This thesis consists of an introduction and sevenindependent, but closely related, papers which all deal withproblems in structural optimization. In particular, we considermodels and methods for global optimization of problems intopology design of discrete and continuum structures. In the first four papers of the thesis the nonconvex problemof minimizing the weight of a truss structure subject to stressconstraints is considered. First itis shown that a certainsubclass of these problems can equivalently be cast as linearprograms and thus efficiently solved to global optimality.Thereafter, the behavior of a certain well-known perturbationtechnique is studied. It is concluded that, in practice, thistechnique can not guarantee that a global minimizer is found.Finally, a convergent continuous branch-and-bound method forglobal optimization of minimum weight problems with stress,displacement, and local buckling constraints is developed.Using this method, several problems taken from the literatureare solved with a proof of global optimality for the firsttime. The last three papers of the thesis deal with topologyoptimization of discretized continuum structures. Theseproblems are usually modeled as mixed or pure nonlinear 0-1programs. First, the behavior of certain often usedpenalization methods for minimum compliance problems isstudied. It is concluded that these methods may fail to producea zero-one solution to the considered problem. To remedy this,a material interpolation scheme based on a rational functionsuch that compli- ance becomes a concave function is proposed.Finally, it is shown that a broad range of nonlinear 0-1topology optimization problems, including stress- anddisplacement-constrained minimum weight problems, canequivalently be modeled as linear mixed 0-1 programs. Thisresult implies that any of the standard methods available forgeneral linear integer programming can now be used on topologyoptimization problems. <b>Keywords:</b>topology optimization, global optimization,stress constraints, linear programming, mixed integerprogramming, branch-and-bound.

This thesis contributes to theoretical and quantitative aspects of machine scheduling. In fact, it is dedicated to the issue of scheduling n jobs on one single machine. The scope is limited to deterministic problems - i.e. those with all data available and known with certainty in advance - with tardiness involved objectives; hence, the common denominator of all problems addressed are jobs with a predetermined due date assigned to. A job is finished on time as long as it is completed before its due date, otherwise it is said to be tardy. Since the single machine utilized is assumed to be restricted to process at most one job at a time, the aim is to find a proper sequence - a schedule - of how to process the jobs in order to best fulfill a certain objective. The contribution of this thesis aims at giving a state of the art survey and detailed review of research effort considering the objectives "minimizing the number of tardy jobs" and "minimizing the weighted number of tardy jobs". Further, the objectives of "minimizing the total tardiness", "minimizing the total weighted tardiness" and "minimizing the maximum tardiness" are adumbrated but reduced to a rough overview of research effort made.

In certain applications involving direction of arrival (DOA) estimation the operator may have a-priori information on some of the DOAs. This information could refer to a target known to be present at a certain position or to a reflection. In this study, the authors investigate a methodology for array processing that exploits the information on the known DOAs for estimating the unknown DOAs as accurately as possible. Algorithms are presented that can efficiently handle the case of both correlated and uncorrelated sources when the receiver is a uniform linear array. The authors find a major improvement in estimator accuracy in feasible scenarios, and they compare the estimator performance to the corresponding theoretical stochastic Cramer-Rao bounds as well as to the performance of other methods capable of exploiting such prior knowledge. In addition, real data from an ultra-sound array is applied to the investigated estimators. / <p>QC 20130107</p>

Data aggregation is an important technique in wireless sensor networks. The data are gathered together by data fusion routines along the routing path, which is called data-centralized routing. We propose a localized, Delay-bounded and Energy-efficient Data Aggregation framework(DEDA) based on the novel concept of DEsired Progress (DEP). This framework works under request-driven networks with realistic MAC layer protocols. It is based on localized minimal spanning tree (LMST) which is an energy-efficient structure. Besides the energy consideration, delay reliability is also considered by means of the DEP. A node’s DEP reflects its desired progress in LMST which should be largely satisfied. Hence, the LMST edges might be replaced by unit disk graph (UDG) edges which can progress further in LMST. The DEP metric is rooted on realistic degree-based delay model so that DEDA increases the delay reliability to a large extent compared to other hop-based algorithms. We also combine our DEDA framework with area coverage and localized connected dominating set algorithms to achieve two more resilient DEDA implementations: A-DEDA and AC-DEDA. The simulation results confirm that our original DEDA and its two enhanced variants save more energy and attain a higher delay reliability ratio than existing protocols.

Communication complexity is an area of complexity theory that studies an abstract model of computation called a communication protocol. In a $k$-player communication protocol, an input to a known function is partitioned into $k$ pieces of $n$ bits each, and each piece is assigned to one of the players in the protocol. The goal of the players is to evaluate the function on the distributed input by using as little communication as possible. In a Number-On-Forehead (NOF) protocol, the input piece assigned to each player is metaphorically placed on that player's forehead, so that each player sees everyone else's input but its own. In a Number-In-Hand (NIH) protocol, the piece assigned to each player is seen only by that player. Overall, the study of communication protocols has been used to obtain lower bounds and impossibility results for a wide variety of other models of computation. Two of the main contributions presented in this thesis are negative results on the NOF model of communication, identifying limitations of NOF protocols. Together, these results consitute stepping stones towards a better fundamental understanding of this model. As the first contribution, we show that randomized NOF protocols are exponentially more powerful than deterministic NOF protocols, as long as $k \le n^c$ for some constant $c$. As the second contribution, we show that nondeterministic NOF protocols are exponentially more powerful than randomized NOF protocols, as long as $k \le \delta \cdot \log n$ for some constant $\delta < 1$. For the third major contribution, we turn to the NIH model and we present a positive result. Informally, we show that a NIH communication protocol for a function $f$ can simulate a Stack Machine (a Turing Machine augmented with a stack) for a related function $F$, consisting of several instances of $f$ bundled together. Using this simulation and known communication complexity lower bounds, we obtain the first known (space vs. number of passes) trade-off lower bounds for Stack Machines.

A Multiple-Input Multiple Output (MIMO) radar can be broadly defined as a radar system employing multiple transmit waveforms and having the ability to jointly process signals received at multiple receive antennas. In terms of configurations, the antennas can be widely separated or co-located. The first part of the thesis is on detection under Gaussian and non-Gaussian environments using a MIMO radar which contains several widely separated subarrays with one or more elements each. Two different situations are considered. Firstly, we consider that the interference is Gaussian but correlation between subarrays can arise due to insufficient spacing and the imperfect orthogonality of waveforms. Secondly, we consider that the interference is non-Gaussian, a situation which arises under sea and ground clutter and when the resolution is very high. The second part is on the application of MIMO techniques to Space-Time Adaptive Processing (STAP). The coherent MIMO configuration is studied in terms of antenna element distribution and inter-element spacing to improve detection and estimation performance. A preliminary study is also done on the use of spatial diversity to improve detection stability w.r.t. target Radar Cross Section (RCS) fluctuations and velocity direction changes.

Communication complexity is an area of complexity theory that studies an abstract model of computation called a communication protocol. In a $k$-player communication protocol, an input to a known function is partitioned into $k$ pieces of $n$ bits each, and each piece is assigned to one of the players in the protocol. The goal of the players is to evaluate the function on the distributed input by using as little communication as possible. In a Number-On-Forehead (NOF) protocol, the input piece assigned to each player is metaphorically placed on that player's forehead, so that each player sees everyone else's input but its own. In a Number-In-Hand (NIH) protocol, the piece assigned to each player is seen only by that player. Overall, the study of communication protocols has been used to obtain lower bounds and impossibility results for a wide variety of other models of computation. Two of the main contributions presented in this thesis are negative results on the NOF model of communication, identifying limitations of NOF protocols. Together, these results consitute stepping stones towards a better fundamental understanding of this model. As the first contribution, we show that randomized NOF protocols are exponentially more powerful than deterministic NOF protocols, as long as $k \le n^c$ for some constant $c$. As the second contribution, we show that nondeterministic NOF protocols are exponentially more powerful than randomized NOF protocols, as long as $k \le \delta \cdot \log n$ for some constant $\delta < 1$. For the third major contribution, we turn to the NIH model and we present a positive result. Informally, we show that a NIH communication protocol for a function $f$ can simulate a Stack Machine (a Turing Machine augmented with a stack) for a related function $F$, consisting of several instances of $f$ bundled together. Using this simulation and known communication complexity lower bounds, we obtain the first known (space vs. number of passes) trade-off lower bounds for Stack Machines.

The use of polymer supports for transition metal catalysts are very important and useful in synthetic organic chemistry as they make possible the separation and isolation of catalysts and products quite easy. These polymer-bound ligands/catalysts/reagents can, often, be recovered and recycled numerous times and typically yield products in high purity, negating the need for further purification steps (i.e. column chromatography). Because of this, interest in these systems has garnered international attention in the scientific community as being “Green”. Historically, insoluble, polymer-supports (i.e. Merrifield resin) were used to develop recoverable catalysts. This has the advantage of easy separation and isolation from products after a reaction; because of their insolubility, such supported catalysts can be easily removed by gravity filtration. However, these catalysts often have relatively poor reactivity and selectivity when compared to homogeneous catalysts. Because of this disadvantage, our lab has had interest in the development of soluble polymer-supports for transition metal catalysts. We have developed several separation methods for these soluble polymer-bound catalysts. These include thermomorphic liquid/liquid and solid/liquid as well as latent biphasic liquid/liquid separation techniques. This dissertation describes the use of both, latent biphasic liquid/liquid separation systems and thermomorphic solid/liquid separation systems. In order to perform a latent biphasic iii liquid/liquid separation, a polymer-bound catalyst must have a very high selectivity for one liquid phase over the other. Our lab has pioneered the use of polyisobutylene (PIB) oligomers as supports for transition metal catalysts. Previous work has shown that these oligomers are > 99.96 % phase selectively soluble in nonpolar solvents. This has allowed us to prepare PIB-supported salen Cr(III) complexes that can be used in a latent biphasic liquid/liquid solvent system. The synthesis of these complexes is quite straightforward and such species can be characterized using solution state 1H and 13C NMR spectroscopy. Also, these complexes can be used to catalyze the ring opening of meso epoxides with azidotrimethylsilane (TMS-N3) and can be recovered and recycled up to 6 times, with no loss in catalytic activity. To perform a thermomorphic solid/liquid separation, a polymer-bound catalyst that is completely insoluble at room temperature but soluble upon heating must be used. Our lab has pioneered the use of polyethylene oligomers (PEOlig) as supports for transition metal catalysts. Such PEOlig-supported catalysts are able perform homogeneous catalytic reactions at elevated temperatures (ca. 65 ○C), but, upon cooling, precipitate out of solution as solids while the products stay in solution. This process allows for the easy separation of a solid catalyst from the product solution. Described herein, is the development of PEOlig-supported salen-Cr(III) complexes and PEOlig-supported NHC-Ru complexes. The preparation of these complexes is also straightforward and such species can be characterized using solution state variable temperature (VT) 1H and 13C NMR spectroscopy. In the case of the PEOlig-supported salen-Cr(III) complex, it was found to be a recoverable/recyclable catalyst for the ring opening of epoxides with TMS-N3 and could be reused 6 times with no loss in activity. The PE-supported NHC-Ru complex was able to be used as a recyclable ring closing metathesis (RCM) catalyst and could be used up to 10 times.

Data aggregation is an important technique in wireless sensor networks. The data are gathered together by data fusion routines along the routing path, which is called data-centralized routing. We propose a localized, Delay-bounded and Energy-efficient Data Aggregation framework(DEDA) based on the novel concept of DEsired Progress (DEP). This framework works under request-driven networks with realistic MAC layer protocols. It is based on localized minimal spanning tree (LMST) which is an energy-efficient structure. Besides the energy consideration, delay reliability is also considered by means of the DEP. A node’s DEP reflects its desired progress in LMST which should be largely satisfied. Hence, the LMST edges might be replaced by unit disk graph (UDG) edges which can progress further in LMST. The DEP metric is rooted on realistic degree-based delay model so that DEDA increases the delay reliability to a large extent compared to other hop-based algorithms. We also combine our DEDA framework with area coverage and localized connected dominating set algorithms to achieve two more resilient DEDA implementations: A-DEDA and AC-DEDA. The simulation results confirm that our original DEDA and its two enhanced variants save more energy and attain a higher delay reliability ratio than existing protocols.

Dans le domaine de l'Optimisation Combinatoire, la résolution de manière optimale de problèmes de grande taille par le biais d'algorithmes Branch-and-Bound requiert un nombre très élevé de ressources de calcul. De nos jours, de telles ressources sont accessibles grâce aux grilles de calcul, composées de grappes de clusters réparties sur différents sites géographiques. Ces environnements parallèles posent de nombreux défis scientifiques, notamment en termes de passage à l'échelle, de la prise en compte de l'hétérogénéité des ressources ainsi qu'en termes de tolérance aux pannes. La plupart des approaches existantes pour l'algorithme Branch-and-Bound parallèle sont basées sur une architecture de type Maître-Esclave, où un processus maître répartit les tâches à accomplir auprès de processus esclaves en charge de les traîter. L'utilisation d'une telle entité centrale constitue un obstacle majeur en ce qui concerne le passage à l'échelle. Dans cette thèse, nous proposons de relever ces défis ainsi que de surmonter cet obstacle grâce à une approche innovante et complètement distribuée, basée sur une architecture Pair-à-Pair (P2P). Celle-ci repose sur un seul type de processus (le pair), qui a pour mission d'explorer son propre ensemble de tâches, de le partager avec d'autres pairs et de diffuser l'information globale. Nous définissons des mécanismes adaptés en lien avec l'algorithme Branch-and-Bound, qui traitent de la répartition de la charge, de la diffusion de la meilleure solution trouvée et de la détection de la terminaison des calculs. En plus de multiples expérimentations sur le problème d'ordonnancement du Flow-Shop sur la grille de calcul Grid'5000, nous proposons une preuve formelle de la correction de notre approche. Par ailleurs, nous traîtons une problématique souvent ignorés dans les travaux relatifs au calcul P2P, qui est l'importance de la topologie du réseau P2P. Généralement, une topologie très simple est utilisée. Les résultats obtenus montrent que notre approche permet le déploiement de réseaux de calculs à de très grandes échelles, constitués potentiellement de centaines de milliers de coeurs de calcul. Notre dernière contribution consiste en une approche Pair-à-Pair tolérante aux pannes afin de prendre en compte la nature généralement très volatile des ressources de calcul. Les résultats obtenus prouvent la robustesse de l'approche dans des environnements à la fois réalistes et sujets à de nombreux dysfinctionnements