The capacitated m two node survivable star problem

The problem addressed in this paper attempts to efficiently solve a network design with redundant connections, often used by telephone operators and internet services. This network connects customers with one master node and sets some rules that shape its construction, such as number of customers, number of components and types of links, in order to meet operational needs and technical constraints. We propose a combinatorial optimization problem called CmTNSSP (Capacitated m Two- Node-Survivable Star Problem), a relaxation of CmRSP (Capacitated m Ring Star Problem). In this variant of CmRSP the rings are not constrained to be cycles; instead, they can be two node connected components. The contributions of this paper are (a) introduction and definition of a new problem (b) the specification of a mathematical programming model of the problem to be treated, and (c) the approximate resolution thereof through a GRASP metaheuristic, which alternates local searches that obtain incrementally better solutions, and exact resolution local searches based on mathematical programming models, particularly Integer Linear Programming ones. Computational results obtained by developed algorithms show robustness and competitiveness when compared to results of the literature relative to benchmark instances. Likewise, the experiments show the relevance of considering the specific variant of the problem studied in this work

Diseño topológico de redes. Caso de estudio: Capacitated m Two-Node Survivable Star Problem

Hoy en día prácticamente todas las actividades inherentes al ser humano tienen un soporte de hardware y software que las gestiona o las controla. Los elementos de comunicaciones cumplen un papel vital en este entramado. El diseño de topologías de redes tolerantes a fallos ha pasado a tener una importancia fundamental en la infraestructura de estas redes y constituye un elemento crítico a la hora de mantener la comunicación ante la falla de un enlace o alguno de sus nodos. El problema tratado en esta tesis intenta resolver eficientemente el diseño de una red con conexiones redundantes utilizada a menudo por los operadores telefónicos y servicios de internet. Dicha red conecta un nodo principal con clientes y establece algunas normas que modelan su construcción, tales como cantidad de clientes, número de componentes y tipos de enlaces, con el fin de satisfacer restricciones técnicas y necesidades operativas. Se considera en este trabajo un problema de optimización combinatoria denominado CmTNSSP (Capacitated m Two-Node-Survivable Star Problem), una relajación del problema CmRSP (Capacitated m Ring Star Problem). La variante relajada consiste en que los anillos (rings) del problema CmRSP pueden ser componentes 2-nodo-conexas, las cuales no necesariamente deben ser ciclos. El objetivo de esta tesis consta de la especificación de un modelo de programación matemática del problema a tratar, la resolución exacta mediante un lenguaje algebraico y un solver, y la resolución aproximada del mismo a través de una metaheurística que alterna búsquedas locales que obtienen soluciones incrementalmente mejores y búsquedas locales de resolución exacta basadas en modelos de programación matemática, en particular Programación Lineal Entera. Los resultados computacionales obtenidos por los algoritmos desarrollados muestran la robustez y competitividad de los mismos, comparados con las instancias benchmark publicadas en la literatura. Así mismo los experimentos muestran la relevancia de considerar la variante concreta del problema estudiado en esta tesis

Topological Design of Survivable Networks

In the field of telecommunications there are several ways of establishing links between different physical places that must be connected according to the characteristics and the type of service they should provide. Two main considerations to be taken into account and which require the attention of the network planners are, in one hand the economic effort necessary to build the network, and in the other hand the resilience of the network to remain operative in the event of failure of any of its components. A third consideration, which is very important when quality of services required, such as video streaming or communications between real-time systems, is the diameter constrained reliability. In this thesis we study a set of problems that involve such considerations. Firstly, we model a new combinatorial optimization problem called Capacitated m-Two Node Survivable Star Problem (CmTNSSP). In such problem we optimize the costs of constructing a network composed of 2-node-connected components that converge in a central node and whose terminals can belong to these connected 2-node structures or be connected to them by simple edges. The CmTNSSP is a relaxation of the Capacitated Ring Star Problem (CmRSP), where the cycles of the latter can be replaced by arbitrary 2-node-connected graphs. According to previous studies, some of the structural properties of 2-node-connected graphs can be used to show a potential improvement in construction costs, over solutions that exclusively use cycles. Considering that the CmTNSSP belongs to the class of NP-Hard computational problems, a GRASP-VND metaheuristic was proposed and implemented for its approximate resolution, and a comparison of results was made between both problems (CmRSP and CmTNSSP) for a series of instances. Some local searches are based on exact Integer Linear Programming formulations. The results obtained show that the proposed metaheuristic reaches satisfactory levels of accuracy, attaining the global optimum in several instances. Next, we introduce the Capacitated m Ring Star Problem under Diameter Constrained Reliability (CmRSP-DCR) wherein DCR is considered as an additional restriction, limiting the number of hops between nodes of the CmRSP problem and establishing a minimum level of network reliability. This is especially useful in networks that should guarantee minimum delays and quality of service. The solutions found in this problem can be improved by applying some of the results obtained in the study of the CmTNSSP. Finally, we introduce a variant of the CmTNSSP named Capacitated Two-Node Survivable Tree Problem, motivated by another combinatorial optimization problem most recently treated in the literature, called Capacitated Ring Tree Problem (CRTP). In the CRTP, an additional restriction is added with respect to CmRSP, where the terminal nodes are of two different types and tree structures are also allowed. Each node in the CRTP may be connected exclusively in one cycle, or may be part of a cycle or a tree indistinctly, depending on the type of node. In the variant we introduced, the cycles are replaced by 2-node-connected structures. This study proposes and implements a GRASP-VND metaheuristic with specific local searches for this type of structures and adapts some of the exact local searches used in the resolution CmTNSSP. A comparison of the results between the optimal solutions obtained for the CRTP and the CTNSTP is made. The results achieved show the robustness and efficiency of the metaheuristi

Diámetro confiabilidad : optimización y complejidad computacional

En el contexto de redes, el principal objetivo es la optimización de costos, disponibilidad y robustez del servicio que se brinda a través de ellas. Naturalmente, con el desarrollo, surgen nuevas aplicaciones como son por ejemplo las llamadas por video y voz. Estas poseen la característica de ser sensibles a retardo. Es así que surge la necesidad de incorporar como factor restrictivo en el proceso de optimización la distancia existente entre los sitios que interesa comunicar entre si, lo que se denomina diámetro de una red. La medida de diámetro confiabilidad refleja la capacidad que tiene una red de permanecer operativa luego de que fallan alguno de sus enlaces. En esta tesis se exponen algunos célebres resultados del diseño topológico de redes, para los cuales se encuetnran expresiones explicitas de la medida de diámetro confiabilidad

The capacitated m two node survivable star problem

In this paper, we address the problem of network design with redundant connections, often faced by operators of telephone and internet services. The network connects customers with one master node and is built by taking into account the rules that shape its construction, such as number of customers, number of components and types of links, in order to meet operational needs and technical constraints. We propose a combinatorial optimization problem called CmTNSSP (Capacitated m Two-Node-Survivable Star Problem), a relaxation of CmRSP (Capacitated m Ring Star Problem). In this variant of CmRSP, the rings are not constrained to be cycles; instead, they can be two-node connected components. The contributions of this paper are: (a) the introduction and definition of a new problem, (b) the specification of a mathematical programming model of the problem to be treated, and (c) the approximate resolution thereof through a GRASP metaheuristic, which alternates local searches that obtain incrementally better solutions, and exact resolution local searches based on mathematical programming models, particularly Integer Linear Programming ones. Computational results obtained by the developed algorithms show robustness and competitiveness when compared to results of the literature relative to benchmark instances. Likewise, the experiments show the relevance of considering the specific variant of the problem studied in this work