On Alternative Problem Formulations for Multidisciplinary Design Optimization

In this paper we introduce a perspective on multidisciplinary design optimization (MDO) problem formulation that provides a basis for choosing among existing formulations and suggests provocative, new ones. MDO problems offer a richer specmm of possibilities for problem formulation than do single discipline design optimization problems, or multidisciplinary analysis problems. This is because the variables and the equations that characterize the MDO problem can be "partitioned" in some interesting ways between what we traditionally think of as the "analysis code(s)" and the "optimization code." An MDO approach can be characterized by what part of the overall computation is done in each code, how that computation is done, and what information is communicated between the codes. The key issue in the three fundamental approachcs to MDO formulation that we discuss is the kind of feasibility that is maintained at each optimization iteration. In the most familiar "multidisciplinary feasible" approach, the multidisciplinary analysis problem is solved at each optimization iteration. At the other end of the spectrum is the "all-at-once" approach where feasibility happens only at optimization convergence. Between these extremes lie other, new, possibilities that amount to maintaining feasibility of the individual analysis disciplines at each optimization iteration, while allowing the optimizer to drive the computation toward multidisciplinary feasibility as convergence is approached. There are further considerations completing the classification such as how the optimization is actually done, * Senior Member AIAA Copyright O 1992 by The Boeing Company. Published by the American Institute of Aeronautics and Astronautics, Inc. with permission. how sensitivity information is computed from each discipline, and how, if necessary, individual gradients are combined to obtain overall problem gradients. This view of MDO problem formulation highlights the trade-offs between reuse of existing software, computing resources required, and probability of success.