Optimization is used in daily practice with fixed input quantities and assuming constancy of all internal and external factors that may affect the results. But the reality that surrounds us is not so straightforward and clear. It is a complex and variable system. We learn new information about it every moment and it changes and evolves constantly. If the variability is included in the optimization model, it will change from the deterministic to stochastic model. Simulation offers a way how to work with the variability of inputs and the risk that the future development will be different from the assumptions. It uses probability distributions of entering risk factors. The most frequent method is Monte Carlo simulation, which is based on the generation of large amount of scenarios of possible future developments. Crystal Ball was used as simulation software program.

This thesis deals with Canadian traveller problem (CTP), which can be defined as the shortest path problem in a stochastic environment. The overview of different CTP variants is presented in theoretical part of this thesis, as well as known solutions to these variants. In the next parts, the thesis focuses on the stochastic variation of CTP (SCTP). For this variant chosen solutions (strategies) are discussed more in depth. At the same time, the original strategies named UCTO and UCTP are presented. Further, the thesis deals with the description of a window application implemented in Java, which has been developed to validate and test the functionality of selected strategies. The final part contains experiments and comparison of selected strategies.

abstract: The mobile crowdsensing (MCS) applications leverage the user data to derive useful information by data-driven evaluation of innovative user contexts and gathering of information at a high data rate. Such access to context-rich data can potentially enable computationally intensive crowd-sourcing applications such as tracking a missing person or capturing a highlight video of an event. Using snippets and pictures captured from multiple mobile phone cameras with specific contexts can improve the data acquired in such applications. These MCS applications require efficient processing and analysis to generate results in real time. A human user, mobile device and their interactions cause a change in context on the mobile device affecting the quality contextual data that is gathered. Usage of MCS data in real-time mobile applications is challenging due to the complex inter-relationship between: a) availability of context, context is available with the mobile phones and not with the cloud, b) cost of data transfer to remote cloud servers, both in terms of communication time and energy, and c) availability of local computational resources on the mobile phone, computation may lead to rapid battery drain or increased response time. The resource-constrained mobile devices need to offload some of their computation. This thesis proposes ContextAiDe an end-end architecture for data-driven distributed applications aware of human mobile interactions using Edge computing. Edge processing supports real-time applications by reducing communication costs. The goal is to optimize the quality and the cost of acquiring the data using a) modeling and prediction of mobile user contexts, b) efficient strategies of scheduling application tasks on heterogeneous devices including multi-core devices such as GPU c) power-aware scheduling of virtual machine (VM) applications in cloud infrastructure e.g. elastic VMs. ContextAiDe middleware is integrated into the mobile application via Android API. The evaluation consists of overheads and costs analysis in the scenario of ``perpetrator tracking" application on the cloud, fog servers, and mobile devices. LifeMap data sets containing actual sensor data traces from mobile devices are used to simulate the application run for large scale evaluation. / Dissertation/Thesis / Doctoral Dissertation Electrical Engineering 2019

The deterministic theory of graphs and networks is used successfully in cases where no random component is needed. However in practice, a number of decision-making and conflict situations require the inclusion of a stochastic element directly into the model. The objective of this thesis is the introduction of stochastic optimization and its application on random networks. The reader will become familiar with three approaches to stochastic optimization. Namely two-stage optimization, multi-stage optimization and chance constraint optimization. Finally, the studied issue is demonstrated on a real telecommunication network example.

My PhD thesis concentrates on the field of stochastic analysis, with focus on stochastic optimization and applications in finance. It is composed of two parts: the first part studies an optimal stopping problem, and the second part studies an optimal control problem. The first topic considers a one-dimensional transient and downwards drifting diffusion process X, and detects the optimal times of a random time(denoted as ρ). In particular, we consider two classes of random times: (1) the last time when the process exits a certain level l; (2) the time when the process reaches its maximum. For each random time, we solve the optimization problem infτ E[λ(τ- ρ)+ +(1-λ)(ρ - τ)+] overall all stopping times. For the last exit time, the process should stop optimally when it runs below some fixed level k the first time, where k is the solution of an explicit defined equation. For the ultimate maximum time, the process should stop optimally when it runs below a boundary which is the maximal positive solution (if exists) of a first-order ordinary differential equation which lies below the line λs for all s > 0 . The second topic solves an optimal consumption and investment problem for a risk-averse investor who is sensitive to declines than to increases of standard living (i.e., the investor is loss averse), and the investment opportunities are constant. We use the tools of stochastic control and duality methods to solve the resulting free-boundary problem in an infinite time horizon. Briefly, the investor consumes constantly when holding a moderate amount of wealth. In bliss time, the investor increases the consumption so that the consumption-wealth ratio reaches some fixed minimum level; in gloom time, the investor decreases the consumption gradually. Moreover, high loss aversion tends to raise the consumption-wealth ratio, but cut the investment-wealth ratio overall.

Le fil rouge de cette thèse est l'étude des processus de Hawkes. Ces processus ponctuels décryptent l'inter-causalité qui peut avoir lieu entre plusieurs séries d'événements. Concrètement, ils déterminent l'influence qu'ont les événements d'une série sur les événements futurs de toutes les autres séries. Par exemple, dans le contexte des réseaux sociaux, ils décrivent à quel point l'action d'un utilisateur, par exemple un Tweet, sera susceptible de déclencher des réactions de la part des autres.Le premier chapitre est une brève introduction sur les processus ponctuels suivie par un approfondissement sur les processus de Hawkes et en particulier sur les propriétés de la paramétrisation à noyaux exponentiels, la plus communément utilisée. Dans le chapitre suivant, nous introduisons une pénalisation adaptative pour modéliser, avec des processus de Hawkes, la propagation de l'information dans les réseaux sociaux. Cette pénalisation est capable de prendre en compte la connaissance a priori des caractéristiques de ces réseaux, telles que les interactions éparses entre utilisateurs ou la structure de communauté, et de les réfléchir sur le modèle estimé. Notre technique utilise des pénalités pondérées dont les poids sont déterminés par une analyse fine de l'erreur de généralisation.Ensuite, nous abordons l'optimisation convexe et les progrès réalisés avec les méthodes stochastiques du premier ordre avec réduction de variance. Le quatrième chapitre est dédié à l'adaptation de ces techniques pour optimiser le terme d'attache aux données le plus couramment utilisé avec les processus de Hawkes. En effet, cette fonction ne vérifie pas l'hypothèse de gradient-Lipschitz habituellement utilisée. Ainsi, nous travaillons avec une autre hypothèse de régularité, et obtenons un taux de convergence linéaire pour une version décalée de Stochastic Dual Coordinate Ascent qui améliore l'état de l'art. De plus, de telles fonctions comportent beaucoup de contraintes linéaires qui sont fréquemment violées par les algorithmes classiques du premier ordre, mais, dans leur version duale ces contraintes sont beaucoup plus aisées à satisfaire. Ainsi, la robustesse de notre algorithme est d'avantage comparable à celle des méthodes du second ordre dont le coût est prohibitif en grandes dimensions.Enfin, le dernier chapitre présente une nouvelle bibliothèque d'apprentissage statistique pour Python 3 avec un accent particulier mis sur les modèles temporels. Appelée tick, cette bibliothèque repose sur une implémentation en C++ et les algorithmes d'optimisation issus de l'état de l'art pour réaliser des estimations très rapides dans un environnement multi-cœurs. Publiée sur Github, cette bibliothèque a été utilisée tout au long de cette thèse pour effectuer des expériences. / The common thread of this thesis is the study of Hawkes processes. These point processes decrypt the cross-causality that occurs across several event series. Namely, they retrieve the influence that the events of one series have on the future events of all series. For example, in the context of social networks, they describe how likely an action of a certain user (such as a Tweet) will trigger reactions from the others.The first chapter consists in a general introduction on point processes followed by a focus on Hawkes processes and more specifically on the properties of the widely used exponential kernels parametrization. In the following chapter, we introduce an adaptive penalization technique to model, with Hawkes processes, the information propagation on social networks. This penalization is able to take into account the prior knowledge on the social network characteristics, such as the sparse interactions between users or the community structure, to reflect them on the estimated model. Our technique uses data-driven weighted penalties induced by a careful analysis of the generalization error.Next, we focus on convex optimization and recall the recent progresses made with stochastic first order methods using variance reduction techniques. The fourth chapter is dedicated to an adaptation of these techniques to optimize the most commonly used goodness-of-fit of Hawkes processes. Indeed, this goodness-of-fit does not meet the gradient-Lipschitz assumption that is required by the latest first order methods. Thus, we work under another smoothness assumption, and obtain a linear convergence rate for a shifted version of Stochastic Dual Coordinate Ascent that improves the current state-of-the-art. Besides, such objectives include many linear constraints that are easily violated by classic first order algorithms, but in the Fenchel-dual problem these constraints are easier to deal with. Hence, our algorithm's robustness is comparable to second order methods that are very expensive in high dimensions.Finally, the last chapter introduces a new statistical learning library for Python 3 with a particular emphasis on time-dependent models, tools for generalized linear models and survival analysis. Called tick, this library relies on a C++ implementation and state-of-the-art optimization algorithms to provide very fast computations in a single node multi-core setting. Open-sourced and published on Github, this library has been used all along this thesis to perform benchmarks and experiments.

This thesis stems from the interest of Holmen group to investigate the opportunitiesavailable for large electricity consumers in the Swedish primary reserve markets.The study performed focuses on one of Holmen's paper mill and it aims at identifyinga load inside the production process that is suitable for providing frequency containmentservices for the grid. The evaluation of the mill's consumption prole and the technicalrequirements of the reserve market led to the identication of the electric boiler coupledwith a steam accumulator as the most appropriate load.Five case study simulating the participation of the mill to dierent energy and reservemarkets have been evaluated. For each case a linear optimization problem has beenformulated. The rst simulation represents the current practice of the mill in relation tothe energy purchased on the spot market (following it will be also referred as referencecase). The second case study (II c.s.) integrates the use of the steam accumulator asa tool to perform thermal load shifting. In the third case study (III c.s.) the mill ismodelled to bid on the spot and primary reserve market by oering some capacity ofthe electric boiler. The last two case studies (IV and V c.s.) recalls the rst and lastpreviously mentioned, but also include the possibility of having energy imbalance. Thismeans that the imbalance settlement operated by eSett will produce an additional costor prot for the mill.The last three problem formulations fall under the denition of stochastic problems,since two random variable are present, namely: average hourly frequency value andimbalance settlement price. The uncertainty of the variables is represented throughscenarios.The outcome derived from the combination of the results for the winter and summercases shows that each strategy brings an economic saving when compared to the referencecase (I c.s.). The less interesting strategies are the ones that do not involve the reservemarket, leading to about 0.03% (II c.s.) and 0.06% (IV c.s.) of saving on the overallyearly energy cost. Contrariwise, by oering FCR-N capacity, the cost of electricitycan be cut by 5.15% (III c.s.) and 6.69% (V c.s.), respectively considering and notconsidering the imbalance settlement. / Avhandlingen har sitt ursprung i skogsindustrikoncernen Holmens intresse att undersökamöjligheten för stora elförbrukare att delta på den svenska primär-reservmarknaden. Studien som utförts fokuserar på ett av Holmens pappersbruk och syftar till att identifiera en elektrisk process som, inom bruksgränserna, är lämplig för att tillhandahålla frekvensregleringstjänster till det nationella nätet. En utvärdering av brukets elförbrukning samt de tekniska krav som ställs på reservmarknaden ledde till att en elektrisk panna med tillkopplad ångackumulator identifierades som mest lämplig.Fem budstrategier som simulerar brukets deltagande till olika energioch reservmarknader har presenterats. För varje strategi är ett linjärt optimeringsproblem formulerat. Den första strategin visar på nuvarande sätt bruket köper elektricitet på spotmarknaden. Den andra strategin integrerar användning av ångackumulatorn som ett verktyg för att utföra termisk lastskiftning. I den tredje modelleras deltagande också på primärreservmarknaden genom att erbjuda en viss kapacitet hos elpannan. De två sista strategierna baseras på den första och tredje, men tillåter i tillägg obalanser vilket innebär en extra kostnad eller möjlig intjäning för bruket.De tre sista problemformuleringarna faller under definitionen stokastiska problem, eftersom två slumpmässiga variabler är närvarande, nämligen: genomsnittligt timfrekvensvärde och priset för obalans. Osäkerheten för variablerna representeras genom scenarier.Resultatet visar att varje strategi ger en ekonomisk besparing jämfört med refer-ensfallet (strategi ett). De mindre intressanta strategierna är de som inte involverarreservmarknaden, vilka endast leder till ca 0,03% och 0,06% minskning av den totalaårliga energikostnaden. Däremot, genom att erbjuda FCR-N-kapacitet kan kostnaden för el minskas med 6,69% och 5,15% beroende s eller ej.

[pt] A volatilidade inerente ao mercado de fretes marítimos e as incertezas relacionadas à demanda de transportes prevista contribuem para a complexidade do problema de dimensionamento da frota. Este trabalho aborda o problema da renovação da frota marítima de uma empresa brasileira do setor de óleo e gás, para o transporte, em viagens de cabotagem e longo curso, de derivados de petróleo. Para tal, é apresentado um modelo estocástico de programação inteira-mista de dois estágios para capaz de gerar indicações de contratos de afretamento a serem realizados considerando incertezas nos níveis de mercado de fretes e na previsão de volume movimentado. O modelo é capaz de fornecer composições de frota capazes de atender as especificações do problema, contudo, para os casos analisados, a avaliação das soluções obtidas ao se considerar a incerteza mostrou potencial de ganho pouco significativo em comparação com uma modelagem similar considerando valores esperados dos parâmetros. Este trabalho evidencia uma situação em que é útil a avaliação das soluções Wait-and-See (WS) e Expected Value of Expected Solution (EEV), menos demandantes computacionalmente, para calcular o potencial ganho da solução do modelo estocástico. / [en] The inherent volatility in the maritime freight market and the uncertainties related to the expected transport demand contribute to the complexity of the fleet size and mix problem. This work addresses the problem of the maritime fleet renewal of a Brazilian oil and gas company, for the transportation, in cabotage and international voyages, of oil products. To this end, we present a two-stage stochastic mixed-integer programming model capable of giving recommendations of which chartering contracts to be performed, considering uncertainties in freight market levels and in the forecasted volume movement. The model is able to provide fleet compositions capable of meeting the problem specifications, however, in the evaluated cases, little gain potential was observed by comparing the stochastic solutions to solutions considering expected parameter values. This work highlights a situation in which the evaluation of the computationally less demanding Waitand-See (WS) and Expected Value of Expected Solution (EEV) solutions is useful to calculate the potential gain of the stochastic model solution.

Lowering the degree of component commonality may yield a higher type-II service level for a periodic review assemble-to-order system that aims to maximize reward. This is achieved via separating inventories of all the shared components for different products. We investigate the optimal bill-of-materials structure for two-product assemble-to-order systems with arbitrary number of components. The inventory of a shared component can be separated or common between different products. We show that an optimal bill-of-materials can be characterized between the following two extremal configurations: either two products share all common components, or they do not share any common component. / Thesis / Doctor of Philosophy (PhD)

In this dissertation, we study the effects of emerging biomass markets on land use changes between alternatives of agricultural production, conventional timber production, and forest woody biomass production for energy use. Along with the uncertainty associated with woody biomass prices and rents, transaction costs incurred to land use play an important role in land allocation decisions and make this study distinct from other work. In Chapter 1, we introduce the background and objectives of our study. In Chapter 2, we analyze the behavior of a risk-neutral private landowner and social planner under uncertainty of woody biomass prices, assuming that there is a market emergence at some unknown time point in the future. Market emergence is characterized by a price jump and a certain timing of the price jump. Six different price jumps and five different timings of bioenergy market emergence are adopted to study their collective effects on land use change between agriculture and forestry. Chapter 3 studies this problem for a risk-averse private landowner. Two measures of relative risk aversion are used to examine how a landowner's preference may affect his or her land use decision. In Chapter 2, we find that, for three different quality categories of land, land rents from forestry increase significantly for higher price jumps and decreases in the length of time until bioenergy market emergence. One of the most important results is concerned with the presence of transaction costs. Here, we find that these costs may require unrealistic market emergence scenarios to lead to bioenergy adoption on any large scale. This result is even more likely with nonlinear transaction costs. Land allocation decisions in Chapter 3 are distinctly different from those in Chapter 2, due to the introduction of landowner risk aversion. In certain market emergence cases, some land units retain in agriculture entirely when the landowner is risk averse . The Chapter 4 studies a stochastic optimization problem of land use, assuming that woody biomass rents follow a stochastic diffusion called geometric Brownian motion that is later discretized by a binomial option pricing approach. The problems in Chapters 2 and 3 assume that the landowner must make all decisions at the beginning of his or her time horizon. This assumption is relaxed in Chapter 4. Now, the landowner is allowed to revise his or her land allocation decision among three alternatives over time as information about market emergence is collected. We observe that the different forms of transaction costs are not as significant as in Chapters 2 and 3. However, different values of volatility of forest biomass rents give rise to different land allocation decisions, especially for the land of high quality. / Ph. D.