Cette thèse porte sur trois questions qui se posent en optimisation multi-objectif. Dansun premier temps, nous étudions l’existence de solutions efficaces via des techniquesde scalarisation. On étend le théorème de Benson du cas convexe à un cas général.De plus, nous examinons d’autres techniques de scalarisation. Dans un second temps,nous abordons la question de robustesse. Nous examinons les concepts proposés dansla littérature sur le sujet. On étend au cas d’optimisation multi-objectif non-linéairela définition de Georgiev et ses collaborateurs. Quelques conditions nécessaires etsuffisantes pour obtenir une solution robuste moyennant des hypothèses appropriéessont données. Les relations entre cette notion de robustesse et certaines définitionsmentionnées sont mises en évidence. Deux types de modifications des fonctions objectifsont traités et les relations entre les solutions faibles/propres/ robustes efficacessont établies. Le dernier chapitre est consacré à l’analyse de sensibilité et de stabilitéen optimisation multi-objectif paramétrée. On montre sous des conditions faibles quela multi-application de l’ensemble des solutions réalisables et des valeurs réalisablessont strictement semi-différentiables. On donne quelques conditions suffisantes pourla semi-différentiabilité de l’ensemble efficace et des valeurs efficaces. De plus, nousétudions la pseudo-Lipschitz continuité des multi-applications ci dessus citées. / In this thesis, three crucial questions arising in multi-objective optimization are investigated.First, the existence of properly efficient solutions via scalarization toolsis studied. A basic theorem credited to Benson is extended from the convex caseto the general case. Some further scalarization techniques are also discussed. Thesecond part of the thesis is devoted to robustness. Various notions from the literatureare briefly reviewed. Afterwards, a norm-based definition given by Georgiev, Lucand Pardalos is generalized to nonlinear multi-objective optimization. Necessary andsufficient conditions for robust solutions under appropriate assumptions are given.Relationships between new robustness notion and some known ones are highlighted.Two kinds of modifications in the objective functions are dealt with and relationshipsbetween the weak/proper/robust efficient solutions of the problems, before and afterthe perturbation, are established. Finally, we discuss the sensitivity analysis andstability in parametrized multi-objective optimization. Strict semi-differentiability ofset-valued mappings of feasible sets and feasible values is proved under appropriateassumptions. Furthermore, some sufficient conditions for semi-differentiability of efficientsets and efficient values are presented. Finally, pseudo-Lipschitz continuity ofaforementioned set-valued mappings is investigated

Today's modern aerospace systems exhibit strong interdisciplinary coupling and require a multidisciplinary, collaborative approach. Analysis methods that were once considered feasible only for advanced and detailed design are now available and even practical at the conceptual design stage. This changing philosophy for conducting conceptual design poses additional challenges beyond those encountered in a low fidelity design of aircraft. This thesis takes some steps towards bridging the gaps in existing technologies and advancing the state-of-the-art in aircraft design. The first part of the thesis proposes a new Pareto front approximation method for multiobjective optimization problems. The method employs a hybrid optimization approach using two derivative free direct search techniques, and is intended for solving blackbox simulation based multiobjective optimization problems with possibly nonsmooth functions where the analytical form of the objectives is not known and/or the evaluation of the objective function(s) is very expensive (very common in multidisciplinary design optimization). A new adaptive weighting scheme is proposed to convert a multiobjective optimization problem to a single objective optimization problem. Results show that the method achieves an arbitrarily close approximation to the Pareto front with a good collection of well-distributed nondominated points. The second part deals with the interdisciplinary data communication issues involved in a collaborative mutidisciplinary aircraft design environment. Efficient transfer, sharing, and manipulation of design and analysis data in a collaborative environment demands a formal structured representation of data. XML, a W3C recommendation, is one such standard concomitant with a number of powerful capabilities that alleviate interoperability issues. A compact, generic, and comprehensive XML schema for an aircraft design markup language (ADML) is proposed here to provide a common language for data communication, and to improve efficiency and productivity within a multidisciplinary, collaborative environment. An important feature of the proposed schema is the very expressive and efficient low level schemata. As a proof of concept the schema is used to encode an entire Convair B58. As the complexity of models and number of disciplines increases, the reduction in effort to exchange data models and analysis results in ADML also increases. / Ph. D.

<p>The properties of neutron stars and black holes are investigated within a class of alternative theories of gravity known as Scalar-Tensor theories, which extend General Relativity by introducing additional light scalar fields to mediate the gravitational interaction.</p> <p>It has been known since 1993 that neutron stars in certain Scalar-Tensor theories may undergo ‘scalarization’ phase transitions. The Weak Central Coupling (WCC) expansion is introduced for the purpose of describing scalarization in a perturbative manner, and the leading-order WCC coefficients are calculated analytically for constant-density stars. Such stars are found to scalarize, and the critical value of the quadratic scalar-matter coupling parameter β_s = −4.329 for the phase transition is found to be similar to that of more realistic neutron star models.</p> <p>The influence of cosmological and galactic effects on the structure of an otherwise isolated black hole in Scalar-Tensor gravity may be described by incorporating the Miracle Hair Growth Formula discovered by Jacobson in 1999, a perturbative black hole solution with scalar hair induced by time-dependent boundary conditions at spatial infinity. It is found that a double-black-hole binary (DBHB) subject to these boundary conditions is inadequately described by the Eardley Lagrangian and emits scalar dipole radiation.</p> <p>Combining this result with the absence of observable dipole radiation from quasar OJ287 (whose quasi-periodic ‘outbursts’ are consistent with the predictions of a general-relativistic DBHB model at the 6% level) yields the bound |φ/Mpl| < (16 days)^-1 on the cosmological time variation of canonically-normalized light (m < 10⁻²³ eV) scalar fields at redshift z ∼ 0.3.</p> / Doctor of Philosophy (PhD)

Reinforcement Learning (RL) has in recent years become a core method for sequential decision making in complex dynamical systems, being of great interest to support improvements in scheduling problems. This could prove important to areas in the newer generation of cellular networks. One such area is the base stations scheduler which allocates radio resources to users. This is posed as large-scale optmization problem which needs to be solved in millisecond intervals, while at the same time accounting for multiple, sometimes conflicting, objectives like latency or Quality of Service requirements. In this thesis, multi-objective RL (MORL) solutions are proposed and evaluated in order to identify desired features for novel applications to the scheduling problem. The posed solution classes were tested in common MORL benchmark environments such as Deep Sea Treasure for efficient and informative evaluation of features. It was ultimately tested in environments to solve combinatorial optmization and scheduling problems. The results indicate that outer-loop multi-policy solutions are able to produce models that comply with desired features for scheduling. A multi-policy multi-objective deep Q-network was implemented and showed it can produce an adaptive-at-run-time discrete model, based on an outer-loop approach that calls a single-policy algorithm. The presented approach does not increase in complexity when adding objectives but generally requires larger sampling quantities for convergence. Differing scalarization techniques of the reward was tested, indicating effect on variance that could effect performance in certain environment characteristics. / Försärkningsinlärning som en gångbar metod för sekventiellt beslutsfattande i komplexa dynamiska system har ökat under de senaste åren tack vare förbättrade hårdvaru möjligheter. Intressenter av denna teknik finns bland annat inom telekom-indistrin vars aktörer har som mål att uteveckla nya generationens mobilnätverk. En av de grundläggande funktionerna i en basstation är scheduleraren vars uppgift är att allokera radio resurser till användare i nätverket. Detta ställs med fördel upp som ett optimeringsproblem som nödvändiggör att problemet måste lösas på millisekund nivå samtidigt som den kan ta flera typer av mål i beaktning, såsom QoS krav och latens. I detta examensarbete så presenteras och utvärderas förstärningsinlärnings algoritmer för flera mål inom flera lösningsklasser i syfte att identifiera önskvärda funktioner för nya tillämpningar inom radio resurs schemaläggning. De presenterade lösningsklasserna av algoritmer testades i vanligt förekommande riktmärkesmiljöer för denna typ av teknik såsom Deep Sea Treasure för att på effektivt sätt utvärdera de kvalitéer och funktioner varje algoritm har. Slutligen testades lösningen i miljöer inom kombinatorisk optimering och schemaläggning. Resultaten indikerar att fler-policy lösningar har kapaciteten att producera modeller som ligger inom de krav problemet kräver. Fler-policy modeller baserade på djupa Q-närverk av flera mål kunde framställa adaptiva, diskreta realtidsmodeller. Denna lösning ökar inte komplexiteten när fler mål läggs till men har generellt behov av större mängder samplade preferenser för att konvergera. Olika skaläriseringstekniker av belöningen testades och indikerade att dessa påverkade variansen, vilket i vissa typer av miljö konfigurationer påverkade resultaten.