Generalized hill climbing (GHC) algorithms provide a framework for using local search algorithms to address intractable discrete optimization problems. Many well-known local search algorithms can be formulated as GHC algorithms, including simulated annealing, threshold accepting, Monte Carlo search, and pure local search (among others). This dissertation develops a mathematical framework for simultaneously addressing a set of related discrete optimization problems using GHC algorithms. The resulting algorithms, termed simultaneous generalized hill climbing (SGHC) algorithms, can be applied to a wide variety of sets of related discrete optimization problems. The SGHC algorithm probabilistically moves between these discrete optimization problems according to a problem generation probability function. This dissertation establishes that the problem generation probability function is a stochastic process that satisfies the Markov property. Therefore, given a SGHC algorithm, movement between these discrete optimization problems can be modeled as a Markov chain. Sufficient conditions that guarantee that this Markov chain has a uniform stationary probability distribution are presented. Moreover, sufficient conditions are obtained that guarantee that a SGHC algorithm will visit the globally optimal solution over all the problems in a set of related discrete optimization problems. Computational results are presented with SGHC algorithms for a set of traveling salesman problems. For comparison purposes, GHC algorithms are also applied individually to each traveling salesman problem. These computational results suggest that optimal/near optimal solutions can often be reached more quickly using a SGHC algorithm. / Ph. D.

Generalized hill climbing (GHC) algorithms provide a unifying framework for describing several discrete optimization problem local search heuristics, including simulated annealing and tabu search. A necessary and a sufficient convergence condition for GHC algorithms are presented. The convergence conditions presented in this dissertation are based upon a new iteration classification scheme for GHC algorithms. The convergence theory for particular formulations of GHC algorithms is presented and the implications discussed. Examples are provided to illustrate the relationship between the new convergence conditions and previously existing convergence conditions in the literature. The contributions of the necessary and the sufficient convergence conditions for GHC algorithms are discussed and future research endeavors are suggested. / Ph. D.

Identifying a globally optimal solution for an intractable discrete optimization problem is often cost prohibitive. Therefore, solutions that are within a predetermined threshold are often acceptable in practice. This dissertation introduces the concept of B-acceptable solutions where B is a predetermined threshold for the objective function value. It is difficult to assess a priori the effectiveness of local search algorithms, which makes the process of choosing parameters to improve their performance difficult. This dissertation introduces the B-acceptable solution probability in terms of B-acceptable solutions as a finite-time performance measure for local search algorithms. The B-acceptable solution probability reflects how effectively an algorithm has performed to date and how effectively an algorithm can be expected to perform in the future. The B-acceptable solution probability is also used to obtain necessary asymptotic convergence (with probability one) conditions. Upper and lower bounds for the B-acceptable solution probability are presented. These expressions assume particularly simple forms when applied to specific local search strategies such as Monte Carlo search and threshold accepting. Moreover, these expressions provide guidelines on how to manage the execution of local search algorithm runs. Computational experiments are reported to estimate the probability of reaching a B-acceptable solution for a fixed number of iterations. Logistic regression is applied as a tool to estimate the probability of reaching a B-acceptable solution for values of B close to the objective function value of a globally optimal solution as well as to estimate this objective function value. Computational experiments are reported with logistic regression for pure local search, simulated annealing and threshold accepting applied to instances of the TSP with known optimal solutions. / Ph. D.

The focus of this research project was to investigate morphological and mechanical properties of both extruded and dispersion-cast Nafion® membranes. The project can be divided into three primary objectives; obtaining a fundamental understanding of the glass transition temperature of Nafion®, determining the effect of thermal annealing treatments on the morphology and mechanical properties of dispersion-cast Nafion®, and examination of dispersion-cast Nafion® subjected to an ex-situ, Fenton's chemical degradation test. Nafion®, a perfluorosulfonate ionomer, is considered a commercially successful semi-crystalline ionomer with primary applications in chlor-alkali cells and proton exchange membrane fuel cells. With the aid of dynamic mechanical analysis (DMA) and dielectric spectroscopy (DS), we were able to provide definitive evidence for a genuine glass transition in Nafion®. DMA of Nafion® samples that were partially neutralized with tetrabutylammonium counterions showed a strong compositional dependence suggesting that the β-relaxations of H+-form Nafion® and the neutralized ionomers have the same molecular origin with respect to backbone segmental motions. Building upon our previous studies of the molecular and morphological origins of the dynamic mechanical relaxations of Nafion® neutralized with a series of organic ions, the glass transition temperature of H+-form Nafion® is now confirmed to be the weak β-relaxation centered at -20 °C. Dielectric spectra also showed this transition from the perspective of dipole relaxation. The signature of cooperative long range segmental motions in dielectric spectra was seen here, as with other polymers, mainly through the excellent agreement of the β-relaxation time-temperature dependence with the Vogel-Fulcher-Tammann equation. We have also discovered that new dispersion-cast H+ form Nafion® membranes are susceptible to disintegration/dissolution when subjected to boiling methanol. In this work, we have achieved significant decreases in the percent solubility of H+-form Nafion® by either thermally annealing above 175 °C or solution-processing at 180 °C using a high boiling point solvent. Small Angle X ray Scattering (SAXS) displayed a change in the morphology of H+ form membranes with increasing annealing temperature by a shift in the crystalline scattering peak (q â 0.05 Ã 1) to lower q values. Counterion exchange of Nafion® from H+ to Na+ form had no influence on the membrane's susceptibility to disintegration in boiling methanol. In order to achieve mechanical stability in boiling methanol, Na+ form membranes had to be annealed at 275 °C for at least fifteen minutes. The SAXS data of annealed Na+ form membranes showed a dramatic decrease in crystalline order with annealing temperature, ultimately leading to the disappearance of the crystalline scattering peak after fifteen minutes at 275 °C. The onset of methanol stability with the melting of Nafion® crystallites suggests that chain entanglement is an important parameter in obtaining solvent stability. With respect to chemical stability, we performed studies aimed at examining the effects of Fenton's Reagent on the resistance to radical attack of new generation, dispersion-cast Nafion®. Changes in the 19F solid-state NMR spectra of dispersion-cast Nafion® before and after chemical degradation via Fenton's Reagent predicts a rather random attack by ·OH and ·OOH radicals. Several membranes were also thermally annealed between 100-250 °C in an attempt to correlate crystallinity with chemical degradation kinetics of Nafion® via Fenton's Reagent. The results indicate that the effect of counterion exchange into the Na+ form was minimal, but the degree of thermal degradation had a tremendous effect on the fluoride release rate and chemical degradation kinetics. By exchanging the membranes into the Na+ form, thermal degradation was avoided, allowing us to study the role of crystallinity as a function of fluoride release. Ultimately, Nafion® crystallinity was deemed an important factor in deterring peroxide radical attack. As the percent crystallinity decreased with annealing temperature, the fluoride concentration in the resulting Fenton's media increased accordingly, indicating that the amorphous regions of the polymer are more susceptible to chemical degradation via peroxide radical attack. / Ph. D.

Generalized hill climbing (GHC) algorithms are introduced, as a tool to address difficult discrete optimization problems. Particular formulations of GHC algorithms include simulated annealing (SA), local search, and threshold accepting (T A), among. others. A proof of convergence of GHC algorithms is presented, that relaxes the sufficient conditions for the most general proof of convergence for stochastic search algorithms in the literature (Anily and Federgruen [1987]). Proofs of convergence for SA are based on the concept that deteriorating (hill climbing) transitions between neighboring solutions are accepted by comparing a deterministic function of both the solution change cost and a temperature parameter to a uniform (0,1) random variable. GHC algorithms represent a more general model, whereby deteriorating moves are accepted according to a general random variable. Computational results are reported that illustrate relationships that exist between the GHC algorithm's finite-time performance on three problems, and the general random variable formulations used. The dissertation concludes with suggestions for further research. / Ph. D.

This thesis describes the synthesis of yttrium oxide nanoparticles in an AOT/isooctane reverse micelle solution. Two synthetic methods are compared. First is the precipitation reaction between yttrium nitrate and ammonia, second is the hydrolysis of yttrium isopropoxide. The effects of annealing of the resulting the yttrium oxide nanoparticles are also described. The nitrate method produced network-like aggregates of yttrium oxide nanoparticles ranging from 10 nm to 40 nm in diameter. Reaction conditions, including the water/AOT ratio (1 to 15), the nitrate concentration (0.02 M to 1.0 M), the ammonia concentration (2 M to 14.8 M), the AOT concentration (0.1 M and 0.5 M), the aging time (1 h to 5 d), and the washing method, were varied to investigate their influence on nanoparticle formation. The optimized synthetic conditions were: a water/AOT ratio of 7.5, [NO₃⁻] = 0.5 M, [NH₃] = 2 M, and [AOT] = 0.1 M. The as-prepared yttrium oxide nanoparticles had highly distorted structures related to the cubic Y2O3 phase. Annealing improved the crystallinity of the as-prepared nanoparticle products and led to larger particles. As annealing temperatures increased, the yttrium oxide nanoparticles gradually evolved into the cubic Y₂O₃ phase. However, an unknown intermediate phase was also observed during the annealing process, which disappeared when the annealing temperature was sufficiently high and the annealing time was long enough (>1000 °C and 4 h). As-prepared products from the isopropoxide hydrolysis also contained network-like nanoparticle aggregates. Particle sizes ranged from 10 nm to 20 nm. Some experimental conditions were varied; they were the water/AOT ratio (10 to 40), the isopropoxide concentration (0.0001 M to 0.003 M), the aqueous phase pH (7.0 and 12.0), the aging temperature (room temperature, approximately 25 °C, and refluxing temperature, approximately, 100 °C), and the aging time (1 h to 5 d). Transmission Electronic Micrographs showed that products of desirable morphology could be produced in a much wider range of experimental conditions by this method compared to those produced by nitrate hydrolysis. / Master of Science

The use of the discrete wavelet transform (DWT) for the JPEG2000 image compression standard has sparked interest in the design of fast, efficient hardware implementations of the perfect reconstruction filter bank used for computing the DWT. The accuracy and efficiency with which the filter coefficients are quantized in a multiplierless implementation impacts the image compression and hardware performance of the filter bank. A high precision representation ensures good compression performance, but at the cost of increased hardware resources and processing time. Conversely, lower precision in the filter coefficients results in smaller, faster hardware, but at the cost of poor compression performance. In addition to filter coefficient quantization, the filter bank structure also determines critical hardware properties such as throughput and power consumption. This thesis first investigates filter coefficient quantization strategies and filter bank structures for the hardware implementation of the biorthogonal 9/7 wavelet filters in a traditional convolution-based filter bank. Two new filter bank properties—"no-distortion-mse" and "deviation-at-dc"—are identified as critical to compression performance, and two new "compensating" filter coefficient quantization methods are developed to minimize degradation of these properties. The results indicate that the best performance is obtained by using a cascade form for the filters with coefficients quantized using the "compensating zeros" technique. The hardware properties of this implementation are then improved by developing a cascade polyphase structure that increases throughput and decreases power consumption. Next, this thesis investigates implementations of the lifting structure—an orthogonal structure that is more robust to coefficient quantization than the traditional convolution-based filter bank in computing the DWT. Novel, optimal filter coefficient quantization techniques are developed for a rational and an irrational set of lifting coefficients. The results indicate that the best quantized lifting coefficient set is obtained by starting with the rational coefficient set and using a "lumped scaling" and "gain compensation" technique for coefficient quantization. Finally, the image compression properties and hardware properties of the convolution and lifting based DWT implementations are compared. Although the lifting structure requires fewer computations, the cascaded arrangement of the lifting filters requires significant hardware overhead. Consequently, the results depict that the convolution-based cascade polyphase structure (with "<i>z</i>₁-compensated" coefficients) gives the best performance in terms of image compression performance and hardware metrics like throughput, latency and power consumption. / Master of Science

A good strategy to test a software component involves the generation of the whole set of cases that participate in its operation. While testing only individual values may not be enough, exhaustive testing of all possible combinations is not always feasible. An alternative technique to accomplish this goal is called combinato- rial testing. Combinatorial testing is a method that can reduce cost and increase the effectiveness of software testing for many applications. It is based on con- structing functional test-suites of economical size, which provide coverage of the most prevalent configurations. Covering arrays are combinatorial objects, that have been applied to do functional tests of software components. The use of cov- ering arrays allows to test all the interactions, of a given size, among the input parameters using the minimum number of test cases. For software testing, the fundamental problem is finding a covering array with the minimum possible number of rows, thus reducing the number of tests, the cost, and the time expended on the software testing process. Because of the importance of the construction of (near) optimal covering arrays, much research has been carried out in developing effective methods for constructing them. There are several reported methods for constructing these combinatorial models, among them are: (1) algebraic methods, recursive methods, (3) greedy methods, and (4) metaheuristics methods. Metaheuristic methods, particularly through the application of simulated anneal- ing has provided the most accurate results in several instances to date. Simulated annealing algorithm is a general-purpose stochastic optimization method that has proved to be an effective tool for approximating globally optimal solutions to many optimization problems. However, one of the major drawbacks of the simulated an- nealing is the time it requires to obtain good solutions. In this thesis, we propose the development of an improved simulated annealing algorithm / Avila George, H. (2012). Constructing Covering Arrays using Parallel Computing and Grid Computing [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/17027

No

The three-stage (extrusion, annealing, stretching) method of producing microporous membranes from linear polyethylene (HDPE) was investigated in this dissertation. Two different HDPE resins with identical M̅_n (14,600) values but different distributions (M̅_w/M̅_n=10.3, 15.1) were utilized for this study. In the extrusion process, the two HDPE resins were melt extruded into uniaxially oriented tubular films. Systematical changes were made in the process variables -- these being the melt temperature at the die exit, the quench height, the cooling rate, and the line speed. The melt relaxation time behavior of the HDPE resins was studied by a Carreau-Yasuda analysis. The orientation morphological features of the extruded films were examined by TEM, HSEM, birefringence, WAXS, SAXS, and linear IR dichroism. The molecular weight distribution of the raw resins as well as the specific processing variables of quench height and melt temperature were found to be important in determining the final structure of the HDPE extruded films. Following the extrusion process, the effect of annealing on the structure and properties of the HDPE extruded films was investigated. The HDPE extruded films were annealed under different conditions. The annealing variables studied included the temperature, the line speed (or annealing time), and the amount of extension applied during annealing. The extruded films before and after annealing were characterized by DSC, WAXS, SAXS, birefringence, and TEM. The results suggest that upon annealing, perfection of the crystalline phase occurs by removal of the defects from the crystalline phase. In the last step, the precursors (either the extruded films or the extruded films after being annealed) were uniaxially deformed along the extrusion direction. The variables of cold stretch ratio, hot stretch ratio, and total stretch percent were varied to alter the properties of the stretched microporous membranes. The pore structure, porosity, and permeability of the stretched microporous films were analyzed by TEM, HSEM, AFM, DSC, and Gurley number measurements. The importance of the orientation and morphological properties of the precursors, the annealing effects of the HDPE extruded films, and the stretching variables for influencing the microporosity behavior of the HDPE microporous membranes is clearly made evident in this dissertation. / Ph. D.