The main subject of the research in this thesis is the study of conjugate gradient methods for optimization and the development of improved algorithms. After an introductory first chapter, Chapter 2 contains a background of numerical methods for optimization in general and of conjugate gradient-type algorithms in particular. In Chapter 3 we study the convergence properties of conjugate gradient methods and discuss Powell's (1983) counter example that proves that there exist twice continuously differentiable functions with bounded level sets for which the Polak-Ribiere method fails to achieve global convergence whereas the Fletcher-Reeves method is shown to be globally convergent, despite the fact that in numerical computations the Polak-Ribiere method is far more efficient than that of Fletcher-Reeves. Chapters 4 and 5 deal with the development of a number of new hybrid algorithms, three of which are shown to satisfy the descent property at every iteration and achieve global convergence regardless of whether exact or inexact line searches are used. A new restarting procedure for conjugate gradient methods is also given that ensures a descent property to hold and global convergence for any conjugate gradient method using a non negative update. The application of these hybrid algorithms and that of the new restarting procedure to a wide class of well-known test problems is given and discussed in the final Chapter "Discussions and Conclusions". The results obtained, given in the appendices, show that a considerable improvement is achieved by these hybrids and by methods using the new restarting procedure over the existing conjugate gradient methods and also over quasi-Newton methods.

A central topic in the research of nanophotonics is the geometrical optimization of the nanostructures since the geometries are deeply related to the Mie resonances and the localized surface plasmon resonances in dielectric and metallic nanomaterials. When many nanostructures are assembled to form a metamaterial, the tuning of the geometrical parameters can bring even more profound effects, such as bound states in the continuum (BIC) with infinite quality factors (Q factors). Moreover, with the development of nanofabrication technologies, there is a trend of integrating nanostructures in the vertical direction, which provides more degrees of freedom for controlling the device performance and functionality. The main topic of this dissertation is to explore some of the abovementioned tuning possibilities to enhance the performance of nanophotonic devices. The dissertation contains two major parts: In chapters 2 and 3, the vertical integration of metalenses is studied. We discover a phenomenon similar to the Moiré effect in the bilayer Pancharatnam-Berry phase metalenses and reveal the role of geometrical imperfections on the focusing performance of reflective metalenses. Novel multifocal and reflective metalenses, with smaller footprints and enhanced performance compared to their bulky conventional counterparts, are designed based on the theoretical findings. The study of geometrical imperfections also provides guidelines for analyzing and compensating the fabrication errors, which is vital for large scale production and commercialization of metalenses. In chapters 4 and 5, we use machine learning to harness the full tuning power of the complicated geometries, which is challenging with conventional design methods. Plasmonic metasurfaces with on-demand optical responses are designed by manipulating the coupling of multiple nanodisks using neural networks. An accuracy of ± 8 nm is achieved, which is higher than previous reports and close to the fabrication limits of nanofabrication technologies. We also demonstrate, for the first time, the control of multiple BIC states using freeform geometries with predefined symmetry. It is a new method to exploit the untapped potential of freeform photonics structures. The discoveries we have made in both dielectric and plasmonic nanophotonic devices could benefit applications such as imaging, sensing, and light-emitting devices.

Industry and researchers are investigating both battery electric vehicles (BEVs) and fuel cell hybrid vehicles (FCHV) for the future of sustainable passenger vehicle technology. While BEVs have clear efficiency advantages, FCHVs have key benefits in terms of refueling time and energy density. This thesis first proposes the concept of a fuel cell range extended vehicle (FCREV) that uses Whole-Day Driving Prediction (WDDP) control, which uses driver destination inputs to determine whether the planned driving trips that day will exceed the useable battery energy capacity. If so, the fuel cell is turned on at the start of the day. The benefit of WDDP control is that a smaller, lower cost fuel cell can be used to greatly extend the driving range, since the fuel cell can charge the battery during both driving and parked periods of the day. Furthermore, this research proposes a fast analytical optimization algorithm for designing a WDDP-FCREV to maximize range on a given drive cycle for a set cost. The results show an optimized WDDP-FCREV can greatly exceed the range of a same-cost BEV, by 105% to 150% for no H2 refueling and by 150% to 250% when H2 refueling is allowed every 4 hours. / Thesis / Master of Applied Science (MASc)

Reducers are commonly used in many types of machines to reduce the speed and increase the torque of motors. For general industrial applications, the reduction ratio of a reducer is usually limited in consideration to its size. To provide high reduction ratios, harmonic drives (speed reducers) can be made very compact and lightweight and thus have been popular with robot manufactures and in other applications where weight is critical. In this study, an innovative design for reducers composed of planar cams and roller followers with high reduction ratios is proposed. It uses the relative motion between rollers and their cams to generate a high reduction ratio. In this thesis, the synthesis procedure of the reducer and the analysis results of the kinematic and dynamic characteristics based on the design parameters are also described. Furthermore, the experiments for testing and verifying the characteristics of the reducer are presented. Finally, a set of design parameters which meets the demand of an application is found by optimization methods.

Solar cells are at the frontier of renewable energy technologies. Photovoltaic energy is clean, reusable, can be used anywhere in our solar system and can be very well integrated with power distribution grids and advanced technological systems. Thin film solar cells are a class of solar cells that offer low material cost, efficient fabrication process and compatibility with advanced electronics. However, as of now, the conversion efficiency of thin film solar cells is inferior to that of thick crystalline cells. Research efforts to improve the performance bottlenecks of thin film solar cells are highly motivated. A class of techniques towards this goal is called light trapping methods, which aims at improving the spectral absorptivity of a thin film cell by using surface texturing. The precise mathematical and physical characterization of these techniques is very challenging. This dissertation proposes a numerical and computational framework to optimize, design, and fabricate efficient light trapping structures in thin film solar cells, as well as methods to verify the fabricated designs. The numerical framework is based on the important "inverse optimization" technique, which is very is widely applicable to engineering design problems. An overview of the state-of-the-art thin film technology and light trapping techniques is presented in this thesis. The inverse problem is described in details with numerous examples in engineering applications, and is then applied to light trapping optimization. The proposed designs are studied for sensitivity analysis and fabrication error, as other aspects of the proposed computational framework. At the end, reports of fabrication, measurement and verification of some of the proposed designs are presented. / text

Diss. (sammanfattning) Umeå : Sveriges lantbruksuniv., 2009. / Härtill 3 uppsatser.

This thesis proposes a novel framework for solving the energy management problem of Hybrid Electric Vehicles (HEVs). We aim to establish a practical and effective approach targeting an optimal Energy Management Strategy (EMS). A situation-specific Equivalent Consumption Minimization Strategy (ECMS) is developed to minimize fuel consumption and improve battery charge sustainability while maintaining an acceptable drive quality. The investigated methodology will be broadly applicable to all HEV applications; however, it will be well-suited for hybrid electric delivery applications. / Thesis / Master of Applied Science (MASc)

We propose solution strategies for hard Mixed Integer Programming (MIP) problems, with a focus on distributed parallel MIP optimization. Although our proposals are inspired by the Less-than-truckload (LTL) freight routing problem, they are more generally applicable to hard MIPs from other domains. We start by developing an Integer Programming model for the Less-than-truckload (LTL) freight routing problem, and present a novel heuristic for solving the model in a reasonable amount of time on large LTL networks. Next, we identify some adaptations to MIP branching strategies that are useful for achieving improved scaling upon distribution when the LTL routing problem (or other hard MIPs) are solved using parallel MIP optimization. Recognizing that our model represents a pseudo-Boolean optimization problem (PBO), we leverage solution techniques used by PBO solvers to develop a CPLEX based look-ahead solver for LTL routing and other PBO problems. Our focus once again is on achieving improved scaling upon distribution. We also analyze a technique for implementing subtree parallelism during distributed MIP optimization. We believe that our proposals represent a significant step towards solving big-data driven optimization problems (such as the LTL routing problem) in a more efficient manner. / Thesis / Doctor of Philosophy (PhD) / Less-than-truckload (LTL) freight transportation is a vital part of Canada's economy, with revenues running into billions of dollars and a cascading impact on many other industries. LTL operators often have to deal with large volumes of shipments, unexpected changes in traffic conditions, and uncertainty in demand patterns. In an industry that already has low profit margins, it is therefore vitally important to make good routing decisions without expending a lot of time. The optimization of such LTL freight networks often results in complex big-data driven optimization problems. In addition to the challenge of finding optimal solutions for these problems, analysts often have to deal with the complexities of big-data driven inputs. In this thesis we develop several solution strategies for solving the LTL freight routing problem including an exact model, novel heuristics, and techniques for solving the problem efficiently on a cluster of computers. Although the techniques we develop are inspired by LTL routing, they are more generally applicable for solving big-data driven optimization problems from other domains. Experiments conducted over the years in consultation with industry experts indicate that our proposals can significantly improve solution quality and reduce time to solution. Furthermore, our proposals open up interesting avenues for future research.

Yes / Distributed generators (DGs) are a reliable solution to supply economic and reliable electricity to customers. It is the last stage in delivery of electric power which can be defined as an electric power source connected directly to the distribution network or on the customer site. It is necessary to allocate DGs optimally (size, placement and the type) to obtain commercial, technical, environmental and regulatory advantages of power systems. In this context, a comprehensive literature review of uncertainty modeling methods used for modeling uncertain parameters related to renewable DGs as well as methodologies used for the planning and operation of DGs integration into distribution network. / This work was supported in part by the SITARA project funded by the British Council and the Department for Business, Innovation and Skills, UK and in part by the University of Bradford, UK under the CCIP grant 66052/000000.

Abstract The application of optimization techniques for resource management in wireless communication networks is considered in this thesis. It is understood that a wide variety of resource management problems of recent interest, including power/rate control, link scheduling, cross-layer control, network utility maximization, beamformer design of multiple-input multiple-output networks, and many others are directly or indirectly reliant on the general weighted sum-rate maximization (WSRMax) problem. Thus, in this dissertation a greater emphasis is placed on the WSRMax problem, which is known to be NP-hard. A general method, based on the branch and bound technique, is developed, which solves globally the nonconvex WSRMax problem with an optimality certificate. Efficient analytic bounding techniques are derived as well. More broadly, the proposed method is not restricted to WSRMax. It can also be used to maximize any system performance metric, which is Lipschitz continuous and increasing on signal-to-interference-plus-noise ratio. The method can be used to find the optimum performance of any network design method, which relies on WSRMax, and therefore it is also useful for evaluating the performance loss encountered by any heuristic algorithm. The considered link-interference model is general enough to accommodate a wide range of network topologies with various node capabilities, such as singlepacket transmission, multipacket transmission, simultaneous transmission and reception, and many others. Since global methods become slow in large-scale problems, fast local optimization methods for the WSRMax problem are also developed. First, a general multicommodity, multichannel wireless multihop network where all receivers perform singleuser detection is considered. Algorithms based on homotopy methods and complementary geometric programming are developed for WSRMax. They are able to exploit efficiently the available multichannel diversity. The proposed algorithm, based on homotopy methods, handles efficiently the self interference problem that arises when a node transmits and receives simultaneously in the same frequency band. This is very important, since the use of supplementary combinatorial constraints to prevent simultaneous transmissions and receptions of any node is circumvented. In addition, the algorithm together with the considered interference model, provide a mechanism for evaluating the gains when the network nodes employ self interference cancelation techniques with different degrees of accuracy. Next, a similar multicommodity wireless multihop network is considered, but all receivers perform multiuser detection. Solutions for the WSRMax problem are obtained by imposing additional constraints, such as that only one node can transmit to others at a time or that only one node can receive from others at a time. The WSRMax problem of downlink OFDMA systems is also considered. A fast algorithm based on primal decomposition techniques is developed to jointly optimize the multiuser subcarrier assignment and power allocation to maximize the weighted sum-rate (WSR). Numerical results show that the proposed algorithm converges faster than Lagrange relaxation based methods. Finally, a distributed algorithm for WSRMax is derived in multiple-input single-output multicell downlink systems. The proposed method is based on classical primal decomposition methods and subgradient methods. It does not rely on zero forcing beamforming or high signal-to-interference-plus-noise ratio approximation like many other distributed variants. The algorithm essentially involves coordinating many local subproblems (one for each base station) to resolve the inter-cell interference such that the WSR is maximized. The numerical results show that significant gains can be achieved by only a small amount of message passing between the coordinating base stations, though the global optimality of the solution cannot be guaranteed. / Tiivistelmä Tässä työssä tutkitaan optimointimenetelmien käyttöä resurssienhallintaan langattomissa tiedonsiirtoverkoissa. Monet ajankohtaiset resurssienhallintaongelmat, kuten esimerkiksi tehonsäätö, datanopeuden säätö, radiolinkkien ajastus, protokollakerrosten välinen optimointi, verkon hyötyfunktion maksimointi ja keilanmuodostus moniantenniverkoissa, liittyvät joko suoraan tai epäsuorasti painotetun summadatanopeuden maksimointiongelmaan (weighted sum-rate maximization, WSRMax). Tästä syystä tämä työ keskittyy erityisesti WSRMax-ongelmaan, joka on tunnetusti NP-kova. Työssä kehitetään yleinen branch and bound -tekniikkaan perustuva menetelmä, joka ratkaisee epäkonveksin WSRMax-ongelman globaalisti ja tuottaa todistuksen ratkaisun optimaalisuudesta. Työssä johdetaan myös tehokkaita analyyttisiä suorituskykyrajojen laskentatekniikoita. Ehdotetun menetelmän käyttö ei rajoitu vain WSRMax-ongelmaan, vaan sitä voidaan soveltaa minkä tahansa suorituskykymetriikan maksimointiin, kunhan se on Lipschitz-jatkuva ja kasvava signaali-häiriö-plus-kohinasuhteen funktiona. Menetelmää voidaan käyttää minkä tahansa WSRMax-ongelmaan perustuvan verkkosuunnittelumenetelmän optimaalisen suorituskyvyn määrittämiseen, ja siksi sitä voidaan hyödyntää myös minkä tahansa heuristisen algoritmin aiheuttaman suorituskykytappion arvioimiseen. Tutkittava linkki-häiriömalli on riittävän yleinen monien erilaisten verkkotopologioiden ja verkkosolmujen kyvykkyyksien mallintamiseen, kuten esimerkiksi yhden tai useamman datapaketin siirtoon sekä yhtäaikaiseen lähetykseen ja vastaanottoon. Koska globaalit menetelmät ovat hitaita suurien ongelmien ratkaisussa, työssä kehitetään WSRMax-ongelmalle myös nopeita paikallisia optimointimenetelmiä. Ensiksi käsitellään yleistä useaa eri yhteyspalvelua tukevaa monikanavaista langatonta monihyppyverkkoa, jossa kaikki vastaanottimet suorittavat yhden käyttäjän ilmaisun, ja kehitetään algoritmeja, joiden perustana ovat homotopiamenetelmät ja komplementaarinen geometrinen optimointi. Ne hyödyntävät tehokkaasti saatavilla olevan monikanavadiversiteetin. Esitetty homotopiamenetelmiin perustuva algoritmi käsittelee tehokkaasti itsehäiriöongelman, joka syntyy, kun laite lähettää ja vastaanottaa samanaikaisesti samalla taajuuskaistalla. Tämä on tärkeää, koska näin voidaan välttää lisäehtojen käyttö yhtäaikaisen lähetyksen ja vastaanoton estämiseksi. Lisäksi algoritmi yhdessä tutkittavan häiriömallin kanssa auttaa arvioimaan, paljonko etua saadaan, kun laitteet käyttävät itsehäiriön poistomenetelmiä erilaisilla tarkkuuksilla. Seuraavaksi tutkitaan vastaavaa langatonta monihyppyverkkoa, jossa kaikki vastaanottimet suorittavat monen käyttäjän ilmaisun. Ratkaisuja WSRMax-ongelmalle saadaan asettamalla lisäehtoja, kuten että vain yksi lähetin kerrallaan voi lähettää tai että vain yksi vastaanotin kerrallaan voi vastaanottaa. Edelleen tutkitaan WSRMax-ongelmaa laskevalla siirtotiellä OFDMA-järjestelmässä, ja johdetaan primaalihajotelmaan perustuva nopea algoritmi, joka yhteisoptimoi monen käyttäjän alikantoaalto- ja tehoallokaation maksimoiden painotetun summadatanopeuden. Numeeriset tulokset osoittavat, että esitetty algoritmi suppenee nopeammin kuin Lagrangen relaksaatioon perustuvat menetelmät. Lopuksi johdetaan hajautettu algoritmi WSRMax-ongelmalle monisoluisissa moniantennilähetystä käyttävissä järjestelmissä laskevaa siirtotietä varten. Esitetty menetelmä perustuu klassisiin primaalihajotelma- ja aligradienttimenetelmiin. Se ei turvaudu nollaanpakotus-keilanmuodostukseen tai korkean signaali-häiriö-plus-kohinasuhteen approksimaatioon, kuten monet muut hajautetut muunnelmat. Algoritmi koordinoi monta paikallista aliongelmaa (yhden kutakin tukiasemaa kohti) ratkaistakseen solujen välisen häiriön siten, että WSR maksimoituu. Numeeriset tulokset osoittavat, että merkittävää etua saadaan jo vähäisellä yhdessä toimivien tukiasemien välisellä viestinvaihdolla, vaikka globaalisti optimaalista ratkaisua ei voidakaan taata.