The present work aims at an efficient, portable, and robust design of a data-distributed massively parallel DIRECT, the deterministic global optimization algorithm widely used in multidisciplinary engineering design, biological science, and physical science applications. The original algorithm is modified to adapt to different problem scales and optimization (exploration vs.\ exploitation) goals. Enhanced with a memory reduction technique, dynamic data structures are used to organize local data, handle unpredictable memory requirements, reduce the memory usage, and share the data across multiple processors. The parallel scheme employs a multilevel functional and data parallelism to boost concurrency and mitigate the data dependency, thus improving the load balancing and scalability. In addition, checkpointing features are integrated to provide fault tolerance and hot restarts. Important algorithm modifications and design considerations are discussed regarding data structures, parallel schemes, error handling, and portability. Using several benchmark functions and real-world applications, the present work is evaluated in terms of optimization effectiveness, data structure efficiency, memory usage, parallel performance, and checkpointing overhead. Modeling and analysis techniques are used to investigate the design effectiveness and performance sensitivity under various problem structures, parallel schemes, and system settings. Theoretical and experimental results are compared for two parallel clusters with different system scale and network connectivity. An analytical bounding model is constructed to measure the load balancing performance under different schemes. Additionally, linear regression models are used to characterize two major overhead sources---interprocessor communication and processor idleness, and also applied to the isoefficiency functions in scalability analysis. For a variety of high-dimensional problems and large scale systems, the data-distributed massively parallel design has achieved reasonable performance. The results of the performance study provide guidance for efficient problem and scheme configuration. More importantly, the generalized design considerations and analysis techniques are beneficial for transforming many global search algorithms to become effective large scale parallel optimization tools. / Ph. D.

Two parallel deterministic direct search algorithms are combined to find improved parameters for a system of differential equations designed to simulate the cell cycle of budding yeast. Comparing the model simulation results to experimental data is difficult because most of the experimental data is qualitative rather than quantitative. An algorithm to convert simulation results to mutant phenotypes is presented. Vectors of the 143 parameters defining the differential equation model are rated by a discontinuous objective function. Parallel results on a 2200 processor supercomputer are presented for a global optimization algorithm, DIRECT, a local optimization algorithm, MADS, and a hybrid of the two. A second formulation is presented that uses a system of smooth inequalities to evaluate the phenotype of a mutant. Preliminary results of this formulation are given. / Master of Science

The DIRECT (DIviding RECTangles) algorithm JONESJOTi, a variant of Lipschitzian methods for bound constrained global optimization, has been applied to the optimal transmitter placement for indoor wireless systems. Power coverage and BER (bit error rate) are considered as two criteria for optimizing locations of a specified number of transmitters across the feasible region of the design space. The performance of a DIRECT implementation in such applications depends on the characteristics of the objective function, the problem dimension, and the desired solution accuracy. Implementations with static data structures often fail in practice because of unpredictable memory requirements. This is especially critical in S⁴W (Site-Specific System Simulator for Wireless communication systems), where the DIRECT optimization is just one small component connected to a parallel 3D propagation ray tracing modeler running on a 200-node Beowulf cluster of Linux workstations, and surrogate functions for a WCDMA (wideband code division multiple access) simulator are also used to estimate the channel performance. Any component failure of this large computation would abort the entire design process. To make the DIRECT global optimization algorithm efficient and robust, a set of dynamic data structures is proposed here to balance the memory requirements with execution time, while simultaneously adapting to arbitrary problem size. The focus is on design issues of the dynamic data structures, related memory management strategies, and application issues of the DIRECT algorithm to the transmitter placement optimization for wireless communication systems. Results for two indoor systems are presented to demonstrate the effectiveness of the present work. / Master of Science

In this thesis, we present two different approaches for the stochastic volatility and stochastic interest rate model with jump and analyze the performance of four alternative models. In the first approach, suggested by Scott, the closed form solution for prices on European call stock options are developed by deriving characteristic functions with the help of martingale methods. Here, we study the asset price process and give in detail the derivation of the European call option price process. The second approach, suggested by Bashki-Cao-Chen, describes the closed form solution of European call option by deriving the partial integro-differential equation. In this one we g ive the derivations of both asset price dynamics and the European call option price process. Finally, in the application part of the thesis, we examine the performance of four alternative models using General Electric Stock Option Data. These models are constructed by using the theoretical results of the second approach.

Une nouvelle approche appelée “Approche Pseudo Inverse” (API) est développée pour la modélisation du procédé de forgeage à froid des pièces axisymétriques. L'API est basée sur la connaissance de la forme de la pièce finale. Certaines configurations intermédiaires « réalistes » ont été introduites dans l'API pour considérer le chemin de déformations. Elles sont créées géométriquement sans traitement de contact et ensuite corrigées par la méthode de surface libre afin de respecter l'équilibre, les conditions aux limites et la condition d'incompressibilité. Un nouvel algorithme direct de plasticité est développé, conduisant à une méthode d'intégration plastique très rapide, précise et robuste même dans le cas de très grands incréments de déformations. Un modèle d'endommagement en déformation, est couplé à la plasticité et implémenté dans l'API. Les validations numériques montrent que l'API donne des résultats très proches des résultats de l'approche incrémentale mais en utilisant beaucoup moins de temps de calcul.L'API est adoptée comme solveur du forgeage pour la conception et l'optimisation des préformes du forgeage multi-passes. La rapidité et la robustesse de l'API rendent la procédure d'optimisation très performante. Une nouvelle technique est développée pour générer automatiquement le contour initial d'un outil de préforme pour la procédure d'optimisation. Les variables de conception sont les positions verticales des points de contrôle des courbes B-spline définissant les formes des outils de préforme. Notre optimisation multi-objectif consiste à minimiser la variation de la déformation plastique équivalente dans la pièce finale et la force du poinçon au cours du forgeage. Un algorithme génétique et un algorithme de recuit simulé sont utilisés pour trouver les points d'optimum de Pareto. Pour réduire le nombre de simulations de forgeage, un méta-modèle de substitution basé sur la méthode de krigeage est adopté pour établir une surface de réponse approximative. Les résultats obtenus par l'API en utilisant les outils de préforme optimaux issues de l'optimisation sont comparés à ceux obtenus par les approches incrémentales classiques pour montrer l'efficacité et les limites de l'API. La procédure d'optimisation combinée avec l'API peut être un outil numérique rapide et performant pour la conception et l'optimisation des outillages de préforme. / A new method called “Pseudo Inverse Approach” (PIA) is developed for the axi-symmetrical cold forging modelling. The PIA is based on the knowledge of the final part shape. Some « realistic » intermediate configurations are introduced in the PIA to consider the deformation path. They are created geometrically without contact treatment, and then corrected by using a free surface method in order to satisfy the equilibrium, the boundary conditions and the metal incompressibility. A new direct algorithm of plasticity is proposed, leading to a very fast, accurate and robust plastic integration method even in the case of very large strain increments. An isotropic damage model in deformation is coupled with the plasticity and implemented in the PIA. Numerical tests have shown that the Pseudo Inverse Approach gives very close results to those obtained by the incremental approach, but using much less calculation time.The PIA is adopted as forging solver for the design and optimization of preform tools in the multi-stage forging process. The rapidity and robustness of the PIA make the optimization procedure very powerful. A new method is developed to automatically generate the initial preform tool shape for the optimization procedure. The design variables are the vertical positions of the control points of B-spline curves describing the preform tool shape. Our multi-objective optimization is to minimize the equivalent plastic strain in the final part and the punch force during the forging process. The Genetic algorithm and Simulated Annealing algorithm are used to find optimal Pareto points. To reduce the number of forging simulations, a surrogate meta-model based on the kriging method is adopted to build an approximate response surface. The results obtained by the PIA using the optimal preform tools issued from the optimization procedure are compared to those obtained by using the classical incremental approaches to show the effectiveness and limitations of the PIA. The optimization procedure combined with the PIA can be a rapid and powerful tool for the design and optimization of the preform tools.