Exact and Approximate Schemes for Robust Optimization Problems with Decision Dependent Information Discovery

Uncertain optimization problems with decision dependent information discovery allow the decision maker to control the timing of information discovery, in contrast to the classic multistage setting where uncertain parameters are revealed sequentially based on a prescribed filtration. This problem class is useful in a wide range of applications, however, its assimilation is partly limited by the lack of efficient solution schemes. In this paper we study two-stage robust optimization problems with decision dependent information discovery where uncertainty appears in the objective function. The contributions of the paper are twofold: (i) we develop an exact solution scheme based on a nested decomposition algorithm, and (ii) we improve upon the existing K-adaptability approximate by strengthening its formulation using techniques from the integer programming literature. Throughout the paper we use the orienteering problem as our working example, a challenging problem from the logistics literature which naturally fits within this framework. The complex structure of the routing recourse problem forms a challenging test bed for the proposed solution schemes, in which we show that exact solution method outperforms at times the K-adaptability approximation, however, the strengthened K-adaptability formulation can provide good quality solutions in larger instances while significantly outperforming existing approximation schemes even in the decision independent information discovery setting. We leverage the effectiveness of the proposed solution schemes and the orienteering problem in a case study from Alrijne hospital in the Netherlands, where we try to improve the collection process of empty medicine delivery crates by co-optimizing sensor placement and routing decisions

Local, multi-resolution detection of network communities by Markovian dynamics

Complex networks are used to represent systems from many disciplines, including biology, physics, medicine, engineering and the social sciences; Many real-world networks are organised into densely connected communi- ties, whose composition gives some insight into the underlying network. Most approaches for nding such communities do so by partitioning the network into disjoint subsets, at the cost of requiring global information and that nodes belong to exactly one community. In recent years, some effort has been devoted towards the development of local methods, but these are either limited in resolution or ignore relevant network features such as directedness. Here we show that introducing a dynamic process onto the network allows us to de ne a community quality function severability which is inherently multi-resolution, takes into account edge-weight and direction, can accommodate overlapping communities and orphan nodes and crucially does not require global knowledge. Both constructive and real-world examples| drawn from elds as diverse as image segmentation, metabolic networks and word association|are used to illustrate the characteristics of this approach. We envision this approach as a starting point for the future analysis of both evolving networks and networks too large to be readily analysed as a whole (e.g. the World Wide Web).Open Acces

Multiscale hybrid simulation of brittle fracture

When a brittle material is loaded to the limit of its strength, it fails by nucleation and propagation of a crack. The conditions for crack propagation are created by the concentration of a long-range stress field at an atomically sharp crack tip, creating a complex and strongly coupled multiscale system. This thesis reports the results of multiscale simulations of the brittle fracture of silicon on the (111) cleavage plane. The simulations are made possible by combining a quantum mechanical description of the processes taking place near the crack tip with a classical atomistic model that captures the long-range elastic relaxation. The ‘Learn on The Fly’ technique is used to couple the quantum and classical models, allowing accurate quantum forces to be combined with classical forces using a simple adjustable potential to give stable dynamics. The simulations predict that fracture is unstable on the (111) plane at low speeds; conventionally this has been thought of as the most stable crack plane. The instability is caused by a crack tip reconstruction which triggers a positive feedback ‘sinking’ mechanism leading to macroscopic, experimentally observable corrugations. Recent experiments have observed crack surface features consistent with these predictions. The instability is the first example in a crystalline material of a fracture instability which onsets below a critical velocity, and shows how subtle atomistic details at the crack tip can control the qualitative macroscopic fracture behaviour.EPSR

Aerodynamic analysis of morphing geometry application to sailplane winglet design

Diplomová práce se zabývá aerodynamickou analýzou a optimalizací wingletu kluzáku. Winglet je uvažován s možností změny tvaru v průběhu letu a optimalizační proces je zaměřen na odhalení optimálních tvarů v odlišných letových režimech. První část práce popisuje současné snahy v oblasti návrhu a vývoje wingletů s měnitelnou geometrií. Druhá část je zaměřena na popis funkce wingletu, následována třetí částí, která popisuje optimalizační metody, které mohou být použity během optimalizace. Další částí práce je popis letadla vybaveného wingletem, který byl vybrán pro optimalizaci. Tato část je následována požadavky stavebního předpisu kategorie letadla, které bylo vybráno. Následuje model typického letu tohoto letadla. Zbytek práce je organizován dle procesu hledání optimálních tvarů wingletu. Popis tvorby CAD modelu je následován popisem tvorby CFD modelu a popisem přípravy CDF simulací. V předposlední kapitole jsou odhaleny detaily optimalizačního procesu. Závěrečná část práce obsahuje vyhodnocení výsledků optimalizačního procesu.This master’s thesis deals with aerodynamic analysis and optimisation of sailplane winglet. Winglet is considered with ability of in-flight shape changing and optimisation process is focused to revealing of optimal shapes for different flight regimes. First part of thesis describes current efforts in the field of design and development of winglets with variable geometry. Second part is focused on the description of winglet function, followed by third part which describing optimisation methods, which may be used for the winglet optimisation. Description of the aircraft fitted with winglet chosen for the optimisation process is next part of thesis followed by airworthiness requirements for the category of chosen aircraft. Model of typical flight of this aircraft is next part. Rest of the thesis is organized according to the process of searching optimum winglet shapes. Wing and winglet parametric CAD model description is followed by CFD model creation process and CFD simulation pre-processing description. Optimisation process details are revealed in the penultimate chapter. The final part of the thesis contains evaluation of the optimisation process results.

PhaseTracer: tracing cosmological phases and calculating transition properties

We present a C++ software package called PhaseTracer for mapping out cosmological phases, and potential transitions between them, for Standard Model extensions with any number of scalar fields. PhaseTracer traces the minima of effective potential as the temperature changes, and then calculates the critical temperatures, at which the minima are degenerate. PhaseTracer is constructed with modularity, flexibility and practicality in mind. It is fast and stable, and can receive potentials provided by other packages such as FlexibleSUSY. PhaseTracer can be useful analysing cosmological phase transitions which played an important role in the very early evolution of the Universe. If they were first order they could generate detectable gravitational waves and/or trigger electroweak baryogenesis to generate the observed matter anti-matter asymmetry of the Universe. The code can be obtained from https://github.com/PhaseTracer/PhaseTracer.Comment: 32 pages, 5 figures, matches published versio

Future of nuclear fission theory

There has been much recent interest in nuclear fission, due in part to a new appreciation of its relevance to astrophysics, stability of superheavy elements, and fundamental theory of neutrino interactions. At the same time, there have been important developments on a conceptual and computational level for the theory. The promising new theoretical avenues were the subject of a workshop held at the University of York in October 2019; this report summarises its findings and recommendations.Peer reviewe

Learning and generalization in radial basis function networks

The aim of supervised learning is to approximate an unknown target function by adjusting the parameters of a learning model in response to possibly noisy examples generated by the target function. The performance of the learning model at this task can be quantified by examining its generalization ability. Initially the concept of generalization is reviewed, and various methods of measuring it, such as generalization error, prediction error, PAC learning and the evidence, are discussed and the relations between them examined. Some of these relations are dependent on the architecture of the learning model.Two architectures are prevalent in practical supervised learning: the multi -layer perceptron (MLP) and the radial basis function network (RBF). While the RBF has previously been examined from a worst -case perspective, this gives little insight into the performance and phenomena that can be expected in the typical case. This thesis focusses on the properties of learning and generalization that can be expected on average in the RBF.There are two methods in use for training the RBF. The basis functions can be fixed in advance, utilising an unsupervised learning algorithm, or can adapt during the training process. For the case in which the basis functions are fixed, the typical generalization error given a data set of particular size is calculated by employing the Bayesian framework. The effects of noisy data and regularization are examined, the optimal settings of the parameters that control the learning process are calculated, and the consequences of a mismatch between the learning model and the data -generating mechanism are demonstrated.The second case, in which the basis functions are adapted, is studied utilising the on -line learning paradigm. The average evolution of generalization error is calculated in a manner which allows the phenomena of the learning process, such as the specialization of the basis functions, to be eludicated. The three most important stages of training: the symmetric phase, the symmetry- breaking phase and the convergence phase, are analyzed in detail; the convergence phase analysis allows the derivation of maximal and optimal learning rates. Noise on both the inputs and outputs of the data -generating mechanism is introduced, and the consequences examined. Regularization via weight decay is also studied, as are the effects of the learning model being poorly matched to the data generator

Routing and scheduling optimisation under uncertainty for engineering applications

The thesis aims to develop a viable computational approach suitable for solving large vehicle routing and scheduling optimisation problems affected by uncertainty. The modelling framework is built upon recent advances in Stochastic Optimisation, Robust Optimisation and Distributionally Robust Optimization. The utility of the methodology is presented on two classes of discrete optimisation problems: scheduling satellite communication, which is a variant of Machine Scheduling, and the Vehicle Routing Problem with Time Windows and Synchronised Visits. For each problem class, a practical engineering application is formulated using data coming from the real world. The significant size of the problem instances reinforced the need to apply a different computational approach for each problem class. Satellite communication is scheduled using a Mixed-Integer Programming solver. In contrast, the vehicle routing problem with synchronised visits is solved using a hybrid method that combines Iterated Local Search, Constraint Programming and the Guided Local Search metaheuristic. The featured application of scheduling satellite communication is the Satellite Quantum Key Distribution for a system that consists of one spacecraft placed in the Lower Earth Orbit and a network of optical ground stations located in the United Kingdom. The satellite generates cryptographic keys and transmits them to individual ground stations. Each ground station should receive the number of keys in proportion to the importance of the ground station in the network. As clouds containing water attenuate the signal, reliable scheduling needs to account for cloud cover predictions, which are naturally affected by uncertainty. A new uncertainty sets tailored for modelling uncertainty in predictions of atmospheric phenomena is the main contribution to the methodology. The uncertainty set models the evolution of uncertain parameters using a Multivariate Vector Auto-Regressive Time Series, which preserves correlations over time and space. The problem formulation employing the new uncertainty set compares favourably to a suite of alternative models adapted from the literature considering both the computational time and the cost-effectiveness of the schedule evaluated in the cloud cover conditions observed in the real world. The other contribution of the thesis in the satellite scheduling domain is the formulation of the Satellite Quantum Key Distribution problem. The proof of computational complexity and thorough performance analysis of an example Satellite Quantum Key Distribution system accompany the formulation. The Home Care Scheduling and Routing Problem, which instances are solved for the largest provider of such services in Scotland, is the application of the Vehicle Routing Problem with Time Windows and Synchronised Visits. The problem instances contain over 500 visits. Around 20% of them require two carers simultaneously. Such problem instances are well beyond the scalability limitations of the exact method and considerably larger than instances of similar problems considered in the literature. The optimisation approach proposed in the thesis found effective solutions in attractive computational time (i.e., less than 30 minutes) and the solutions reduced the total travel time threefold compared to alternative schedules computed by human planners. The Essential Riskiness Index Optimisation was incorporated into the Constraint Programming model to address uncertainty in visits' duration. Besides solving large problem instances from the real world, the solution method reproduced the majority of the best results reported in the literature and strictly improved the solutions for several instances of a well-known benchmark for the Vehicle Routing Problem with Time Windows and Synchronised Visits.The thesis aims to develop a viable computational approach suitable for solving large vehicle routing and scheduling optimisation problems affected by uncertainty. The modelling framework is built upon recent advances in Stochastic Optimisation, Robust Optimisation and Distributionally Robust Optimization. The utility of the methodology is presented on two classes of discrete optimisation problems: scheduling satellite communication, which is a variant of Machine Scheduling, and the Vehicle Routing Problem with Time Windows and Synchronised Visits. For each problem class, a practical engineering application is formulated using data coming from the real world. The significant size of the problem instances reinforced the need to apply a different computational approach for each problem class. Satellite communication is scheduled using a Mixed-Integer Programming solver. In contrast, the vehicle routing problem with synchronised visits is solved using a hybrid method that combines Iterated Local Search, Constraint Programming and the Guided Local Search metaheuristic. The featured application of scheduling satellite communication is the Satellite Quantum Key Distribution for a system that consists of one spacecraft placed in the Lower Earth Orbit and a network of optical ground stations located in the United Kingdom. The satellite generates cryptographic keys and transmits them to individual ground stations. Each ground station should receive the number of keys in proportion to the importance of the ground station in the network. As clouds containing water attenuate the signal, reliable scheduling needs to account for cloud cover predictions, which are naturally affected by uncertainty. A new uncertainty sets tailored for modelling uncertainty in predictions of atmospheric phenomena is the main contribution to the methodology. The uncertainty set models the evolution of uncertain parameters using a Multivariate Vector Auto-Regressive Time Series, which preserves correlations over time and space. The problem formulation employing the new uncertainty set compares favourably to a suite of alternative models adapted from the literature considering both the computational time and the cost-effectiveness of the schedule evaluated in the cloud cover conditions observed in the real world. The other contribution of the thesis in the satellite scheduling domain is the formulation of the Satellite Quantum Key Distribution problem. The proof of computational complexity and thorough performance analysis of an example Satellite Quantum Key Distribution system accompany the formulation. The Home Care Scheduling and Routing Problem, which instances are solved for the largest provider of such services in Scotland, is the application of the Vehicle Routing Problem with Time Windows and Synchronised Visits. The problem instances contain over 500 visits. Around 20% of them require two carers simultaneously. Such problem instances are well beyond the scalability limitations of the exact method and considerably larger than instances of similar problems considered in the literature. The optimisation approach proposed in the thesis found effective solutions in attractive computational time (i.e., less than 30 minutes) and the solutions reduced the total travel time threefold compared to alternative schedules computed by human planners. The Essential Riskiness Index Optimisation was incorporated into the Constraint Programming model to address uncertainty in visits' duration. Besides solving large problem instances from the real world, the solution method reproduced the majority of the best results reported in the literature and strictly improved the solutions for several instances of a well-known benchmark for the Vehicle Routing Problem with Time Windows and Synchronised Visits

Charge transport in bulk hematite and at the hematite/water interface

Transition metal oxide materials have attracted much attention for photoelectrochemical water splitting, but problems remain, e.g. the sluggish transport of excess charge carriers in these materials, which is not well understood. In this thesis I will show how periodic, spin-constrained and gap-optimised hybrid density functional theory can be used to uncover the nature and transport mechanisms of excess electrons and electron holes in a widely used water splitting material, hematite (α-Fe2O3). I will show that upon ionisation the electron hole relaxes from a delocalized band state to a polaron localised on a single iron atom with localisation induced by tetragonal distortion of the 6 surrounding iron-oxygen bonds. This distortion is responsible for the sluggish hopping transport in bulk hematite, characterised by an activation energy of 70 meV and a hole mobility of 0.031 cm2/Vs. By contrast, the excess electron induces a smaller distortion of the iron-oxygen bonds resulting in delocalisation over two neighbouring Fe units. I will show that 2-site delocalisation is advantageous for charge transport due to the larger spatial displacements per transfer step. As a result, the electron mobility is predicted to be a factor of 3 higher than the hole mobility, 0.098 cm2/Vs, in qualitative agreement with experimental observations. Extending this analysis to the hematite/liquid water interface, I will show that both excess electrons and electron holes localise at the interface with qualitatively similar structures to bulk hematite. However, the presence of the interface breaks the symmetry present in the bulk crystal and as a result the hole mobility is expected to be greatly reduced. These calculations provide new fundamental insights essential for a better understanding of rate-limiting transport processes governing photocatalytic water splitting efficiency at the hematite/liquid water interface

Structural dynamics of(bio-) macromolecules probed by optical spectroscopy

In this thesis, spectroscopic analyses on one biological and one non-biological macromolecular system are presented. In both cases, optical experiments shed light onto the (binding resp. conformational) dynamics of the systems’ structure. The first system under examination was the enzyme CO dehydrogenase (CODH) from the bacterium Oligotropha carboxydovorans. Fluores-cence correlation spectroscopy was used as a relatively un-complex assay for the confirmation of a binding between enzymes and larger substrates – here, the specificity of the binding of CODH and the cyto-plasmic membrane was examined by replacing the binding partners. Instrumentation for further investigations on CODH, especially using time-resolved fluorescence spectroscopy had already been developed, but no agreement with the cooperation partner on the continuation of this line of research could be found. Hence, this instrumentation was further used for the characterisation of a different (non-biological) compound. This second system was a dimer of two flexibly linked perylene bisi-mide dyes: di- (perylene bisimide acrylate) – (PerAcr)2. It served as a model system for higher oligomers resp. polymers containing perylene bisimide, which are candidates for the application in organic solar cells. A combination of spectroscopic techniques was used for the character-ization, with time-resolutions down to picoseconds (time-resolved fluorescence spectroscopy resp. anisotropy) and in part with single-molecule sensitivity (fluorescence correlation spectroscopy). By using global analysis methods a description of the measured data with mini-mised sets of free parameters was pursued, yielding robust hypothesis testing. Additionally, comparisons with molecular dynamics simula-tions and modelling were conducted. Among other results, it was thus possible to show that the examined dimers change conformation on μs timescales between two aggregated and one isolated state; and that the isolated conformation shows a fast transfer of excitation energy be-tween the two dyes. The findings were reported in three publications, which are the core of this thesis (chapter 4). In particular the last two publications show a possible way for using poly- (perylene bisimide) in organic solar cells: Instead of relying on the aggregation of the dyes, it should be decidedly avoided and non-coherent energy transfer should be exploited as an efficient transport mechanism