| The question of parallelisms in the structural optimization process is investigated in this dissertation. The study reveals that parallelism can be used in most steps of the process. For example, during analysis, substructuring techniques and element-by-element preconditioned conjugate gradient methods are excellent for parallel computation; and in the optimization process, multilevel optimization, design sensitivity analysis, and optimization algorithms lend themselves very well to parallelism. It is found that multilevel parallelism exists in solving structural optimization problems.; Next, the study focuses on parallel optimization algorithms. Most of these algorithms have been designed for unconstrained optimization problems; they are not directly applicable to constrained optimization. There are only a few parallel constrained optimization algorithms and none of them is meant for general applications.; A sequential SQP algorithm using the primal QP approach is implemented and tested on a set of test problems including 113 mathematical programming problems, 31 truss design problems and 9 frame design problems. The results are compared with the ones from an existing program that uses the dual QP approach. The comparison shows the two approaches to be quite comparable.; Several QP subproblems are defined and their influence on the performance of the optimization algorithm is studied. The numerical results reveal that no single QP definition is superior to others. Therefore, a parallel SQP algorithm is proposed where multiple QP subproblems are defined and solved. The proposed algorithm is implemented on a shared memory parallel machine. Each QP subproblem gives a different search direction. A criterion is developed to choose the "best" direction. The parallel algorithm is run on one, two, and three processors. The numerical results show that the parallel SQP algorithm using multiple QP subproblems improves the efficiency as well as robustness. A parallel line search scheme that tries several step sizes along the search direction is also implemented. This scheme further enhances the numerical performance of the algorithm. |
