Les schématisations de termes permettent de représenter des ensembles infinis de termes ayant une structure similaire de manière finie et compacte. Dans ce travail, nous étudions certains aspects liés à l'utilisation des schématisations de termes en déduction automatique, plus particulièrement dans les méthodes de démonstration de théorèmes du premier ordre par saturation. Après une brève étude comparée des formalismes de schématisation existants, nous nous concentrons plus particulièrement sur les termes avec exposants entiers (ou I-termes). Dans un premier temps, nous proposons une nouvelle approche permettant de détecter automatiquement des régularités dans les espaces de recherche. Cette détection des régularités peut avoir plusieurs applications, notamment la découverte de lemmes nécessaires à la terminaison dans certaines preuves inductives. Nous présentons DS3, un outil qui implémente ces idées. Nous comparons notre approche avec d'autres techniques de généralisation de termes. Notre approche diffère complètement des techniques existantes car d'une part, elle est complètement indépendante de la procédure de preuve utilisée et d'autre part, elle utilise des techniques de généralisation inductive et non déductives. Nous discutons également les avantages et les inconvénients liés à l'utilisation de notre méthode et donnons des éléments informels de comparaison avec les approches existantes. Nous nous intéressons ensuite aux aspects théoriques de l'utilisation des I-termes en démonstration automatique. Nous démontrons que l'extension aux I-termes du calcul de résolution ordonnée est réfutationnellement complète, que l'extension du calcul de superposition n'est pas réfutationnellement complète et nous proposons une nouvelle règle d'inférence pour restaurer la complétude réfutationnelle. Nous proposons ensuite un algorithme d'indexation (pour une sous-classe) des I-termes, utile pour le traitement des règles de simplification et d'élimination de la redondance. Finalement nous présentons DEI, un démonstrateur automatique de théorèmes capable de gérer directement des formules contenant des I-termes. Nous évaluons les performances de ce logiciel sur un ensemble de benchmarks. / Term schematisations allow one to represent infinite sets of terms having a similar structure by a finite and compact form. In this work we study some issues related to the use of term schematisation in automated deduction, in particular in saturation-based first-order theorem proving. After a brief comparative study of existing schematisation formalisms, we focus on terms with integer exponents (or I-terms). We first propose a new approach allowing to automatically detect regularities (obviously not always) on search spaces. This is motivated by our aim at extending current theorem provers with qualitative improvements. For instance, detecting regularities permits to discover lemmata which is mandatory for terminating in some kinds of inductive proofs. We present DS3, a tool which implements these ideas. Our approach departs from existing techniques since on one hand it is completely independent of the proof procedure used and on the other hand it uses inductive generalization techniques instead of deductive ones. We discuss advantages and disadvantages of our method and we give some informal elements of comparison with similar approaches. Next we tackle some theoretical aspects of the use of I-terms in automated deduction. We prove that the direct extension of the ordered resolution calculus is refutationally complete. We provide an example showing that a direct extension of the superposition calculus is not refutationally complete and we propose a new inference rule to restore refutational completeness. We then propose an indexing algorithm for (a subclass of) I-terms. This algorithm is an extension of the perfect discrimination trees that are are employed by many efficient theorem provers to implement redundancy elimination rules. Finally we present DEI, a theorem prover with built-in capabilities to handle formulae containing I-terms. This theorem-prover is an extension of the E-prover developed by S. Schulz. We evaluate the performances of this software on a set of benchmarks.

The Multi-Layer Perceptron (MLP) is one of the most widely applied and researched Artificial Neural Network model. MLP networks are normally applied to performing supervised learning tasks, which involve iterative training methods to adjust the connection weights within the network. This is commonly formulated as a multivariate non-linear optimization problem over a very high-dimensional space of possible weight configurations. Analogous to the field of mathematical optimization, training an MLP is often described as the search of an error surface for a weight vector which gives the smallest possible error value. Although this presents a useful notion of the training process, there are many problems associated with using the error surface to understand the behaviour of learning algorithms and the properties of MLP mappings themselves. Because of the high-dimensionality of the system, many existing methods of analysis are not well-suited to this problem. Visualizing and describing the error surface are also nontrivial and problematic. These problems are specific to complex systems such as neural networks, which contain large numbers of adjustable parameters, and the investigation of such systems in this way is largely a developing area of research. In this thesis, the concept of the error surface is explored using three related methods. Firstly, Principal Component Analysis (PCA) is proposed as a method for visualizing the learning trajectory followed by an algorithm on the error surface. It is found that PCA provides an effective method for performing such a visualization, as well as providing an indication of the significance of individual weights to the training process. Secondly, sampling methods are used to explore the error surface and to measure certain properties of the error surface, providing the necessary data for an intuitive description of the error surface. A number of practical MLP error surfaces are found to contain a high degree of ultrametric structure, in common with other known configuration spaces of complex systems. Thirdly, a class of global optimization algorithms is also developed, which is focused on the construction and evolution of a model of the error surface (or search spa ce) as an integral part of the optimization process. The relationships between this algorithm class, the Population-Based Incremental Learning algorithm, evolutionary algorithms and cooperative search are discussed. The work provides important practical techniques for exploration of the error surfaces of MLP networks. These techniques can be used to examine the dynamics of different training algorithms, the complexity of MLP mappings and an intuitive description of the nature of the error surface. The configuration spaces of other complex systems are also amenable to many of these techniques. Finally, the algorithmic framework provides a powerful paradigm for visualization of the optimization process and the development of parallel coupled optimization algorithms which apply knowledge of the error surface to solving the optimization problem.

Nous adaptons une heuristique de recherche à voisinage variable pour traiter le problème du voyageur de commerce avec fenêtres de temps (TSPTW) lorsque l'objectif est la minimisation du temps d'arrivée au dépôt de destination. Nous utilisons des méthodes efficientes pour la vérification de la réalisabilité et de la rentabilité d'un mouvement. Nous explorons les voisinages dans des ordres permettant de réduire l'espace de recherche. La méthode résultante est compétitive avec l'état de l'art. Nous améliorons les meilleures solutions connues pour deux classes d'instances et nous fournissons les résultats de plusieurs instances du TSPTW pour la première fois. / We adapt a general variable neighborhood search heuristic to solve the traveling salesman problem with time windows (TSPTW) where the objective is to minimize the completion time. We use efficient methods to check the feasibility and the profitability of a movement. We use a specific order to reduce the search space while exploring the neighborhoods. The resulting method is competitive with the state-of-the-art. We improve the best known solutions for two classes of instances and provide the results of multiple instances of TSPTW for the first time.

In the context of evolutionary robotics and neurorobotics, artificial neural networks, used as controllers for animats, are examined to identify principles of neuro-control, network organization, the interaction between body and control, and other likewise properties. Before such an examination can take place, suitable neuro-controllers have to be identified. A promising and widely used technique to search for such networks are evolutionary algorithms specifically adapted for neural networks. These allow the search for neuro-controllers with various network topologies directly on physically grounded (simulated) animats. This neuro-evolution approach works well for small neuro-controllers and has lead to interesting results. However, due to the exponentially increasing search space with respect to the number of involved neurons, this approach does not scale well with larger networks. This scaling problem makes it difficult to find non-trivial, larger networks, that show interesting properties. In the context of this thesis, networks of this class are called mid-scale networks, having between 50 and 500 neurons. Searching for networks of this class involves very large search spaces, including all possible synaptic connections between the neurons, the bias terms of the neurons and (optionally) parameters of the neuron model, such as the transfer function, activation function or parameters of learning rules. In this domain, most evolutionary algorithms are not able to find suitable, non-trivial neuro-controllers in feasible time. To cope with this problem and to shift the frontier for evolvable network topologies a bit further, a novel evolutionary method has been developed in this thesis: the Interactively Constrained Neuro-Evolution method (ICONE). A way to approach the problem of increasing search spaces is the introduction of measures that reduce and restrict the search space back to a feasible domain. With ICONE, this restriction is realized with a unified, extensible and highly adaptable concept: Instead of evolving networks freely, networks are evolved within specifically designed constraint masks, that define mandatory properties of the evolving networks. These constraint masks are defined primarily using so called functional constraints, that actively modify a neural network to enforce the adherence of all required limitations and assumptions. Consequently, independently of the mutations taking place during evolution, the constraint masks repair and readjust the networks so that constraint violations are not able to evolve. Such functional constraints can be very specific and can enforce various network properties, such as symmetries, structure reuse, connectivity patterns, connectivity density heuristics, synaptic pathways, local processing assemblies, and much more. Constraint masks therefore describe a narrow, user defined subset of the parameter space -- based on domain knowledge and user experience -- that focuses the search on a smaller search space leading to a higher success rate for the evolution. Due to the involved domain knowledge, such evolutions are strongly biased towards specific classes of networks, because only networks within the defined search space can evolve. This, surely, can also be actively used to lead the evolution towards specific solution approaches, allowing the experimenter not only to search for any upcoming solution, but also to confirm assumptions about possible solutions. This makes it easier to investigate specific neuro-control principles, because the experimenter can systematically search for networks implementing the desired principles, simply by using suitable constraints to enforce them. Constraint masks in ICONE are built up by functional constraints working on so called neuro-modules. These modules are used to structure the networks, to define the scope for constraints and to simplify the reuse of (evolved) neural structures. The concept of functional, constrained neuro-modules allows a simple and flexible way to construct constraint masks and to inherit constraints when neuro-modules are reused or shared. A final cornerstone of the ICONE method is the interactive control of the evolution process, that allows the adaptation of the evolution parameters and the constraint masks to guide evolution towards promising domains and to counteract undesired developments. Due to the constraint masks, this interactive guidance is more effective than the adaptation of the evolution parameters alone, so that the identification of promising search space regions becomes easier. This thesis describes the ICONE method in detail and shows several applications of the method and the involved features. The examples demonstrate that the method can be used effectively for problems in the domain of mid-scale networks. Hereby, as effects of the constraint masks and the herewith reduced complexity of the networks, the results are -- despite their size -- often easy to comprehend, well analyzable and easy to reuse. Another benefit of constraint masks is the ability to deliberately search for very specific network configurations, which allows the effective and systematic exploration of distinct variations for an evolution experiment, simply by changing the constraint masks over the course of multiple evolution runs. The ICONE method therefore is a promising novel evolution method to tackle the problem of evolving mid-scale networks, pushing the frontier of evolvable networks a bit further. This allows for novel evolution experiments in the domain of neurorobotics and evolutionary robotics and may possibly lead to new insights into neuro-dynamical principles of animat control.

Tesis por compendio / [ES] Actualmente, la mayor parte de la población mundial vive en ciudades y se espera que esta tendencia continúe, trasladando cada año más población rural hacia las áreas urbanas. Este fenómeno se debe principalmente al desarrollo económico que se genera en las ciudades. Estas condiciones plantean desafíos importantes para las ciudades en cuanto a su planificación y gestión. Si el crecimiento de la urbanización se gestiona adecuadamente puede contribuir al crecimiento sostenible, aumentando la productividad y el nivel de vida de las personas. Sin embargo, no se puede pasar por alto que el crecimiento de las ciudades implica una afectación al medioambiente. Uno de los problemas que más preocupación causa es la expansión de las ciudades que sustituyen los espacios verdes y agrícolas que rodean a las ciudades por calles y estructuras impermeables. Este proceso disminuye la capacidad del suelo para absorber el agua en un evento de lluvia, incrementando la escorrentía y el riesgo de inundaciones. Si a este problema particular de las ciudades, le sumamos el innegable cambio climático que aumenta la frecuencia de eventos de lluvias extremas en ciertas zonas del planeta, la adaptación de la infraestructura de las ciudades para hacerlas más seguras es una necesidad imperiosa. Los sistemas de drenaje son infraestructuras esenciales, concebidos para captar y transportar el agua producto de las precipitaciones, su buen funcionamiento genera seguridad y bienestar a las personas mientras que un funcionamiento inadecuado se asocia al riesgo y a la vulnerabilidad. Bajo escenarios de cambio climático estas estructuras que fueron diseñadas para caudales menores no garantizan la efectiva evacuación de las aguas, volviendo a las ciudades vulnerables a las inundaciones que pueden generar pérdidas sociales y económicas. Para mitigar estos impactos se han desarrollado diferentes medidas como las denominadas buenas prácticas de manejo o la instalación de sistemas de drenaje con tecnología de bajo impacto, entre otras. Sin embargo, estas medidas no son suficientes para controlar el caudal pico de una lluvia extrema. Adaptar la red existente a las nuevas condiciones climáticas, se presenta como una alternativa idónea para el control de las inundaciones en el entorno urbano. Ampliar la capacidad de la red cambiando el tamaño de las tuberías por otras de mayor diámetro ha sido el enfoque tradicional que se ha venido usando desde hace muchos años. La inclusión de tanques de tormenta en el sistema es una medida que se adoptó posteriormente para dotarlo de mayor resiliencia a los picos de lluvias extremas. Desafortunadamente la construcción de estas estructuras en el entorno conlleva una gran dificultad por el tamaño de la intervención, el tiempo y el coste. En este contexto, el presente trabajo, presenta una novedosa forma de mejorar las redes de drenaje combinando el cambio de tuberías, la instalación de tanques de tormenta en la red de drenaje e incluye también elementos de control hidráulico en la red de drenaje. Con estas acciones se considera que la rehabilitación de la red será más eficiente en términos técnicos y económicos. Para lograrlo, se usa un modelo de optimización creado a partir de un algoritmo genético modificado conectado al modelo SWMM mediante una toolkit. El modelo de optimización se enfoca en minimizar el coste de la infraestructura requerida y de los costes asociados a las inundaciones. Planteado así el problema, se define una función objetivo compuesta por funciones de coste que será evaluada para encontrar las mejores soluciones. El desarrollo de diferentes pasos para la obtención de una metodología eficiente, las estrategias para reducir los tiempos de cálculo y el esfuerzo computacional, el análisis económico de las inundaciones y las estructuras requeridas se detalla en cada capítulo de esta tesis. / [CA] Actualment, la major part de la població mundial viu en ciutats i s'espera que aquesta tendència continue, traslladant cada any més població rural cap a les àrees urbanes. Aquest fenomen es deu principalment al desenvolupament econòmic que es genera a les ciutats. Aquestes condicions plantegen desafiaments importants per a les ciutats quant a la seua planificació i gestió. Si el creixement de la urbanització es gestiona adequadament pot contribuir al creixement sostenible, augmentant la productivitat i el nivell de vida de les persones. No obstant això, no es pot passar per alt que el creixement de les ciutats implica una afectació al medi ambient. Un dels problemes que més preocupació causa és l'expansió de les ciutats que substitueixen els espais verds i agrícoles que envolten a les ciutats per carrers i estructures impermeables. Aquest procés disminueix la capacitat del sòl per a absorbir l'aigua en un esdeveniment de pluja, incrementant l'escolament i el risc d'inundacions. Si a aquest problema particular de les ciutats, li sumem l'innegable canvi climàtic que augmenta la freqüència d'esdeveniments de pluges extremes en unes certes zones del planeta, l'adaptació de la infraestructura de les ciutats per a fer-les més segures és una necessitat imperiosa. Els sistemes de drenatge són infraestructures essencials, concebuts per a captar i transportar l'aigua producte de les precipitacions, el seu bon funcionament genera seguretat i benestar a les persones mentre que un funcionament inadequat s'associa al risc i a la vulnerabilitat. Sota escenaris de canvi climàtic aquestes estructures que van ser dissenyades per a cabals menors no garanteixen l'efectiva evacuació de les aigües, tornant a les ciutats vulnerables a les inundacions que poden generar pèrdues socials i econòmiques. Per a mitigar aquests impactes s'han desenvolupat diferents mesures com les denominades bones pràctiques de maneig o la instal·lació de sistemes de drenatge amb tecnologia de baix impacte, entre altres. No obstant això, aquestes mesures no són suficients per a controlar el cabal pique d'una pluja extrema. Adaptar la xarxa existent a les noves condicions climàtiques, es presenta com una alternativa idònia per al control de les inundacions en l'entorn urbà. Ampliar la capacitat de la xarxa canviant la grandària de les canonades per altres de major diàmetre ha sigut l'enfocament tradicional que s'ha vingut usant des de fa molts anys. La inclusió de tancs de tempesta en el sistema és una mesura que es va adoptar posteriorment per a dotar-lo de major resiliència als pics de pluges extremes. Desafortunadament la construcció d'aquestes estructures en l'entorn comporta una gran dificultat per la grandària de la intervenció, el temps i el cost. En aquest context, el present treball, presenta una nova manera de millorar les xarxes de drenatge combinant el canvi de canonades, la instal·lació de tancs de tempesta en la xarxa de drenatge i inclou també elements de control hidràulic en la xarxa de drenatge. Amb aquestes accions es considera que la rehabilitació de la xarxa serà més eficient en termes tècnics i econòmics. Per a aconseguir-ho, s'usa un model d'optimització creat a partir d'un algorisme genètic modificat connectat al model SWMM mitjançant una toolkit. El model d'optimització s'enfoca a minimitzar el cost de la infraestructura requerida i dels costos associats a les inundacions. Plantejat així el problema, es defineix una funció objectiu composta per funcions de cost que serà avaluada per a trobar les millors solucions. El desenvolupament de diferents passos per a l'obtenció d'una metodologia eficient, les estratègies per a reduir els temps de càlcul i l'esforç computacional, l'anàlisi econòmica de les inundacions i les estructures requerides es detalla en cada capítol d'aquesta tesi. / [EN] Currently, most of the world's population lives in cities and this trend is expected to continue, moving more rural population to urban areas every year. This phenomenon is mainly due to the economic development that is generated in the cities. These conditions pose significant challenges for cities in terms of planning and management. If the growth of urbanization is properly managed, it can contribute to sustainable growth, increasing productivity and people's standard of living. However, it cannot be overlooked that the growth of cities implies an impact on the environment. One of the problems that causes the most concern is the expansion of cities that replace the green and agricultural spaces that surround the cities with streets and impermeable structures. This process decreases the capacity of the soil to absorb water in a rain event, increasing runoff and the risk of flooding. If adding to this problem of cities the undeniable climate change that increases the frequency of extreme rainfall events in certain areas of the planet, the adaptation of the infrastructure of cities to make them safer is an urgent need. Drainage systems are essential infrastructures, designed to capture and transport water produced by precipitation, their proper functioning generates security and wellness for people, while inadequate functioning is associated with risk and vulnerability. Under climate change scenarios, these structures, which were designed for lower flows, do not guarantee the effective evacuation of water, making cities vulnerable to floods that can generate social and economic losses. To mitigate these impacts, different measures have been developed, such as the so-called Best Management Practices or the installation of Low Impact Development etc. However, these measures are not enough to control the peak flow of extreme rainfall. Adapting the existing network to the new climatic conditions is presented as an ideal alternative for flood control in the urban environment. Expanding the capacity of the network by changing the size of the pipes for others with a larger diameter has been the traditional approach that has been used for many years. The inclusion of storm tanks in the system is a measure that was later adopted to provide it with greater resilience to extreme rainfall peaks. Unfortunately, the construction of these structures in the environment entails great difficulty due to the size of the intervention, the time, and the cost. In this context, the present work presents a novel way of improving drainage networks combining the replacement of pipes, the installation of storm tanks in the drainage network and also includes elements of hydraulic control in the drainage network. With these actions it is considered that the rehabilitation of the network will be more efficient in technical and economic terms. To achieve this, an optimization model created from a modified genetic algorithm connected to the SWMM model through a toolkit is used. The optimization model focuses on minimizing the cost of the required infrastructure and the costs associated with flooding. Posing the problem in this way, an objective function is defined composed of cost functions that will be evaluated to find the best solutions. The development of different steps to obtain an efficient methodology, the strategies to reduce calculation times and computational effort, the economic analysis of floods and the required structures are detailed in each chapter of this thesis. / I want to mention the support for the realization of this thesis from the Program Fondecyt through Project No. 1210410 and Project No. 1180660 of the National Agency for Research and Development (ANID) of Chile. From the program PAID 12-21 of the Polytechnic University of Valencia and the program E+/EU Erasmus+ Traineeship. / Bayas Jiménez, LA. (2023). Flood control in urban areas through the rehabilitation of drainage networks [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/199234 / Compendio