Source: Dissertation Abstracts International, Volume: 33-10, Section: B, page: 4933. / Thesis (Ph.D.)--The Florida State University, 1972.

Many results in mathematical programming involving convex functions hold for a more general class of functions, called invex functions. Examples of such functions are given. It is shown that several types of generalized convex functions are special cases of invex functions. The relationship between convexity and some generalizations of invexity is illustrated. A nonlinear problem with equality constraints is studied and necessary and sufficient conditions for optimality are stated in terms of invexity. Also, weak, strong and converse dual theorems for fractional programming are given using invexity conditions. Finally, a sufficient condition for invexity is established through the use of linear programming. / Source: Dissertation Abstracts International, Volume: 48-07, Section: B, page: 2087. / Thesis (Ph.D.)--The Florida State University, 1987.

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The nonstationary Erlang loss model is a queueing system consisting of a finite number of servers and no waiting room with a nonstationary arrival process or a time-dependent service rate. The Erlang loss model is commonly used to model and evaluate many communication systems. Often, these types of service systems encounter a change in the arrival rate over time while the service rate remains either constant or changes very little over time. In view of this, the focus in this research is the nonstationary Erlang loss queues and network with time-dependent arrival rate and constant service rate. We developed an iterative scheme referred to as the fixed point approximation (FPA) in order to obtain the time-dependent blocking probability and other measures for a single-class nonstationary Erlang loss queue and a nonstationary multi-rate Erlang loss queue. The FPA method was compared against exact numerical results, and two other methods, namely, MOL and PSA, for various nonstationary Erlang loss queues with sinusoidal arrival rates. Although we used sinusoidal functions to model the time-dependent arrival rate, the solution can be obtained for any arrival rate function. Experimental results demonstrate that the FPA algorithm provides an exact solution for nonstationary Erlang loss queue. The FPA algorithm was also applied to the case of multi-rate nonstationary Erlang loss queues and the results obtained were compared with simulation. We generalized the FPA algorithm for networks of nonstationary Erlang loss queues with Markovian branching, and compared its accuracy to simulation. Finally, FPA was used to analyze networks of nonstationary Erlang loss queues with population constraints. Numerical results showed that FPA provides a good approximation.

Network Flow problems are prevalent in Operations Research, Computer Science, Industrial Engineering and Management Science. They constitute a class of problems that are frequently faced by real world applications, including transportation, telecommunications, production planning, etc. While many problems can be modeled as Network Flows, these problems can quickly become unwieldy in size and difficult to solve. One particularly large instance is the Min-Cost Multicommodity Network Flow problem. Due to the time-sensitive nature of the industry, faster algorithms are always desired: recent advances in decomposition methods may provide a remedy. One area of improvement is the cost reoptimization of the min-cost single commodity network flow subproblems that arise from the decomposition. Since similar single commodity network flow problems are solved, information from the previous solution provides a "warm-start" of the current solution. While certain single commodity network flow algorithms may be faster "from scratch," the goal is to reduce the overall time of computation. Reoptimization is the key to this endeavor. Three single commodity network flow algorithms, namely, cost scaling, network simplex and relaxation, will be examined. They are known to reoptimize well. The overall goal is to analyze the effectiveness of this approach within one particular class of network problems.

In this thesis we present a formal study of the following view-selection problem: Given a set of queries, a database, and an upper bound on the amount of disk space that can be used to store materialized views, return definitions of views that, when materialized in the database, would reduce the evaluation costs of the queries. Optimizing the layout of stored data using view selection has a direct impact on the performance of the entire database system. At the same time, the optimization problem is intractable, even under natural restrictions on the types of queries of interest. We introduce an integer-programming model to obtain optimal solutions for the view-selection problem for aggregate queries on data warehouses. Through a computational experiment we show that this model can be used to solve realistic-size instances of the problem. We also report the results of the post-optimality analysis that we performed to determine the impact of changing certain input characteristics on the optimal solution. We solve large instances by applying several methods of reducing the size of the search space. We compare our approach to the leading heuristic procedure in the field [20].

Following the attacks of September 11th, the growing fear of a bioterrorist attack emerged within the United States and pushed the threat of bioterrorism to the forefront of the public health emergency preparedness and response agenda. Despite the investment of more than six billion dollars in federal funding towards emergency preparedness and response initiatives, well defined and broadly accepted performance measures for determining the efficacy of these systems have yet to be established. Because of the complex and dynamic conditions under which emergency preparedness and response systems must perform, it is becoming apparent that traditional measures of evaluating the performance of public health systems simply will not suffice. The inability to accurately capture and quantify this information has created knowledge gaps which hinder our ability to measure our true level of preparedness and ultimately weakens our response capacity. It is therefore essential that we develop methodologies that enable us to establish valid metrics which capture the information needed to quantify the capacity and efficacy of these systems. As a key information sharing and communication component of North Carolinaâs Public Health Information Network (NC PHIN), the North Carolina Health Alert Network (NCHAN) serves as a promising means to measure emergency preparedness and response capacity. The goal of this thesis is to present a methodology for extending approaches in operations research and systems engineering to better understand the value of emergency preparedness and response systems, such as NCHAN. Ultimately we seek to determine how NCHAN has aided to emergency preparedness and response by quantifying the added value of the system to the greater âpreparedness and responseâ process. We demonstrate the use of statistical analysis, simulation and the IDEF0 mapping process as valid tools for modeling and quantifying the less-tangible aspects of emergency preparedness and response. We find that although the capacity exists within NCHAN to increase emergency preparedness and response, other factors, such as usage variability amongst NCHAN users, lack of integration with other NC PHIN components, and limited capacity of tangible system resources (such as labs, funding and public health practitioners) limits the efficacy of NCHAN. These findings suggest that user standardization, component integration and proper resource allocation will be necessary in order to realize the true value of emergency preparedness and response systems.

Data warehouse management is fast becoming one of the most popular and important topics in industries today. For business executives, it promises significant competitive advantage for their companies, while presenting the information system managers a way to overcome the obstructions in providing business information to managers and other users. Here the company is going through the problem of inefficient performance of its data warehouse. To find an appropriate solution to this problem we first try to understand the data warehouse concept and its basic architecture, followed by an in depth study of the company data warehouse and the various issues affecting it. We propose and evaluate a set of solutions including classification of suppliers, implementing corporate commodity classification and coding system, obtaining level three spend details for PCard purchases, etc. The experimental results show considerable improvement in the data quality and the data warehouse performance. We further support these recommendations by evaluating the return on investment for improved quality data. Lastly, we discuss the future scope and other possible improvement techniques for obtaining better results.

Sequence alignment methods are used to detect and quantify similarities between different DNA and protein sequences that may have evolved from a common ancestor. Effective sequence alignment methodologies also provide insight into the structure function of a sequence and are the first step in constructing evolutionary trees. In this dissertation, we use a tabu search approach to multiple sequence alignment. A tabu search is a heuristic approach that uses adaptive memory features to align multiple sequences. The adaptive memory feature, a tabu list, helps the search process avoid local optimal solutions and explores the solution space in an efficient manner. We develop two main tabu searches that progressively align sequences. A randomly generated bifurcating tree guides the alignment. The objective is to optimize the alignment score computed using either the sum of pairs or parsimony scoring function. The use of a parsimony scoring function provides insight into the homology between sequences in the alignment. We also explore iterative refinement techniques such as a hidden Markov model and an intensification heuristic to further improve the alignment. This approach to multiple sequence alignment provides improved alignments as compared to several other methods.

Phylogenetics is the study of evolutionary relations between different organisms. Phylogenetic trees are the representations of these relations. Researchers have been working on finding fast and systematic approaches to reconstruct phylogenetic trees from observed data for over 40 years. It has been shown that, given a certain criterion to evaluate each tree, finding the best fitted phylogenetic trees among all possible trees is an NP-hard problem. In this study, we focus on the topology searching techniques for the maximum-parsimony and maximum-likelihood phylogeny inference. We proposed two search methods based on tabu search and genetic algorithms. We first explore the feasibility of using tabu search for finding the maximum-parsimony trees. The performance of the proposed algorithm is evaluated based on its efficiency and accuracy. Then we proposed a hybrid method of the tabu search and genetic algorithm. The experimental results indicate that the hybrid method can provide maximum-parsimony trees with a ggood level of accuracy and efficiency. The hybrid method is also implemented for finding maximum-likelihood trees. The experimental results show that the proposed hybrid method produce better maximum-likelihood trees than the default-setting dnaml program in average on the tested data sets. On a much larger data set, the hybrid method outperforms the default-setting dnaml program and has equally good performance as the dnaml program with the selected jumble option.