Network virtualization has become a primary enabler to solve the internet ossi- fication problem. It allows to run multiple architectures or protocols on a shared physical infrastructure. One of the important aspects of network virtualization is to have a virtual network (VN) mapping technique which uses the substrate resources efficiently. Currently, there exists very few VN mapping techniques and there is no common evaluation strategy which can test these algorithms effectively. In this thesis, we advocate the need for such a tool and develop it by considering a wide spectrum of parameters and simulation scenarios. We also provide various performance metrics and do a comparison study of the existing algorithms. Based on the comparative study, we point out the positives and negatives of the existing mapping algorithms and propose a new LP formulation based on Hub location approach that efficiently allocates substrate resources to the virtual network requests. Our results show that our algorithm does better in terms of number of successful network mappings and average time to map while balancing load on the network.

This thesis analyzes the mean variance optimization problem with respect to cardinalityconstraints. The aim of this thesis is to figure out how much of an impact transactionchanges has on the profit and risk of a portfolio. We solve the problem by implementingmixed integer programming (MIP) and solving the problem by using the Gurobi solver.In doing this, we create a mathematical model that enforces the amount of transactionchanges from the initial portfolio. Our results is later showed in an Efficient Frontier,to see how the profit and risk are changing depending on the transaction changes.Overall, this thesis demonstrates that the application of MIP is an effective approachto solve the mean variance optimization problem and can lead to improved investmentoutcomes.

A characteristic challenge of software development is the management of omnipresent change. Classically, this constant change is driven by customers changing their requirements. The wish to optimally leverage available resources opens another source of change: the software systems environment. Software is tailored to specific platforms (e.g., hardware architectures) resulting in many variants of the same software optimized for different environments. If the environment changes, a different variant is to be used, i.e., the system has to reconfigure to the variant optimized for the arisen situation. The automation of such adjustments is subject to the research community of self-adaptive systems. The basic principle is a control loop, as known from control theory. The system (and environment) is continuously monitored, the collected data is analyzed and decisions for or against a reconfiguration are computed and realized. Central problems in this field, which are addressed in this thesis, are the management of interdependencies between non-functional properties of the system, the handling of multiple criteria subject to decision making and the scalability. In this thesis, a novel approach to self-adaptive software--Multi-Quality Auto-Tuning (MQuAT)--is presented, which provides design and operation principles for software systems which automatically provide the best possible utility to the user while producing the least possible cost. For this purpose, a component model has been developed, enabling the software developer to design and implement self-optimizing software systems in a model-driven way. This component model allows for the specification of the structure as well as the behavior of the system and is capable of covering the runtime state of the system. The notion of quality contracts is utilized to cover the non-functional behavior and, especially, the dependencies between non-functional properties of the system. At runtime the component model covers the runtime state of the system. This runtime model is used in combination with the contracts to generate optimization problems in different formalisms (Integer Linear Programming (ILP), Pseudo-Boolean Optimization (PBO), Ant Colony Optimization (ACO) and Multi-Objective Integer Linear Programming (MOILP)). Standard solvers are applied to derive solutions to these problems, which represent reconfiguration decisions, if the identified configuration differs from the current. Each approach is empirically evaluated in terms of its scalability showing the feasibility of all approaches, except for ACO, the superiority of ILP over PBO and the limits of all approaches: 100 component types for ILP, 30 for PBO, 10 for ACO and 30 for 2-objective MOILP. In presence of more than two objective functions the MOILP approach is shown to be infeasible.

[pt] Este trabalho trata do problema real de avaliar a capacidade de processamento de pátios ferroviários planos de classificação. Nesses pátios, os vagões são recebidos em trens e movimentam respeitando a disposição dos trilhos e a formação sequencial do trem de saída. Movimentações ineficientes implicam em uma capacidade de processamento inferior à potencial do pátio dado seu layout. O objetivo desta pesquisa é descrever o problema e incitar um método capaz de calcular a capacidade de processamento de pátios ferroviários planos de classificação no horizonte estratégico, indicando se existe ou não a necessidade de um projeto de expansão para garantir atendimento à demanda prevista. O problema foi modelado através de programação linear inteira mista (MILP) baseado na teoria de sequenciamento de produção. O modelo foi aplicado em instâncias de teste, reproduzindo movimentações reais de vagões, e provou avaliar diferentes layouts adequadamente, porém com elevado tempo de execução. A inicialização de algumas variáveis binárias do modelo permitiu um incremento de tamanho nas instâncias, porém ainda inviável para aplicação na prática. / [en] This work deals with the real problem of evaluating the processing capacity of flat rail classification yards. In these yards, the railway cars are received on trains and move respecting the car sequence of the outgoing train. Inefficient movements imply a lower processing capacity than the yard s potential given its layout. The objective of this research is to describe the problem and to incite a method capable of calculating the processing capacity of flat rail classification yards in the strategic horizon, indicating whether or not there is a need for an expansion project to ensure meeting the expected demand. The problem was modeled using mixed integer linear programming (MILP) based on production scheduling theory. The model was applied to test instances, reproducing real railway car movements, and proved to evaluate different layouts properly, but with a high execution time. The initialization of some binary variables of the model allowed an increase in the size of the instances, however it is still unfeasible for practical application.

Swedish home care industry has been facing both external and internal problems, such as ageing population, varying quality and unsatisfactory continuity. Accordingly, workforce scheduling system, as one of the most common and useful software within home care planning nowadays, is in need of constant improvement and upgrading. This master’s thesis aimed to explore and analyze improvement potential of an established workforce scheduling system for an IT-company. The thesis was divided into two phases, of which a pre-study in Phase I tried to understand the planning process for planners and identify the perceived problems and shortcomings of the current system from a planner’s perspective. Based on the analysis from the pre-study, the caregiver continuity was chosen as the research area for Phase II. The current system was re-implemented and was modelled as an optimization problem. Furthermore, the system mainly consisted of two key parts, mixed integer linear programming (MILP) and heuristics. Different approaches in terms of modifications in both MILP and heuristics were applied to the re-implemented system. The performance of the modifications was measured by multiple evaluation indicators. The test results showed that there was a potential to improve caregiver continuity with 1.2% to almost 13% depending on the modification type. The modifications were lastly suggested for further examination regarding their practical appropriateness by applying them to the current running algorithm. / Den svenska hemtjänsten möter både yttre och inre problem såsom åldrande befolkning, varierande kvalitet och bristande kontinuitet. Schemaläggningssystemet som är en av de vanligaste och användbaraste programvarorna inom hemtjänsten behöver därmed en ständig förbättring och uppgradering som bemöter de existerande utmaningarna. Detta examensarbete hade som syfte att utforska och analysera förbättringspotentialen av ett etablerat schemaläggningssystem för ett ITföretag. Arbetet var indelat i två faser, varav förstudien i Fas I försökte förstå planerarnas planeringsprocesser och identifiera upplevda problem och brister i det nuvarande systemet utifrån ett planerares perspektiv. Baserat på analysen från förstudien, personalkontinuitet valdes som ett forskningsområde för Fas II. Nuvarande systemet implementerades om och det modellerades som ett optimeringsproblem. Systemet bestod huvudsakligen av två nyckeldelar, blandat heltalslinjärprogrammering (MILP) och heuristik. Olika metoder i form av modifieringar i både MILP och heuristik tillämpades på det omimplementerade systemet. Modifieringarnas prestanda mättes sedan med flera utvärderingsindikatorer. Testresultaten visade att, beroende på vilken modifiering det gäller, fanns det en potential att förbättra personalkontinuiteten med 1,2% till nästan 13%. Det föreslogs slutligen att modifieringarnas praktiska lämplighet behövs undersökas ytterligare genom att applicera det på det nuvarande systemet som är i drift.

This master thesis in optimization and systems theory is a development of two different optimization models formulated to schedule multi-skilled agents for contact centers depending on the forecasted demand, assigned by Teleopti. Four mixed integer linear programming models are created with the optimization programming language GAMS and solved by the internet based solver NEOS. Two of the models are formulated to perform an optimal scheduling that matches a forecasted demand per skill and day and the remaining two models are formulated to perform an optimal scheduling that matches a forecasted demand per skill, day and half hour. The first two models are referred to as the Basic Models and the second two are referred to as the Complex Models. The Basic Models includes seven constraints and the Complex Model includes nine constraints, describing regulations at the contact center. The main goal of the project is to find an optimal solution that results in an as even distribution of under or over scheduling. The scheduling optimization covers a period of 28 days, starting on a Monday which results in four weeks. The optimization models are based on two sets of data, there are 104 assigned agents that possesses one, two or three of the skills Channel, Direct and Product. All agents are bound to work according to a contract specified through the constraints. In the Basic Model the forecasted demand is given in amount of hours per day and skill, the demand is non-cyclical. In the Complex model the forecasted demand is given in amount of half hours per day, skill and half hour. Each day is scheduled from 7 a.m. to 11 p.m. resulting in 32 available half hours. All optimization models are developed to correctly mathematically formulate the constraints specified by Teleopti. Any non-linear equation that arises are linearized to maintain linearity, this is favourable in the sense of computational time solving the models. The objective functions in this thesis are formulated to describe the main goal of even distribution as correctly as possible. The result for the Basic Model shows that an optimal solution is achieved after 34 seconds. This model contains 169,080 variables and 39,913 equations. In the Complex Models integer solutions are achieved, but no optimal solution is found in 8 hours of computational time. The larger Complex Model contains 9,385,984 variables and 1,052,253 equations and the smaller Complex Model contains 5,596,952 variables and 210,685 equations. Teleopti’s scheduler produces an integer solution matching the Complex Model in 4 minutes. / Detta examensarbete i optimering och systemteori är framtagningen av två olika optimeringsmodeller formulerade för att schemalägga multikompetenta agenter för kontaktcenters beroende av den förväntade efterfrågan, tilldelad av Teleopti. Fyra blandade heltals linjära programmeringsmodeller skapas med optimeringsprogrammeringsspråket GAMS och löses av den internetbaserade lösaren NEOS. Två av modellerna är formulerade för att utföra en optimal schemaläggning som matchar en prognostiserad efterfrågan per skicklighet och dag och de återstående två modellerna är formulerade för att utföra en optimal schemaläggning som matchar en prognostiserad efterfrågan per färdighet, dag och en halvtimme. De två första modellerna i detta arbete benämns de Grundläggande Modellerna och de resterande två benämns de Komplexa Modellerna. Grundmodellerna inkluderar sju bivillkor och de Komplexa modellerna innehåller nio bivillkor, vilka beskriver arbetsvillkoren på kontaktcentret. Projektets huvudmål är att hitta en optimal lösning som resulterar i en jämn fördelning av under- eller överschemaläggning. Den schemalagda optimeringen täcker en period av 28 dagar, vilken börjar på en måndag vilket resulterar i fyra veckor. Optimeringsmodellerna är baserade på två uppsättningar data, det finns 104 tillgängliga agenter vilka har en, två eller tre av kompetenserna Channel, Direct och Product. Alla agenter är bundna att arbeta enligt det kontrakt som specificeras genom bivillkoren. I grundmodellen anges den prognostiserade efterfrågan i timmar per dygn och kompetens, efterfrågan är icke-cyklisk. I den komplexa modellen anges den beräknade efterfrågan i mängd halvtimmar per dag, kompetens och halvtimme. Varje dag är schemalagd från kl. 07.00 till 23.00 vilket resulterar i 32 tillgängliga halvtimmar. Alla optimeringsmodeller är utvecklade för att matematiskt beskriva de begränsningar som Teleopti specificerar. Alla icke-linjära ekvationer som uppstår linjäriseras för att upprätthålla linjäritet, detta är gynnsamt i avseendet mängd tid beräkningen av modellerna tar. Målfunktionerna i detta arbete är formulerade för att beskriva huvudmålet för jämn distribution så korrekt som möjligt. Resultatet för grundmodellen visar att en optimal lösning uppnås efter 34 sekunder. Denna modell innehåller 169,080 variabler och 39,913 ekvationer. I de komplexa modellerna uppnås heltalslösningar, men ingen optimal lösning hittas på 8 timmars beräkningstid. Den större komplexa modellen innehåller 9,385,984 variabler och 1,052,253 ekvationer och den mindre komplexa modellen innehåller 5,596,952 variabler och 210,665 ekvationer. Teleoptis schemaläggare producerar en heltalslösning som matchar den komplexa modellen på 4 minuter.

As energy demands increase and energy resources change, the traditional energy system has been upgraded and reconstructed for human society development and sustainability. Considerable studies have been conducted in energy expansion planning and electricity generation operations by mainly considering the integration of traditional fossil fuel generation with renewable generation. Because the energy market is full of uncertainty, we realize that these uncertainties have continuously challenged market design and operations, even a national energy policy. In fact, only a few considerations were given to the optimization of energy expansion and generation taking into account the variability and uncertainty of energy supply and demand in energy markets. This usually causes an energy system unreliable to cope with unexpected changes, such as a surge in fuel price, a sudden drop of demand, or a large renewable supply fluctuation. Thus, for an overall energy system, optimizing a long-term expansion planning and market operation in a stochastic environment are crucial to improve the system's reliability and robustness. As little consideration was paid to imposing risk measure on the power management system, this dissertation discusses applying risk-constrained stochastic programming to improve the efficiency, reliability and economics of energy expansion and electric power generation, respectively. Considering the supply-demand uncertainties affecting the energy system stability, three different optimization strategies are proposed to enhance the overall reliability and sustainability of an energy system. The first strategy is to optimize the regional energy expansion planning which focuses on capacity expansion of natural gas system, power generation system and renewable energy system, in addition to transmission network. With strong support of NG and electric facilities, the second strategy provides an optimal day-ahead scheduling for electric power generation system incorporating with non-generation resources, i.e. demand response and energy storage. Because of risk aversion, this generation scheduling enables a power system qualified with higher reliability and promotes non-generation resources in smart grid. To take advantage of power generation sources, the third strategy strengthens the change of the traditional energy reserve requirements to risk constraints but ensuring the same level of systems reliability In this way we can maximize the use of existing resources to accommodate internal or/and external changes in a power system. All problems are formulated by stochastic mixed integer programming, particularly considering the uncertainties from fuel price, renewable energy output and electricity demand over time. Taking the benefit of models structure, new decomposition strategies are proposed to decompose the stochastic unit commitment problems which are then solved by an enhanced Benders Decomposition algorithm. Compared to the classic Benders Decomposition, this proposed solution approach is able to increase convergence speed and thus reduce 25% of computation times on the same cases.

Yes / This article proposes a novel technique for operation of distribution networks with considering active network management (ANM) schemes and demand response (DR) within a joint active and reactive distribution market environment. The objective of the proposed model is to maximize social welfare using market-based joint active and reactive optimal power flow. First, the intermittent behavior of renewable sources (solar irradiance, wind speed) and load demands is modeled through scenario-tree technique. Then, a network frame is recast using mixed-integer linear programming, which is solvable using efficient off-the-shelf branch-and cut solvers. Additionaly, this article explores the impact of wind and solar power penetration on the active and reactive distribution locational prices within the distribution market environment with integration of ANM schemes and DR. A realistic case study (16-bus UK generic medium voltage distribution system) is used to demonstrate the effectiveness of the proposed method. / This work was supported in part by the Ministry of Higher Education Scientific Research in Iraq and in part by British Academy under Grant GCRFNGR3\1541.

[pt] Nesse trabalho, estudamos online packing integer programs, cujas colunas são reveladas uma a uma. Já que algoritmos ótimos foram encontrados para o modelo RANDOMORDER– onde a ordem na qual as colunas são reveladas para o algoritmo é aleatória – o foco da área se voltou para modelo menos otimistas. Um desses modelos é o modelo MIXED, no qual algumas colunas são ordenadas de forma adversária, enquanto outras chegam em ordem aleatória. Pouquíssimos resultados são conhecidos para online packing IPs no modelo MIXED, que é o objeto do nosso estudo. Consideramos problemas de online packing com d dimensões de ocupação (d restrições de empacotamento), cada uma com capacidade B. Assumimos que todas as recompensas e ocupações dos itens estão no intervalo [0, 1]. O objetivo do estudo é projetar um algoritmo no qual a presença de alguns itens adversários tenha um efeito limitado na competitividade do algoritmo relativa às colunas de ordem aleatória. Portanto, usamos como benchmark OPTStoch, que é o valor da solução ótima offline que considera apenas a parte aleatória da instância. Apresentamos um algoritmo que obtém recompensas de pelo menos (1 − 5lambda − Ó de epsilon)OPTStoch com alta probabilidade, onde lambda é a fração de colunas em ordem adversária. Para conseguir tal garantia, projetamos um algoritmo primal-dual onde as decisões são tomadas pelo algoritmo pela avaliação da recompensa e ocupação de cada item, de acordo com as variáveis duais do programa inteiro. Entretanto, diferentemente dos algoritmos primais-duais para o modelo RANDOMORDER, não podemos estimar as variáveis duais pela resolução de um problema reduzido. A causa disso é que, no modelo MIXED, um adversário pode facilmente manipular algumas colunas, para atrapalhar nossa estimação. Para contornar isso, propomos o uso de tecnicas conhecidas de online learning para aprender as variáveis duais do problema de forma online, conforme o problema progride. / [en] We study online packing integer programs, where the columns arrive one by one. Since optimal algorithms were found for the RANDOMORDER model – where columns arrive in random order – much focus of the area has been on less optimistic models. One of those models is the MIXED model, where some columns are adversarially ordered, while others come in random-order. Very few results are known for packing IPs in the MIXED model, which is the object of our study. We consider online IPs with d occupation dimensions (d packing constraints), each one with capacity (or right-hand side) B. We also assume all items rewards and occupations to be less or equal to 1. Our goal is to design an algorithm where the presence of adversarial columns has a limited effect on the algorithm s competitiveness relative to the random-order columns. Thus, we use OPTStoch – the offline optimal solution considering only the random-order part of the input – as a benchmark.We present an algorithm that, relative to OPTStoch, is (1−5 lambda− OBig O of epsilon)-competitive with high probability, where lambda is the fraction of adversarial columns. In order to achieve such a guarantee, we make use of a primal-dual algorithm where the decision variables are set by evaluating each item s reward and occupation according to the dual variables of the IP, like other algorithms for the RANDOMORDER model do. However, we can t hope to estimate those dual variables by solving a scaled version of problem, because they could easily be manipulated by an adversary in the MIXED model. Our solution was to use online learning techniques to learn all aspects of the dual variables in an online fashion, as the problem progresses.

With increasing shares of variable renewable energy sources in the power mix, the need for energy storage solutions is projected to increase as well. Storage can in such combined systems help mitigate the issues with relying on intermittent sources by time-shifting the supply and smoothing out frequency fluctuations, to name some examples. This thesis has focused on Azelio ABs flagship product, the TES.POD, which is a long-duration thermal energy storage technology. When integrated with, for example, solar PV power, the TES.POD can store excess energy and dispatch it during times of low supply or when during the evening/night. The aim of the thesis has been the development of a day-ahead dispatch optimization tool for systems that include multiple TES.PODs, combined into a Cluster, and solar PV. The model was to be built using the Python programming language and based on Mixed-Integer-Linear-Programming (MILP) methods. The PV+storage system was then allowed to be connected to supplementary power sources such as a larger electric grid, or diesel generators in off-grid locations. The purpose of the optimization model is to find the most economic way to operate the individual TES.PODs while also keeping track of other system components, using a cost-based objective function (minimize costs). A focus has been on using high time resolution (small time step) in order to investigate the impact that the TES.PODs dynamic constraints has on operation. Another strength compared to pre-existing models was the ability to operate individual units indifferent to each other, as opposed to having them all operated in unison. Final results from benchmarking tests and two case studies indicated that using the optimization tool with smaller time steps had an effect on key indicators, and could lead to improved economy in the system. It was observed in both cases that the cost of electricity was reduced by running the optimization tool with time steps of either two or three minutes when compared with using an hourly resolution. Furthermore, several usage parameters for the TES.PODs, notably the total amount of operated hours and energy output per cycle, saw improvements which could lead to reduced cost of operation and maintenance. While not the main intent, testing different Cluster sizes and amount of installed PV capacity with the model, it could also be used in strategic decisions for system sizing. However, due to rapidly growing computational times in systems with large TES.POD clusters and using smaller time steps, the possibility of adding more complexity to the model in future work must be done with caution. To combat this issue, either improvements to the model formulation could be attempted, or by using more powerful hardware or optimizer (imported software algorithm that handles solving the model).