Channel routing: Efficient solutions using neural networks

Neural network architectures are effectively applied to solve the channel routing problem. Algorithms for both two-layer and multilayer channel-width minimization, and constrained via minimization are proposed and implemented. Experimental results show that the proposed channel-width minimization algorithms are much superior in all respects compared to existing algorithms. The optimal two-layer solutions to most of the benchmark problems, not previously obtained, are obtained for the first time, including an optimal solution to the famous Deutch\u27s difficult problem. The optimal solution in four-layers for one of the be lchmark problems, not previously obtained, is obtained for the first time. Both convergence rate and the speed with which the simulations are executed are outstanding. A neural network solution to the constrained via minimization problem is also presented. In addition, a fast and simple linear-time algorithm is presented, possibly for the first time, for coloring of vertices of an interval graph, provided the line intervals are given

Mesoscopic descriptions of complex networks

[spa] El objetivo de la presente tesis es el estudio de las subestructuras que aparecen a un nivel de resolución mesoscópico en las redes complejas. Dichas subestructuras, que en el campo de las redes complejas son denominadas comunidades, intentan agrupar los nodos de una red de manera que los nodos que forman parte de una misma comunidad estén más conectados entre ellos que con el resto de nodos de la red. La importada del análisis de estas estructuras radica en que nos permiten comprender mejor las redes complejas dándonos información sobre la funcionalidad de las comunidades que las componen. Hemos llevado a cabo el estudio de estas estructuras mesoscópicas utilizando la información topológica de las redes, y en cuanto a los métodos empleados éstos se pueden agrupar en dos grandes familias conocidas habitualmente como clustering jerárquico y clustering modular. Dentro de la primera familia de métodos nos hemos fijado en la existencia de un problema de no unicidad en el clustering jerárquico aglomerativo, y hemos propuesto una solución a dicho problema basada en el uso de una nueva herramienta de clasificación que denominamos multidendrograma. A continuación, hemos aplicado el resultado de una clasificación jerárquica para resolver un problema dentro de las redes complejas financieras. Más concretamente, hemos aprovechado una partición en clusters para resolver de manera más eficiente el problema de optimizar una cartera de valores. Por lo que respecta a la segunda familia de métodos de clustering estudiados, ésta se basa en la optimización de una función objetivo llamada modularidad El inconveniente que presenta la optimización de la modularidad es su elevado coste computacional, la cual cosa nos ha llevado a idear una reducción analítica del tamaño de las redes complejas de manera que se conserva toda la información necesaria en la red original de cara a hallar la estructura de comunidades que optimice la modularidad. A continuación hemos podido utilizar dicha simplificación de los cálculos en el análisis de toda la mesoescala topológica de las redes complejas. Dicho mesoescala la hemos estudiado añadiendo un mismo valor a todos los nodos de una red que mide su resistencia a formar parte de comunidades, La optimización de la modularidad para estas nuevas instancias de la red original obtenidas a partir de unos valores de resistencia acotados analíticamente, nos permite analizar la mesoescala topológica de las redes. Por último, hemos propuesto una generalización de la función de modularidad donde los bloques constituyentes ya no son solamente arcos sino que pueden ser distintos tipos de motifs. Esto nos permite obtener descripciones más generales de grupos de nodos que incluyen como caso particular a las comunidades

Traveling Salesman Problem

This book is a collection of current research in the application of evolutionary algorithms and other optimal algorithms to solving the TSP problem. It brings together researchers with applications in Artificial Immune Systems, Genetic Algorithms, Neural Networks and Differential Evolution Algorithm. Hybrid systems, like Fuzzy Maps, Chaotic Maps and Parallelized TSP are also presented. Most importantly, this book presents both theoretical as well as practical applications of TSP, which will be a vital tool for researchers and graduate entry students in the field of applied Mathematics, Computing Science and Engineering

Contemporary Methods for Graph Coloring as an Example of Discrete Optimization

This paper provides an insight into graph coloringapplication of the contemporary heuristic methods. It discusses avariety of algorithmic solutions for The Graph Coloring Problem(GCP) and makes recommendations for implementation. TheGCP is the NP-hard problem, which aims at finding the minimumnumber of colors for vertices in such a way, that none of twoadjacent vertices are marked with the same color.With the adventof multicore processing technology, the metaheuristic approachto solving GCP reemerged as means of discrete optimization. Toexplain the phenomenon of these methods, the author makes athorough survey of AI-based algorithms for GCP, while pointingout the main differences between all these techniques

Formal methods for Hopfield-like networks.

International audienceBuilding a meaningful model of biological regulatory network is usually done by specifying the components (e.g. the genes) and their interactions, by guessing the values of parameters, by comparing the predicted behaviors to the observed ones, and by modifying in a trial-error process both architecture and parameters in order to reach an optimal fitness. We propose here a different approach to construct and analyze biological models avoiding the trial-error part, where structure and dynamics are represented as formal constraints. We apply the method to Hopfield-like networks, a formalism often used in both neural and regulatory networks modeling. The aim is to characterize automatically the set of all models consistent with all the available knowledge (about structure and behavior). The available knowledge is formalized into formal constraints. The latter are compiled into Boolean formula in conjunctive normal form and then submitted to a Boolean satisfiability solver. This approach allows to formulate a wide range of queries, expressed in a high level language, and possibly integrating formalized intuitions. In order to explore its potential, we use it to find cycles for 3-nodes networks and to determine the flower morphogenesis regulatory network of Arabidopsis thaliana. Applications of this technique are numerous and concern the building of models from data as well as the design of biological networks possessing specified behaviors