Multidisciplinary Design Optimization (MDO) deals with formulating and solving problems arising in complex organizational systems comprising of a system-level coupled with several subsystems and their interactions. The MDO framework involves a substantial amount of data transfer and interaction between the subsystems and the systems. Maximizing the decision-taking autonomy for each subsystem renders an effective MDO algorithm. In a general framework, the system allocates the resource variables to the subsystems whose duty is to optimize their local domain. The system's objective is in turn a function of the resources and (possibly) of the subsystem objectives. The interacting disciplines typically have conflicting objectives. For complex systems, the optimization model of each subsystem and the system may comprise of highly nonlinear, nonsmooth, nonconvex objective and constraint functions giving rise to a sequence of difficult optimization problems over the design space.

The aim of this research is to design a novel robust MDO algorithm that maximizes subsystem autonomy by allowing each subsystem to have local decisions as well as (proxy) local resource variables. A suitable trust region places bounds on these proxy variables. System-level optimization independently revises the values of the global resource variables. Using the revised values, subsystem-level optimization finds a new optimal local decision. The process is iterated till convergence on the proxy local resource variables and the global resource variable. It is easy to incorporate a parallel computing framework within this algorithm. Analytical expressions for the gradient functions are used if available, otherwise a derivative approximation scheme is presented. Augmented Lagrangians are used in the objective functions at the system and subsystem-level to handle the coupling between the two hierarchies and to promote convergence of the algorithm.

We are currently focusing on refining the algorithm and are trying to handle feasibility issues across the various disciplines. In order to get a consistent solution, it is necessary to address feasibility since some of the local decision variables at the subsystem level could be shared among multiple disciplines. We are also trying to devise a methodology to ensure a suitable size step is taken in the descent direction at each major iteration. We plan to use the problems (a few of which are nonlinear system of equations) at NASA's MDO test suite to test our algorithm.