A direct approach to two-level decomposition: Structural optimization using the generalized reduced gradient
The goal of this thesis is to develop a straight forward approach to multi-level decomposition for the optimization of large engineering systems. The method's organizational structure is based on the Model Coordination approach outlined by Kirsch (1975). In this approach, the system is partitioned into a set of substructures or subsystems, where the local detailed dimensions of quantities in each subsystem are the design variables in that subsystem, while all other problem dimensions are held fixed. The optimization sub-problems formed from each of the subsystems are solved separately. There is one system level sub-problem in which the system's gross geometric dimensions are the design variables, while all other lower level dimensions are held fixed. The set of sub- problems is repeatedly solved until the system level objective function converges. Two new developments contribute to the success of this innovative direct approach to structural decomposition. The first new feature is that each of the sub-problems is solved with the Generalized Reduced Gradient optimization algorithm (Abadie & Carpentier, 1969). Because the Generalized Reduced Gradient method develops a sequence of feasible points as intermediate solutions and the value of the objective function must decrease monotonically with that sequence, the iterations can be stopped at any time with a resulting feasible solution that will have a superior objective function value. This is particularly advantageous when a practical optimum will be accepted if the theoretical optimum can not be found. The second and more significant development is as follows: by adjusting the maximum number of iterations per sub-problem and the initial step size, progress is limited in each of the sub- problems so that none strongly bias the direction that the overall solution takes. This causes the individual sub- problems to approach the system's optimum solution in a uniform manner. Successful convergence of this approach is demonstrated with two planar truss problems. The most valuable advantage of this technique over others discussed in the current literature is its ease of use. The analyst need only supply the objective functions, the constraints, their gradients, an initial starting point and an initial step size. This method has potential applications in the optimization of large multi-disciplinary engineering systems. Different optimization algorithms, specialized for a particular problem type or discipline, could be used for each of the various subsystems as is necessary.
School Location:USA - Ohio
Source Type:Master's Thesis
Keywords:direct approach two level decomposition structural optimization generalized reduced gradient
Date of Publication:01/01/1991