This thesis presents a novel evolutionary optimisation algorithm that can improve the quality of solutions in simulation-based optimisation. Simulation-based optimisation is the process of finding optimal parameter settings without explicitly examining each possible configuration of settings. An optimisation algorithm generates potential configurations and sends these to the simulation, which acts as an evaluation function. The evaluation results are used to refine the optimisation such that it eventually returns a high-quality solution. The algorithm described in this thesis integrates multi-objective optimisation, parallelism, surrogate usage, and noise handling in a unique way for dealing with simulation-based optimisation problems incurred by these characteristics. In order to handle multiple, conflicting optimisation objectives, the algorithm uses a Pareto approach in which the set of best trade-off solutions is searched for and presented to the user. The algorithm supports a high degree of parallelism by adopting an asynchronous master-slave parallelisation model in combination with an incremental population refinement strategy. A surrogate evaluation function is adopted in the algorithm to quickly identify promising candidate solutions and filter out poor ones. A novel technique based on inheritance is used to compensate for the uncertainties associated with the approximative surrogate evaluations. Furthermore, a novel technique for multi-objective problems that effectively reduces noise by adopting a dynamic procedure in resampling solutions is used to tackle the problem of real-world unpredictability (noise). The proposed algorithm is evaluated on benchmark problems and two complex real-world problems of manufacturing optimisation. The first real-world problem concerns the optimisation of a production cell at Volvo Aero, while the second one concerns the optimisation of a camshaft machining line at Volvo Cars Engine. The results from the optimisations show that the algorithm finds better solutions for all the problems considered than existing, similar algorithms. The new techniques for dealing with surrogate imprecision and noise used in the algorithm are identified as key reasons for the good performance.

Traditional clustering algorithms have different criteria and biases, and there is no single algorithm that can be the best solution for a wide range of data sets. This problem often presents a significant obstacle to analysts in revealing meaningful information buried among the huge amount of data. Ensemble Clustering has been proposed as a way to avoid the biases and improve the accuracy of clustering. The difficulty in developing Ensemble Clustering methods is to combine external information (provided by input clusterings) with internal information (i.e. characteristics of given data) effectively to improve the accuracy of clustering. The work presented in this thesis focuses on enhancing the clustering accuracy of Ensemble Clustering by employing heuristic optimisation techniques to achieve a robust combination of relevant information during the consensus clustering stage. Two novel heuristic optimisation-based Ensemble Clustering methods, Multi-Optimisation Consensus Clustering (MOCC) and K-Ants Consensus Clustering (KACC), are developed and introduced in this thesis. These methods utilise two heuristic optimisation algorithms (Simulated Annealing and Ant Colony Optimisation) for their Ensemble Clustering frameworks, and have been proved to outperform other methods in the area. The extensive experimental results, together with a detailed analysis, will be presented in this thesis.

This thesis is concerned with investigating new methods for the analysis of large-scale dynamical systems using convex optimization. The proposed methodology is based on composite Lyapunov theory and is computationally implemented using polynomial programming techniques. The main result of this work is the development of a system decomposition framework that makes it possible to analyze systems that are of such a scale that traditional methods cannot cope with. We begin by addressing the problem of model invalidation. A barrier certificate method for invalidating models in the presence of uncertain data is presented for both continuous and discrete time models. It is shown how a re-parameterization of the time dependent variables can improve the numerical conditioning of the underlying optimization problem. The main contribution of this thesis is the development of an automated dynamical system decomposition framework that permits us to verify the stability of systems that typically have a state dimension large enough to render traditional computational methods intractable. The underlying idea is to decompose a system into a set of lower order subsystems connected in feedback in such a manner that composite methods for stability verification may be employed. What is unique about the algorithm presented is that it takes into account both dynamics and the topology of the interconnection graph. In the first instance we illustrate the methodology with an ecological network and primal Internet congestion control scheme. The versatility of the decomposition framework is also highlighted when it is shown that when applied to a model of the EGF-MAPK signaling pathway it is capable of identifying biologically relevant subsystems in addition to stability verification. Finally we introduce stability metrics for interconnected dynamical systems based on the theory of dissipativity. We conclude by outlining a clustering based decomposition algorithm that explicitly takes into account the input and output dynamics when determining the system decomposition.

Cette thèse vise à développer des stratégies permettant d'augmenter la puissance du calcul séquentiel et des systèmes distribués, elle traite en particulier, la décomposition séquentielle des opérations ainsi que des systèmes d'édition collaboratifs décentralisés. Nous introduisons, une méthode d'indexage avec précision contrôlée. Celle-ci permet la génération d'identifiants uniques utilisés dans l'indexage des communications dans les systèmes distribués, plus particulièrement dans les systèmes d'édition collaboratifs décentralisés. Ces identifiants sont des nombres réels avec un motif de précision contrôlé. Un ensemble fini d'identifiants est conservé pour permettre le calcul de cardinalités locales et globales. Cette propriété joue un rôle prépondérant dans la gestion des communications indexées. De plus, d'autres propriétés incluant la préservation de l'ordre sont observées. La méthode d'indexage a été testée et vérifiée avec succès. Ceci a permis la conception d'un système d'édition collaboratif décentralisé. Aussi, nous explorons les stratégies existantes, relatives a la décomposition séquentielle d'opérations, que nous étendons à de nouvelles stratégies. Ces stratégies mènent à une optimisation (processeur, compilateur, mémoire, code). Ces styles de décomposition portent un intérêt majeur à la communauté scientifique. Des recherches et des implémentations de plus en plus rapides résultent de la conception d'unité arithmétique. / This thesis aims at developing strategies to enhance the power of sequential computation and distributed systems, particularly, it deals with sequential break down of operations and decentralized collaborative editing systems. In this thesis, we introduced precision control indexing method that generates unique identifiers which are used for indexed communication in distributed systems, particularly, in decentralized collaborative editing systems. These identifiers are still real numbers with a specific controlled pattern of precision. Set of identifiers is kept finite that makes it possible to compute local as well as global cardinality. This property plays important role in dealing with indexed communication. Besides this, some other properties including order preservation are observed. The indexing method is tested and verified by experimentation successfully and it leads to design decentralized collaborative editing system. Dealing with sequential break down of operations, we explore limitations of the existing strategies, extended the idea by introducing new strategies. These strategies lead towards optimization (processor, compiler, memory, code). This style of decomposition attracts research communities for further investigation and practical implementation that could lead towards designing an arithmetic unit.

Evolutionary Algorithms (EAs) have been widely used for the optimisation of both theoretical and real-world non-linear problems, although such optimisation methods have found reasonably limited utilisation in fields outside of the academic domain. While the causality of this limited uptake in non-academic fields falls outside the scope of this thesis, the core focus of this research remains strongly influenced by the notions of solution feasibility and making optimisation methods more accessible for engineers, both factors attributed to low EA adoption rates in the commercial space. This thesis focuses on the application of bespoke heuristic methods to the field of water distribution system optimisation. Water distribution systems are complex entities that are difficult to model and optimise as they consist of many interacting components each with a set of considerations to address, hence it is important for the engineer to understand and assess the behaviour of the system to enable its effective design and optimisation. The primary goal of this research is to assess the impact that incorporating water systems knowledge into an evolution algorithm has on algorithm performance when applied to water distribution network optimisation problems. This thesis describes the development of two heuristics influenced by the practices of water systems engineers when designing water distribution networks with the view to increasing an algorithm’s performance and resultant solution feasibility. By utilising heuristics based on engineering design principles and integrating them into existing EAs, it is found that both engineering feasibility and general algorithmic performance can be notably improved. Firstly the heuristics are applied to a standard single-objective EA and then to a multi-objective genetic algorithm. The algorithms are assessed on a number of water distribution network benchmarks from the literature including real-world based, large scale systems and compared to the standard variants of the algorithms. Following this, a set of extensive experiments are conducted to explore how the inclusion of water systems knowledge impacts the sensitivity of an evolutionary algorithm to parameter variance. It was found that the performance of both engineering inspired algorithms were less sensitive to parameter change than the standard genetic algorithm variant meaning that non-experts in the field of meta-heuristics will potentially be able to get much better performance out of the engineering heuristic based algorithms without the need for specialist evolutionary algorithm knowledge. In addition this research explores the notion that visualisation techniques can provide water system engineers with a greater insight into the operation and behaviour of an evolutionary algorithm. The final section of this thesis presents a novel three-dimensional representation of pipe based water systems and demonstrates a range of innovative methods to convey information to the user. The interactive visualisation system presented not only allows the engineer to visualise the various parameters of a network but also allows the user to observe the behaviour and progress of an iterative optimisation method. Examples of the combination of the interactive visualisation system and the EAs developed in this work are shown to enable the user to track and visualise the actions of the algorithm. The visualisation aggregates changes to the network over an EA run and grants significant insight into the operations of an EA as it is optimising a network. The research presented in this thesis demonstrates the effectiveness of integrating water system engineering expertise into evolutionary based optimisation methods. Not only is solution quality improved over standard methods utilising these new heuristic techniques, but the potential for greater interaction between engineer, problem and optimiser has been established.

In recent years, the field of evolutionary dynamic optimisation has seen significant increase in scientific developments and contributions. This is as a result of its relevance in solving academic and real-world problems. Several techniques such as hyper-mutation, hyper-learning, hyper-selection, change detection and many more have been developed specifically for solving dynamic optimisation problems. However, the complex structure of algorithms employing these techniques make them unsuitable for real-world, real-time dynamic optimisation problem using embedded systems with limited memory. The work presented in this thesis focuses on a compact approach as an alternative to population based optimisation algorithm, suitable for solving real-time dynamic optimisation problems. Specifically, a novel compact dynamic optimisation algorithm suitable for embedded systems with limited memory is presented. Three novel dynamic approaches that augment and enhance the evolving properties of the compact genetic algorithm in dynamic environments are introduced. These are 1.) change detection scheme that measures the degree of dynamic change 2.) mutation schemes whereby the mutation rates is directly linked to the detected degree of change and 3.) change trend scheme the monitors change pattern exhibited by the system. The novel compact dynamic optimization algorithm outlined was applied to two differing dynamic optimization problems. This work evaluates the algorithm in the context of tuning a controller for a physical target system in a dynamic environment and solving a dynamic optimization problem using an artificial dynamic environment generator. The novel compact dynamic optimisation algorithm was compared to some existing dynamic optimisation techniques. Through a series of experiments, it was shown that maintaining diversity at a population level is more efficient than diversity at an individual level. Among the five variants of the novel compact dynamic optimization algorithm, the third variant showed the best performance in terms of response to dynamic changes and solution quality. Furthermore, it was demonstrated that information transfer based on dynamic change patterns can effectively minimize the exploration/exploitation dilemma in a dynamic environment.

We study stockpiling problems under uncertain economic and physical factors, and investigate the valuation and optimisation of storage systems where the availability and spot price of the underlying are both subject to stochasticity. Following a Real Options valuation approach, we first study financial derivatives linked to Asian options. A comprehensive set of boundary conditions is compiled, and an alternative (and novel) similarity reduction for fixed-strike Asian options is derived. Hybrid semi-Lagrangian methods for numerically solving the related partial differential equations (PDEs) are implemented, and we assess the accuracy of the valuations thus obtained with respect to results from classical finite-difference valuation methods and with respect to high precision calculations for valuing Asian options with spectral expansion theory techniques. Next we derive a PDE model for valuing the storage of electricity from a wind farm, with an attached back-up battery, that operates by trading electricity in a volatile market in order to meet a contracted fixed rate of energy generation; this system comprises two diffusive-type (stochastic) variables, namely the energy production and the electricity spot price, and two time-like (deterministic) variables, specifically the battery state and time itself. An efficient and novel semi-Lagrangian alternating-direction implicit (SLADI) methodology for numerically solving advection-diffusion problems is developed: here a semi-Lagrangian approach for hyperbolic problems of advection is combined with an alternating-direction implicit method for parabolic problems involving diffusion. Efficiency is obtained by solving (just) tridiagonal systems of equations at every time step. The results are compared to more standard semi-Lagrangian Crank-Nicolson (SLCN) and semi-Lagrangian fully implicit (SLFI) methods. Once he have established our PDE model for a storage-upgraded wind farm, a system that depends heavily on the highly stochastic nature of wind and the volatile market where electricity is sold, we derive a Hamilton-Jacobi-Bellman (HJB) equation for optimally controlling charging and discharging rates of the battery in time, and we assess a series of operation regimes. The solution of the related PDE models is approached numerically using our SLADI methodology to efficiently treat this mixed advection and diffusion problem in four dimensions. Extensive numerical experimentation confirms our SLADI methodology to be robust and yields highly accurate solutions and efficient computations, we also explore effects from correlation between stochastic electricity generation and random prices of electricity as well as effects from a seasonal electricity spot price. Ultimately, the objective of approximating optimal storage policies for a system under uncertain economic and physical factors is accomplished. Finally we examine the steady-state solution of a stochastic storage problem under uncertain electricity market prices and fixed demand. We use a HJB formulation for optimally controlling charging and discharging rates of the storage device with respect to the electricity spot price. A projected successive over-relaxation coupled with the semi-Lagrangian method is implemented, and we explore the use of boundary-fitted coordinates techniques.

Closed-loop optimization deals with problems in which candidate solutions are evaluated by conducting experiments, e.g. physical or biochemical experiments. Although this form of optimization is becoming more popular across the sciences, it may be subject to rather unexplored resourcing issues, as any experiment may require resources in order to be conducted. In this thesis we are concerned with understanding how evolutionary search is affected by three particular resourcing issues -- ephemeral resource constraints (ERCs), changes of variables, and lethal environments -- and the development of search strategies to combat these issues. The thesis makes three broad contributions. First, we motivate and formally define the resourcing issues considered. Here, concrete examples in a range of applications are given. Secondly, we theoretically and empirically investigate the effect of the resourcing issues considered on evolutionary search. This investigation reveals that resourcing issues affect optimization in general, and that clear patterns emerge relating specific properties of the different resourcing issues to performance effects. Thirdly, we develop and analyze various search strategies augmented on an evolutionary algorithm (EA) for coping with resourcing issues. To cope specifically with ERCs, we develop several static constraint-handling strategies, and investigate the application of reinforcement learning techniques to learn when to switch between these static strategies during an optimization process. We also develop several online resource-purchasing strategies to cope with ERCs that leave the arrangement of resources to the hands of the optimizer. For problems subject to changes of variables relating to the resources, we find that knowing which variables are changed provides an optimizer with valuable information, which we exploit using a novel dynamic strategy. Finally, for lethal environments, where visiting parts of the search space can cause the permanent loss of resources, we observe that a standard EA's population may be reduced in size rapidly, complicating the search for innovative solutions. To cope with such scenarios, we consider some non-standard EA setups that are able to innovate genetically whilst simultaneously mitigating risks to the evolving population.

Les phénomènes de croissance et de fragmentation jouent un rôle central dans de nombreux phénomènes biologiques. La première partie de ce manuscript concerne un modèle de l'activité électrique d'un réseau de neurones. Il s'agit d'une équation de croissance-fragmentation non linéaire. Grâce à une technique introduite par B. Perthame et L. Ryzhik, dans un cas particulier, nous quantifions des régimes dans lequels cette équation se relaxe avec un taux exponentiel. La deuxième et la troisième parties traitent de problèmes inverses. Le premier concerne l'équation de croissance-fragmentation ayant un noyau auto-similaire et le second un modèle de transduction olfactive. Après régularisations adéquates, ces deux problèmes reviennent à inverser des opérateurs intégraux dont les noyaux ont une structure auto-similaire. Grâce à la transformée de Mellin des inégalités de continuité et controlabilité de l'opérateur intégral sont établies. à partir de données expérimentales, ces études permettent d'estimer des paramètres importants des équations pour lesquels aucune mesure expérimentale directe n'est possible. La quatrième partie traite d'un modèle probabiliste de sénescence réplicative d'une lignée aléatoire de levures. En se basant sur des données expérimentales et des simulations numériques, le signal de sénescence est identifié et quantifié, et les sources de l'hétérogénéité des tailles des télomères sont analysées. Le modèle permet de mener une analyse complète de l'évolution des tailles des télomères. / Growth and fragmentation phenomena play a central role in several biological phenomena. The first part of this thesis introduces a model of the electrical activity of a neural network. The equation involved is a non-linear growth-fragmentation equation. Thanks to a technique introduced by B. Perthame and L. Ryzhik, in a particular case, we are able to quantify regimes in which the equation has an exponential relaxation. The second and third part of this thesis both deal with inverse problems. The first one involves a growth-fragmentation equation with a self-similar kernel and the second one is a model of olfactive transduction. After regularization steps, these two problems come down to invert some integral operators whose kernels have a self-similar structure. Thanks to the use of the Mellin transform, some continuity and controllability inequalities are established. Using experimental data, these studies make it possible to estimate important parameters of the equations for which no direct experimental measurements can be obtained. The fourth part deals with a probabilistic model of replicative senescence of a random yeast lineage. Based on experimental data and numerical simulations, the senescence signal is identified and quantified, and the different sources of heterogeneity in the lengths of the telomeres are analyzed. This model allows us to completely analyze the evolution of the lengths of the telomeres.

Dans cette thèse, on se propose de participer à la popularisation des méthodes de résolution de problèmes de propagation d'onde basées sur des formulations intégrales en fournissant des indicateurs d'erreur a posteriori utilisable dans le cadre d'algorithmes de raffinement autoadaptatif. Le développement de tels indicateurs est complexe du fait de la non-localité des normes associées aux espaces de Sobolev et des opérateurs entrant en jeu. Des indicateurs de la littérature sont étendus au cas de la propagation d'une onde acoustique. On étend les preuves de convergence quasi-optimale (de la littérature) des algorithmes autoadaptatifs associés dans ce cas. On propose alors une nouvelle approche par rapport à la littérature qui consiste à utiliser une technique de localisation des normes, non pas basée sur des inégalités inverses, mais sur l'utilisation d'un opérateur Λ de localisation bien choisi.On peut alors construire des indicateurs d'erreur a posteriori fiables, efficaces, locaux et asymptotiquement exacts par rapport à la norme de Galerkin de l'erreur. On donne ensuite une méthode pour la construction de tels indicateurs. Les applications numériques sur des géométries 2D et 3D confirment l'exactitude asymptotique ainsi que l'optimalité du guidage de l'algorithme autoadaptatif.On étend ensuite ces indicateurs au cas de la propagation d'une onde électromagnétique. Plus précisément, on s'intéresse au cas de l'EFIE. On propose des généralisations des indicateurs de la littérature. On effectue la preuve de convergence quasi-optimale dans le cas d'un indicateur basé sur une localisation de la norme du résidu. On utilise le principe du Λ pour obtenir le premier indicateur d'erreur fiable, efficace et local pour cette équation. On en propose une seconde forme qui est également, théoriquement asymptotiquement exacte. / The aim of this work is to participate to the popularization of methods for the resolution of wave propagation problems based on integral equations formulations by developping a posteriori error estimates in the context of autoadaptive mesh refinement strategies. The development of such estimates is difficult because of the non-locality of the norms associated to the Sobolev spaces and of the involved integral operators. Estimates from the literature are extended in the case of the propagation of an acoustic wave. The proofs of quasi-optimal convergence of the autoadaptive algorithms are established. We then introduce a new approach with respect to the literature which is based on a new norm-localization technique based on the use of a well-chosen Λ operator and not on inverse inequalities as it was the case previously.We then establish new a posteriori error estimates which are reliable, efficient, local and asymptotically exact with respect to the Galerkin norm of the error. We give a method for the construction of such estimates. Numerical applications on 2D and 3D geometries confirm the asymptotic exactness and the optimality of the autoadaptive algorithm.These estimates are extended in the case of the propagation of an electromagnetic wave. More precisely, we are interested in the EFIE. We suggest generalization of the estimates of the literature. A proof for quasi-optimal convergence is given for an estimate based on a localization of the norm of the residual. The principle of Λ is used to construct the first reliable, efficient, local error estimate for this equation. We give a second forme which is eventually theoretically asymptotically exact.