Many important application problems in engineering can be formalized as nonlinear optimization tasks. However, numerical methods for solving such problems are brittle and do not scale well. For example, these methods depend critically on choosing a good starting point from which to perform the optimization search. In high-dimensional spaces, numerical methods have difficulty finding solutions that are even locally optimal. The objective of this thesis is to demonstrate how machine learning techniques can improve the performance of numerical optimizers and facilitate optimization in engineering design. The machine learning methods have been tested in the domain of 2-dimensional structural design, where the goal is to find a truss of minimum weight that bears a set of fixed loads. Trusses are constructed from pure tension and pure compression members. The difference in the load-bearing properties of tension and compression members causes the gradient of the objective function to be discontinuous, and this prevents the application of powerful gradient-based optimization algorithms in this domain. In this thesis, the approach to numerical optimization is to find ways of transforming the initial problem into a selected set of subproblems where efficient, gradient-based algorithms can be applied. This is achieved by a three-step "compilation" process. The first step is to apply speedup learning techniques to partition the overall optimization task into sub-problems for which the gradient is continuous. Then, the second step is to further simplify each sub-problem by using inductive learning techniques to identify regularities and exploit them to reduce the number of independent variables. Unfortunately, these first two steps have the potential to produce an exponential number of sub-problems. Hence, in the third step, selection rules are derived to identify those sub-problems that are most likely to contain the global optimum. The numerical optimization procedures are only applied to these selected sub-problems. To identify good sub-problems, a novel ID3-like inductive learning algorithm called UTILITYID3 is applied to a collection of training examples to discover selection rules. These rules analyze the problem statement and identify a small number of sub-problems (typically 3) that are likely to contain the global optimum. In the domain of 2-dimensional structural design, the combination of these three steps yields a 6-fold speedup in the time required to find an optimal solution. Furthermore, it turns out that this method is less reliant on a good starting point for optimization. The methods developed in this problem show promise of being applied to a wide range of numerical optimization problems in engineering design. / Graduation date: 1992

In this study, a design procedure incorporating a genetic algorithm (GA) is developed for optimization of structures. The objective function considered is the total weight of the structure. The objective function is minimized subjected to displacement and strength requirements. In order to evaluate the design constraints, finite element analysis are performed either by using conventional finite element solvers (i.e. MSC/NASTRAN&reg / ) or by using in-house codes. The application of the algorithm is shown by a number of design examples. Several strategies for reproduction, mutation and crossover are tested. Several conclusions drawn from the research results are presented.

In this study, an optimization code has been developed based on genetic algorithms associated with the finite element modeling for the shape optimization of plane stress problems. In genetic algorithms, constraints are mostly handled by using the concept of penalty functions, which penalize infeasible solutions by reducing their fitness values in proportion to the degrees of constraint violation. In this study, An Improved GA Penalty Scheme is used. The proposed method gives information about unfeasible individual fitness as near as possible to the feasible region in the evaluation function. The objective function in this study is the area of the structure. The area is minimized considering the Von-Misses stress criteria. In order to minimize the objective function, one-point crossover with roulette-wheel selection approach is used. Optimum dimensions of four problems available in the literature have been solved by the code developed . The algorithm is tested using several strategies such as / different initial population number, different probability of mutation and crossover. The results are compared with the ones in literature and conclusions are driven accordingly.

The purpose of this study is to discuss the fitness of using PHMGA (Parallel Multilevel Hybrid Genetic Algorithm), which is a fast and efficient method, in the geometrically nonlinear structural optimization. Parallel genetic algorithms can solve the problem of traditional sequential genetic algorithms, such as premature convergence, large number of function evaluations, and a difficulty in setting parameters. By using several concurrent sub-population, parallel genetic algorithms can avoid premature convergence resulting from the single genetic searching environment of sequential genetic algorithms. It is useful to speed up the operation rate of joining timely multilevel optimization with parallel genetic algorithms. Because multilevel optimization can resolve one problem into several smaller subproblems, each subproblem is independent and not interference with one another. Then the subsystem of each level can be connected by sensitivity analysis. So we can solve the entire problem. Because each subproblem contains less variables and constrains, it can achieve the faster converge rate of the entire optimization. PHMGA integrates advantages of two methods including the parallel genetic algorithms and the multilevel optimization. In this study, PHMGA is adopted to solve several design optimization problems for nonlinear geometrically trusses on the parallel computer IBM SP2. The use of PHMGA helps reduce execution time because of integrating a multilevel optimization and a parallel technique. PHMGA helps speed up the searching efficiency in solving structural optimization problems of nonlinear truss. It is hoped that this study will demonstrate PHMGA is an efficient and powerful tool in solving large geometrically nonlinear structural optimization problems.

Thesis (Ph. D.)--Ohio State University, 2003. / Title from first page of PDF file. Document formatted into pages; contains xvi, 131 p.; also includes graphics (some col.). Includes abstract and vita. Advisor: Tamal K. Dey, Dept. of Computer and Information Science. Includes bibliographical references (p. 126-131).

As the use of carbon fiber reinforced polymers (CFRP) increases in aerospace struc- tures it is important to use this material in an efficient manner such that both the weight and cost of the structure are minimized while maintaining its performance. To com- bat undesirable vibrational characteristics of a structure an optimization program was developed which takes advantage of the orthotropic nature of composite materials to maximize eigenfrequency bandgaps. The results from the optimization process were then fabricated and subjected to modal testing. The experiments show that local fiber angle optimization is a valid method for modifying the natural frequencies of a structure with the theoretical results generally predicting the performance of the optimized composite plates.

As the use of carbon fiber reinforced polymers (CFRP) increases in aerospace struc- tures it is important to use this material in an efficient manner such that both the weight and cost of the structure are minimized while maintaining its performance. To com- bat undesirable vibrational characteristics of a structure an optimization program was developed which takes advantage of the orthotropic nature of composite materials to maximize eigenfrequency bandgaps. The results from the optimization process were then fabricated and subjected to modal testing. The experiments show that local fiber angle optimization is a valid method for modifying the natural frequencies of a structure with the theoretical results generally predicting the performance of the optimized composite plates.

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This dissertation presents a synthesis of methods for structural optimization of aircraft wing boxes. The optimization problem considered herein is the minimization of structural weight with respect to component sizes, subject to stress constraints. Different aspects of structural optimization methods representing the current state-of-the-art are discussed, including sequential quadratic programming, sensitivity analysis, parameterization of design variables, constraint handling, and multiple load treatment. Shortcomings of the current techniques are identified and a B-spline parameterization representing the structural sizes is proposed to address them. A new configurable B-spline parameterization method for structural optimization of wing boxes is developed that makes it possible to flexibly explore design spaces. An automatic scheme using different levels of B-spline parameterization configurations is also proposed, along with a constraint aggregation method in order to reduce the computational effort. Numerical results are compared to evaluate the effectiveness of the B-spline approach and the constraint aggregation method. To evaluate the new formulations and explore design spaces, the wing box of an airliner is optimized for the minimum weight subject to stress constraints under multiple load conditions. The new approaches are shown to significantly reduce the computational time required to perform structural optimization and to yield designs that are more realistic than existing methods.