp/icgca

Optimization-based design of fault-tolerant avionics

This dissertation considers the problem of improving the self-consciousness for avionic systems using numerical optimization techniques, emphasizing UAV applications. This self-consciousness implies a sense of awareness for oneself to make a reliable decision on some crucial aspects. In the context of the avionics or aerospace industry, those aspects are SWaP-C as well as safety and reliability. The decision-making processes to optimize these aspects, which are the main contributions of this work, are presented. In addition, implementation on various types of applications related to avionics and UAV are also provided. The first half of this thesis lays out the background of avionics development ranging from a mechanical gyroscope to a current state-of-the-art electronics system. The relevant mathematics regarding convex optimization and its algorithms, which will be used for formulating this self-consciousness problem, are also provided. The latter half presents two problem formulations for redundancy design automation and reconfigurable middleware. The first formulation focuses on the minimization of SWaP-C while satisfying safety and reliability requirements. The other one aims to maximize the system safety and reliability by introducing a fault-tolerant capability via the task scheduler of middleware or RTOS. The usage of these two formulations is shown by four aerospace applications---reconfigurable multicore avionics, a SITL simulation of a UAV GNC system, a modular drone, and a HITL simulation of a fault-tolerant distributed engine control architecture.Ph.D