EFFICIENT SINGLE-LEVEL SOLUTION OF HIERARCHICAL PROBLEMS IN STRUCTURAL OPTIMIZATION

Engineering design is hierarchical in nature, and the hierarchy can be used to improve the efficiency of design optimization. Multilevel optimization techniques incorporate the hierarchy at the formulation stage and result in the coordinated optimization of a number of subsystems. However, the use of these techniques is associated with numerical difficulties such as discontinuous derivatives. Single-level hierarchical solution techniques take advantage of the hierarchical nature at the solution stage. The present paper demonstrates the use of the latter approach in structural optimization for a penalty-function optimization method based on Newton's method. A single-level decomposition technique is developed that reduces the computational costs and memory requirements without incurring the disadvantages of multilevel optimization. The technique is demonstrated for a portal frame example. Substantial savings of about 75% are obtained for a case with 500 design variables and 2408 constraints with indication of higher potential savings for larger problems. For truly large systems, this decomposition technique provides the necessary reduction of computational effort to make the optimization process viable. © 1990 American Institute of Aeronautics and Astronautics, Inc., All rights reserved.