Σε αυτήν την εργασία, παρουσιάζουμε τις βασικότερες κλασικές προσεγγίσεις επίλυσης Πολυ-αντικειμενικών Προβλημάτων Βελτιστοποίησης(ΠΠΒ)καθώς και ένα από τα πιο δημοφιλή λογισμικά για επίλυση ΠΠΒ, το NIMBUS. Συγκεκριμένα, δίνουμε τον ορισμό ενός ΠΠΒ, το θεωρητικό υπόβαθρο -- για την καλύτερη κατανόηση των μεθόδων που θα ακολουθήσουν - και τις διαφορές των ΠΠΒ με τα κλασσικά Μονο-αντικειμενικά προβλήματα Βελτιστοποίησης. Επιπλέον, παρουσιάζουμε τις τρεις κύριες κατηγορίες προσέγγισης των ΠΠΒ (μη-αλληλεπιδραστικές, αλληλεπιδραστικές, εξελικτικές) ο διαχωρισμός των οποίων γίνεται ανάλογα με την άμεση ή έμμεση εμπλοκή του Λήπτη Απόφασης. Η μελέτη μας εστιάζεται κυρίως στην κατηγορία των μη-αλληλεπιδραστικών προσεγγίσεων, στην οποία ο ΛΑ εμπλέκεται έμμεσα. Τέλος, ολοκληρώνουμε την μελέτη μας με την αναλυτική παρουσίαση της επίλυσης ενός ΠΠB με την χρήση του λογισμικού NIMBUS. / In this contribution, we study the classical approaches for solving Multi-objective Optimization Problems (MOOP) as well as one of the most popular software that solves MOOP, namely NIMBUS. More specifically, we present the definition and the theoretical background around MOOP and we discuss the differences between MOOP and the classical single-objective optimization problems. We also present the three main categories of approaches of solving MOOP (non-interactive, interactive, evolutionary) that are characterized by the way the Decision Maker participates in the solution. We focus on the first category by analyzing each of the non-interactive approaches. Finally, we conclude by presenting an analytic illustration of an example that solves a MOOP using the NIMBUS software.

Many concrete problems may be cast in a multi-objective optimisation framework. The redundancy of existing methods for solving multi-objective programming problems susceptible to inconsistencies, coupled with the necessity for making in- herent assumptions before using a given method, make it hard for a nonspecialist to choose a method that ¯ts the situation at hand well. Moreover, using a method blindly, as suggested by the hammer principle (when you only have a hammer, you want everything in your hand to be a nail) is an awkward approach at best and a caricatural one at worst. This brings challenges to the design, development, implementation and deployment of a Decision Support System able to choose a method that is appropriate for a given problem and to apply the chosen method to solve the problem under consideration. The choice of method should be made according to the structure of the problem and the decision maker's opinion. The aim here is to embed a sample of methods representing the main multi-objective programming techniques and to help the decision maker find the most appropriate method for his problem. / Decisions Sciences / M. Sc. (Operations Research )

This document aims on aplication of sophisticated software programs to accomplish hydraulic analysis of real water supply, design and optimization measures for improvement of pressure conditions in water network. In this work is stated a list and description of software enabling to accomplish static or longterm hydraulic analysis of water supply when the most world used program EPANET 2.0 is described more deeply. There is described working of a EPANET and his algorithm also there are explain principles on which EPANET is based. During the hydraulic analysis of real system was used sophisticated software EPANET 2.0. With this program was processed hydraulic analysis of chosen water supply system of small consumption area. Based on the results of analysis pressure conditions has been designed and optimized measure to improve pressure conditions in the water network.

With the breakthrough of machine learning techniques, the research concerning music emotion classification has been getting notable progress combining various audio features and state-of-the-art machine learning models. Still, it is known that the way to preprocess music samples and to choose which machine classification algorithm to use depends on data sets and the objective of each project work. The collaborating company of this thesis, Ichigoichie AB, is currently developing a system to categorize music data into positive/negative classes. To enhance the accuracy of the existing system, this project aims to figure out the best model through experiments with six audio features (Mel spectrogram, MFCC, HPSS, Onset, CENS, Tonnetz) and several machine learning models including deep neural network models for the classification task. For each model, hyperparameter tuning is performed and the model evaluation is carried out according to pareto optimality with regard to accuracy and execution time. The results show that the most promising model accomplished 95% correct classification with an execution time of less than 15 seconds. / I och med genombrottet av maskininlärningstekniker har forskning kring känsloklassificering i musik sett betydande framsteg genom att kombinera olikamusikanalysverktyg med nya maskinlärningsmodeller. Trots detta är hur man förbehandlar ljuddatat och valet av vilken maskinklassificeringsalgoritm som ska tillämpas beroende på vilken typ av data man arbetar med samt målet med projektet. Denna uppsats samarbetspartner, Ichigoichie AB, utvecklar för närvarande ett system för att kategorisera musikdata enligt positiva och negativa känslor. För att höja systemets noggrannhet är målet med denna uppsats att experimentellt hitta bästa modellen baserat på sex musik-egenskaper (Mel-spektrogram, MFCC, HPSS, Onset, CENS samt Tonnetz) och ett antal olika maskininlärningsmodeller, inklusive Deep Learning-modeller. Varje modell hyperparameteroptimeras och utvärderas enligt paretooptimalitet med hänsyn till noggrannhet och beräkningstid. Resultaten visar att den mest lovande modellen uppnådde 95% korrekt klassificering med en beräkningstid på mindre än 15 sekunder.

This thesis attempts to provide a coherent view of the idea of ‘justice as fairness’ and, in particular, the ‘difference principle’ expressed by John Rawls in A Theory of Justice. The main focus of the thesis is the difference principle and its limits. Rawls’s conception of ‘justice as fairness’ is based on the thought experiment of the ‘original position’ in which people, considered as free and equal, deliberate under an imagined ‘veil of ignorance,’ i.e. not knowing which social roles or status they would occupy in their society. Rawls then argues that in the original position people come up with two major principles of justice, understood as principles that would be acceptable to people treated as free and equal. The second principle entails the so-called ‘difference principle,’ according to which the inequalities of, say, wealth and authority are just and fair only if they lead to compensating benefits for everybody and particularly the least advantaged. The thesis proceeds, then, by probing whether compared with other theories, , including a discussion of Dahl’s theory of democracy, Rawls’s difference principle could be a proper answer to one of the main questions of social justice. The questions is: how the economic fortune in a society should be distributed among citizens. However, despite Rawls’s aim to develop the difference principle as a practical normative theory, it fails to give us a pragmatic answer. The reason is: the statement of the difference principle fails to take into account one crucial point: to wit, the matter of time. The thesis develops two empirical economic scenarios to illustrate that there is a trade-off between the interests of the poor in short and long period of time. However, this important issue is not considered and discussed by Rawls which makes the theory inapplicable.

Treatment planning for radiation therapy inherently involves tradeoffs, such as between tumor control and normal tissue sparing, between time-efficiency and dose quality, and between nominal plan quality and robustness. The purpose of this thesis is to develop methods that can facilitate decision making related to such tradeoffs. The main focus of the thesis is on multicriteria optimization methods where a representative set of treatment plans are first calculated and the most appropriate plan contained in this representation then selected by the treatment planner through continuous interpolation between the precalculated alternatives. These alternatives constitute a subset of the set of Pareto optimal plans, meaning plans such that no criterion can be improved without a sacrifice in another. Approximation of Pareto optimal sets is first studied with respect to fluence map optimization for intensity-modulated radiation therapy. The approximation error of a discrete representation is minimized by calculation of points one at the time at the location where the distance between an inner and outer approximation of the Pareto set currently attains its maximum. A technique for calculating this distance that is orders of magnitude more efficient than the best previous method is presented. A generalization to distributed computational environments is also proposed. Approximation of Pareto optimal sets is also considered with respect to direct machine parameter optimization. Optimization of this form is used to calculate representations where any interpolated treatment plan is directly deliverable. The fact that finite representations of Pareto optimal sets have approximation errors with respect to Pareto optimality is addressed by a technique that removes these errors by a projection onto the exact Pareto set. Projections are also studied subject to constraints that prevent the dose-volume histogram from deteriorating. Multicriteria optimization is extended to treatment planning for volumetric-modulated arc therapy and intensity-modulated proton therapy. Proton therapy plans that are robust against geometric errors are calculated by optimization of the worst case outcome. The theory for multicriteria optimization is extended to accommodate this formulation. Worst case optimization is shown to be preferable to a previous more conservative method that also protects against uncertainties which cannot be realized in practice. / En viktig aspekt av planering av strålterapibehandlingar är avvägningar mellan behandlingsmål vilka står i konflikt med varandra. Exempel på sådana avvägningar är mellan tumörkontroll och dos till omkringliggande frisk vävnad, mellan behandlingstid och doskvalitet, och mellan nominell plankvalitet och robusthet med avseende på geometriska fel. Denna avhandling syftar till att utveckla metoder som kan underlätta beslutsfattande kring motstridiga behandlingsmål. Primärt studeras en metod för flermålsoptimering där behandlingsplanen väljs genom kontinuerlig interpolation över ett representativt urval av förberäknade alternativ. De förberäknade behandlingsplanerna utgör en delmängd av de Paretooptimala planerna, det vill säga de planer sådana att en förbättring enligt ett kriterium inte kan ske annat än genom en försämring enligt ett annat. Beräkning av en approximativ representation av mängden av Paretooptimala planer studeras först med avseende på fluensoptimering för intensitetsmodulerad strålterapi. Felet för den approximativa representationen minimeras genom att innesluta mängden av Paretooptimala planer mellan inre och yttre approximationer. Dessa approximationer förfinas iterativt genom att varje ny plan genereras där avståndet mellan approximationerna för tillfället är som störst. En teknik för att beräkna det maximala avståndet mellan approximationerna föreslås vilken är flera storleksordningar snabbare än den bästa tidigare kända metoden. En generalisering till distribuerade beräkningsmiljöer föreslås även. Approximation av mängden av Paretooptimala planer studeras även för direkt maskinparameteroptimering, som används för att beräkna representationer där varje interpolerad behandlingsplan är direkt levererbar. Det faktum att en ändlig representation av mängden av Paretooptimala lösningar har ett approximationsfel till Paretooptimalitet hanteras via en metod där en interpolerad behandlingsplan projiceras på Paretomängden. Projektioner studeras även under bivillkor som förhindrar att den interpolerade planens dos-volym histogram kan försämras. Flermålsoptimering utökas till planering av rotationsterapi och intensitetsmodulerad protonterapi. Protonplaner som är robusta mot geometriska fel beräknas genom optimering med avseende på det värsta möjliga utfallet av de föreliggande osäkerheterna. Flermålsoptimering utökas även teoretiskt till att innefatta denna formulering. Nyttan av värsta fallet-optimering jämfört med tidigare mer konservativa metoder som även skyddar mot osäkerheter som inte kan realiseras i praktiken demonstreras experimentellt. / <p>QC 20130527</p>

In interference-limited wireless networks, interference management techniques are important in order to improve the performance of the systems. Given that spectrum and energy are scarce resources in these networks, techniques that exploit the resources efficiently are desired. We consider a set of base stations operating concurrently in the same spectral band. Each base station is equipped with multiple antennas and transmits data to a single-antenna mobile user. This setting corresponds to the multiple-input single-output (MISO) interference channel (IFC). The receivers are assumed to treat interference signals as noise. Moreover, each transmitter is assumed to know the channels between itself and all receivers perfectly. We study the conflict between the transmitter-receiver pairs (links) using models from game theory and microeconomic theory. These models provide solutions to resource allocation problems which in our case correspond to the joint beamforming design at the transmitters. Our interest lies in solutions that are Pareto optimal. Pareto optimality ensures that it is not further possible to improve the performance of any link without reducing the performance of another link. Strategic games in game theory determine the noncooperative choice of strategies of the players. The outcome of a strategic game is a Nash equilibrium. While the Nash equilibrium in the MISO IFC is generally not efficient, we characterize the necessary null-shaping constraints on the strategy space of each transmitter such that the Nash equilibrium outcome is Pareto optimal. An arbitrator is involved in this setting which dictates the constraints at each transmitter. In contrast to strategic games, coalitional games provide cooperative solutions between the players. We study cooperation between the links via coalitional games without transferable utility. Cooperative beamforming schemes considered are either zero forcing transmission or Wiener filter precoding. We characterize the necessary and sufficient conditions under which the core of the coalitional game with zero forcing transmission is not empty. The core solution concept specifies the strategies with which all players have the incentive to cooperate jointly in a grand coalition. While the core only considers the formation of the grand coalition, coalition formation games study coalition dynamics. We utilize a coalition formation algorithm, called merge-and-split, to determine stable link grouping. Numerical results show that while in the low signal-to-noise ratio (SNR) regime noncooperation between the links is efficient, at high SNR all links benefit in forming a grand coalition. Coalition formation shows its significance in the mid SNR regime where subset link cooperation provides joint performance gains. We use the models of exchange and competitive market from microeconomic theory to determine Pareto optimal equilibria in the two-user MISO IFC. In the exchange model, the links are represented as consumers that can trade goods within themselves. The goods in our setting correspond to the parameters of the beamforming vectors necessary to achieve all Pareto optimal points in the utility region. We utilize the conflict representation of the consumers in the Edgeworth box, a graphical tool that depicts the allocation of the goods for the two consumers, to provide closed-form solution to all Pareto optimal outcomes. The exchange equilibria are a subset of the points on the Pareto boundary at which both consumers achieve larger utility then at the Nash equilibrium. We propose a decentralized bargaining process between the consumers which starts at the Nash equilibrium and ends at an outcome arbitrarily close to an exchange equilibrium. The design of the bargaining process relies on a systematic study of the allocations in the Edgeworth box. In comparison to the exchange model, a competitive market additionally defines prices for the goods. The equilibrium in this economy is called Walrasian and corresponds to the prices that equate the demand to the supply of goods. We calculate the unique Walrasian equilibrium and propose a coordination process that is realized by the arbitrator which distributes the Walrasian prices to the consumers. The consumers then calculate in a decentralized manner their optimal demand corresponding to beamforming vectors that achieve the Walrasian equilibrium. This outcome is Pareto optimal and lies in the set of exchange equilibria. In this thesis, based on the game theoretic and microeconomic models, efficient beamforming strategies are proposed that jointly improve the performance of the systems. The gained results are applicable in interference-limited wireless networks requiring either coordination from the arbitrator or direct cooperation between the transmitters.

Investments in space systems are substantial, indivisible, and irreversible, characteristics that make them high-risk, especially when coupled with an uncertain demand environment. Traditional approaches to system design and acquisition, derived from a performance- or cost-centric mindset, incorporate little information about the spacecraft in relation to its environment and its value to its stakeholders. These traditional approaches, while appropriate in stable environments, are ill-suited for the current, distinctly uncertain and rapidly changing technical, and economic conditions; as such, they have to be revisited and adapted to the present context. This thesis proposes that in uncertain environments, decision-making with respect to space system design and acquisition should be value-based, or at a minimum value-informed. This research advances the value-centric paradigm by providing the theoretical basis, foundational frameworks, and supporting analytical tools for value assessment of priced and unpriced space systems. For priced systems, stochastic models of the market environment and financial models of stakeholder preferences are developed and integrated with a spacecraft-sizing tool to assess the system's net present value. The analytical framework is applied to a case study of a communications satellite, with market, financial, and technical data obtained from the satellite operator, Intelsat. The case study investigates the implications of the value-centric versus the cost-centric design and acquisition choices. Results identify the ways in which value-optimal spacecraft design choices are contingent on both technical and market conditions, and that larger spacecraft for example, which reap economies of scale benefits, as reflected by their decreasing cost-per-transponder, are not always the best (most valuable) choices. Market conditions and technical constraints for which convergence occurs between design choices under a cost-centric and a value-centric approach are identified and discussed. In addition, an innovative approach for characterizing value uncertainty through partial moments, a technique used in finance, is adapted to an engineering context and applied to priced space systems. Partial moments disaggregate uncertainty into upside potential and downside risk, and as such, they provide the decision-maker with additional insights for value-uncertainty management in design and acquisition. For unpriced space systems, this research first posits that their value derives from, and can be assessed through, the value of information they provide. To this effect, a Bayesian framework is created to assess system value in which the system is viewed as an information provider and the stakeholder an information recipient. Information has value to stakeholders as it changes their rational beliefs enabling them to yield higher expected pay-offs. Based on this marginal increase in expected pay-offs, a new metric, Value-of-Design (VoD), is introduced to quantify the unpriced system's value. The Bayesian framework is applied to the case of an Earth Science satellite that provides hurricane information to oil rig operators using nested Monte Carlo modeling and simulation. Probability models of stakeholders' beliefs, and economic models of pay-offs are developed and integrated with a spacecraft payload generation tool. The case study investigates the information value generated by each payload, with results pointing to clusters of payload instruments that yielded higher information value, and minimum information thresholds below which it is difficult to justify the acquisition of the system. In addition, an analytical decision tool, probabilistic Pareto fronts, is developed in the Cost-VoD trade space to provide the decision-maker with additional insights into the coupling of a system's probable value generation and its associated cost risk.

The past decades have seen the state of the art in aerospace system design progress from a scope of simple optimization to one including robustness, with the objective of permitting a single system to perform well even in off-nominal future environments. Integrating flexibility, or the capability to easily modify a system after it has been fielded in response to changing environments, into system design represents a further step forward. One challenge in accomplishing this rests in that the decision-maker must consider not only the present system design decision, but also sequential future design and operation decisions. Despite extensive interest in the topic, the state of the art in designing flexibility into aerospace systems, and particularly space systems, tends to be limited to analyses that are qualitative, deterministic, single-objective, and/or limited to consider a single future time period. To address these gaps, this thesis develops a stochastic, multi-objective, and multi-period framework for integrating flexibility into space system design decisions. Central to the framework are five steps. First, system configuration options are identified and costs of switching from one configuration to another are compiled into a cost transition matrix. Second, probabilities that demand on the system will transition from one mission to another are compiled into a mission demand Markov chain. Third, one performance matrix for each design objective is populated to describe how well the identified system configurations perform in each of the identified mission demand environments. The fourth step employs multi-period decision analysis techniques, including Markov decision processes (MDPs) from the field of operations research, to find efficient paths and policies a decision-maker may follow. The final step examines the implications of these paths and policies for the primary goal of informing initial system selection. Overall, this thesis unifies state-centric concepts of flexibility from economics and engineering literature with sequential decision-making techniques from operations research. The end objective of this thesis' framework and its supporting analytic and computational tools is to enable selection of the next-generation space systems today, tailored to decision-maker budget and performance preferences, that will be best able to adapt and perform in a future of changing environments and requirements. Following extensive theoretical development, the framework and its steps are applied to space system planning problems of (1) DARPA-motivated multiple- or distributed-payload satellite selection and (2) NASA human space exploration architecture selection.

Face à l’érosion globale de la biodiversité des écosystèmes aquatiques continentaux, l’identification des mesures de gestion les plus urgentes à mettre en place est cruciale. En s’appuyant sur une approche innovante et multi-facettes de la diversité, les priorités de conservation pour les assemblages de poissons de rivière ont pu être déterminées à l’échelle de la France. La durabilité de ces priorités de conservation face aux principales composantes des changements globaux a ensuite été évaluée afin d’identifier les zones qui protégeront efficacement la biodiversité actuelle dans le futur. La méthodologie développée a finalement été appliquée au réseau hydrographique du département du Pas-de-Calais dans le but d’identifier précisément les priorités locales de conservation et de restauration. Ces outils pourront par la suite être utilisés comme support d’aide à la décision et adaptés selon les besoins des gestionnaires des milieux aquatiques. / The global loss of biodiversity affects freshwater ecosystems, making it crucial to identify the priority management actions in order to protect freshwater biodiversity in an effective and sustainable way. Based on an innovative multi-faceted framework of diversity, the spatial priorities for the conservation of stream fish assemblages have been identified at the scale of France. Their robustness to several drivers of global changes has then been assessed to identify the areas that are likely to efficiently protect the present-day biodiversity in the future. The methodological framework proposed herein has finally been applied to the river network of the Pas-de-Calais department located in northern France to accurately identify the local conservation and restoration priorities. These management tools can be used to support the establishment of management actions in accordance with the needs of the local environmental decision-makers.