Permutation tests for nonparametric detection

In this paper, the authors provide a methodology to design nonparametric permutation tests and, in particular, nonparametric rank tests for applications in detection. In the first part of the paper, the authors develop the optimization theory of both permutation and rank tests in the Neyman?Pearson sense; in the second part of the paper, they carry out a comparative performance analysis of the permutation and rank tests (detectors) against the parametric ones in radar applications. First, a brief review of some contributions on nonparametric tests is realized. Then, the optimum permutation and rank tests are derived. Finally, a performance analysis is realized by Monte-Carlo simulations for the corresponding detectors, and the results are shown in curves of detection probability versus signal-to-noise ratio

Automatic design of Ant Colony Optimization for permutation problems

In this study, we present a framework based on ant colony optimization (ACO) for tackling combinatorial problems. ACO algorithms have been applied to many diferent problems, focusing on algorithmic variants that obtain high-quality solutions. Usually, the implementations are re-done for various problem even if they maintain the same details of the ACO algorithm. However, our goal is to generate a sustainable framework for applications on permutation problems. We concentrate on understanding the behavior of pheromone trails and specific methods that can be combined. Eventually, we will propose an automatic offline configuration tool to build an efective algorithm. ---RESUMEN---En este trabajo vamos a presentar un framework basado en la familia de algoritmos ant colony optimization (ACO), los cuales están dise~nados para enfrentarse a problemas combinacionales. Los algoritmos ACO han sido aplicados a diversos problemas, centrándose los investigadores en diversas variantes que obtienen buenas soluciones. Normalmente, las implementaciones se tienen que rehacer, inclusos si se mantienen los mismos detalles para los algoritmos ACO. Sin embargo, nuestro objetivo es generar un framework sostenible para aplicaciones sobre problemas de permutaciones. Nos centraremos en comprender el comportamiento de la sendas de feromonas y ciertos métodos con los que pueden ser combinados. Finalmente, propondremos una herramienta para la configuraron automática offline para construir algoritmos eficientes.

Evolutionary computation of forests with Degree- and Role-Constrained Minimum Spanning Trees

Finding the degree-constrained minimum spanning tree (DCMST) of a graph is a widely studied NP-hard problem. One of its most important applications is network design. Here we deal with a new variant of the DCMST problem, which consists of finding not only the degree- but also the role-constrained minimum spanning tree (DRCMST), i.e., we add constraints to restrict the role of the nodes in the tree to root, intermediate or leaf node. Furthermore, we do not limit the number of root nodes to one, thereby, generally, building a forest of DRCMSTs. The modeling of network design problems can benefit from the possibility of generating more than one tree and determining the role of the nodes in the network. We propose a novel permutation-based representation to encode these forests. In this new representation, one permutation simultaneously encodes all the trees to be built. We simulate a wide variety of DRCMST problems which we optimize using eight different evolutionary computation algorithms encoding individuals of the population using the proposed representation. The algorithms we use are: estimation of distribution algorithm, generational genetic algorithm, steady-state genetic algorithm, covariance matrix adaptation evolution strategy, differential evolution, elitist evolution strategy, non-elitist evolution strategy and particle swarm optimization. The best results are for the estimation of distribution algorithms and both types of genetic algorithms, although the genetic algorithms are significantly faster.

Computación evolutiva de bosques de expansión mínimos con restricción de grado y de rol

Encontrar el árbol de expansión mínimo con restricción de grado de un grafo (DCMST por sus siglas en inglés) es un problema NP-complejo ampliamente estudiado. Una de sus aplicaciones más importantes es el dise~no de redes. Aquí nosotros tratamos una nueva variante del problema DCMST, que consiste en encontrar el árbol de expansión mínimo no solo con restricciones de grado, sino también con restricciones de rol (DRCMST), es decir, a~nadimos restricciones para restringir el rol que los nodos tienen en el árbol. Estos roles pueden ser nodo raíz, nodo intermedio o nodo hoja. Por otra parte, no limitamos el número de nodos raíz a uno, por lo que, en general, construiremos bosques de DRCMSTs. El modelado en los problemas de dise~no de redes puede beneficiarse de la posibilidad de generar más de un árbol y determinar el rol de los nodos en la red. Proponemos una nueva representación basada en permutaciones para codificar los bosques de DRCMSTs. En esta nueva representación, una permutación codifica simultáneamente todos los árboles que se construirán. Nosotros simulamos una amplia variedad de problemas DRCMST que optimizamos utilizando ocho algoritmos de computación evolutiva diferentes que codifican los individuos de la población utilizando la representación propuesta. Los algoritmos que utilizamos son: algoritmo de estimación de distribuciones (EDA), algoritmo genético generacional (gGA), algoritmo genético de estado estacionario (ssGA), estrategia evolutiva basada en la matriz de covarianzas (CMAES), evolución diferencial (DE), estrategia evolutiva elitista (ElitistES), estrategia evolutiva no elitista (NonElitistES) y optimización por enjambre de partículas (PSO). Los mejores resultados fueron para el algoritmo de estimación de distribuciones utilizado y ambos tipos de algoritmos genéticos, aunque los algoritmos genéticos fueron significativamente más rápidos.---ABSTRACT---Finding the degree-constrained minimum spanning tree (DCMST) of a graph is a widely studied NP-hard problem. One of its most important applications is network design. Here we deal with a new variant of the DCMST problem, which consists of finding not only the degree- but also the role-constrained minimum spanning tree (DRCMST), i.e., we add constraints to restrict the role of the nodes in the tree to root, intermediate or leaf node. Furthermore, we do not limit the number of root nodes to one, thereby, generally, building a forest of DRCMSTs. The modeling of network design problems can benefit from the possibility of generating more than one tree and determining the role of the nodes in the network. We propose a novel permutation-based representation to encode the forest of DRCMSTs. In this new representation, one permutation simultaneously encodes all the trees to be built. We simulate a wide variety of DRCMST problems which we optimize using eight diferent evolutionary computation algorithms encoding individuals of the population using the proposed representation. The algorithms we use are: estimation of distribution algorithm (EDA), generational genetic algorithm (gGA), steady-state genetic algorithm (ssGA), covariance matrix adaptation evolution strategy (CMAES), diferential evolution (DE), elitist evolution strategy (ElististES), non-elitist evolution strategy (NonElististES) and particle swarm optimization (PSO). The best results are for the estimation of distribution algorithm and both types of genetic algorithms, although the genetic algorithms are significantly faster. iv

Algoritmos de decisión para priorizar las acciones de restauración en el mantenimiento de redes

En la actualidad, cualquier compañía de telecomunicaciones que posea su propia red debe afrontar el problema del mantenimiento de la misma. Ofrecer un mínimo de calidad de servicio a sus clientes debe ser uno de sus objetivos principales. Esta calidad debe mantenerse aunque ocurran incidencias en la red. El presente trabajo pretende resolver el problema de priorizar el orden en que se restauran los cables, caminos y circuitos, dañados por una incidencia, dentro de una red troncal de transporte perteneciente a una operadora de telecomunicaciones. Tras un planteamiento detallado del problema y de todos los factores que influirán en la toma de decisión, en primer lugar se acomete una solución basada en Métodos Multicriterio Discretos, concretamente con el uso de ELECTRE I y AHP. A continuación se realiza una propuesta de solución basada en Redes Neuronales (con dos aproximaciones diferentes al problema). Por último se utiliza un método basado en la Optimización por Enjambre de Partículas (PSO), adaptado a un problema de permutación de enteros (ordenación), y con una forma particular de evaluar la mejor posición global del enjambre. Complementariamente se realiza una exposición de lo que es una empresa Operadora de telecomunicaciones, de sus departamentos y procesos internos, de los servicios que ofrece, de las redes sobre las que se soportan, y de los puntos clave a tener en cuenta en la implementación de sus sistemas informáticos de gestión integral. ABSTRACT: Nowadays, any telecommunications company that owns its own network must face the problem of maintaining it (service assurance). Provide a minimum quality of service to its customers must be one of its main objectives. This quality should be maintained although any incidents happen to occur in the network. This thesis aims to solve the problem of prioritizing the order in which the damaged cables, trails, path and circuits, within a backbone transport network, should be restored. This work begins with a detailed explanation about network maintenance issues and all the factors that influence decision-making problem. First of all, one solution based on Discrete Multicriteria methods is tried (ELECTRE I and AHP algorithms are used). Also, a solution based on neural networks (with two different approaches to the problem) is analyzed. Finally, this thesis proposes an algorithm based on Particle Swarm Optimization (PSO), adapted to a problem of integers permutation, and a particular way of evaluating the best overall position of the swarm method. In addition, there is included an exhibition about telecommunications companies, its departments, internal processes, services offered to clients, physical networks, and key points to consider when implementing its integrated management systems.

Closures of positive braids and the Morton-Franks-Williams inequality

We study the Morton-Franks-Williams inequality for closures of simple braids (also known as positive permutation braids). This allows to prove, in a simple way, that the set of simple braids is an orthonormal basis for the inner product of the Hecke algebra of the braid group defined by Kálmán, who first obtained this result by using an interesting connection with Contact Topology. We also introduce a new technique to study the Homflypt polynomial for closures of positive braids, namely resolution trees whose leaves are simple braids. In terms of these simple resolution trees, we characterize closed positive braids for which the Morton-Franks-Williams inequality is strict. In particular, we determine explicitly the positive braid words on three strands whose closures have braid index three.