Improved Trust Region Model Management for Approximate Optimization

Approximations play an important role in multidisciplinary design optimization (MDO) by offering system behavior information at a relatively low cost. Most approximate optimization strategies are sequential in which an optimization of an approximate problem subject to design variable move limits is iteratively repeated until convergence. The move limits are imposed to restrict the optimization to regions of the design space in which the approximations provide meaningful information. In order to insure convergence of the sequence of approximate optimizations to a Karush Kuhn Tucker solution a move limit management strategy is required. In this paper, issues of move-limit management are reviewed and a new adaptive strategy for move limit management is developed. With its basis in the provably convergent trust region methodology, the TRAM (Trust region Ratio Approximation Method) strategy utilizes available gradient information and employs a backtracking process using various two-point approximation techniques to provide a flexible move-limit adjustment factor. The new strategy is successfully implemented in application to a suite of multidisciplinary design optimization test problems. These implementation studies highlight the ability of the TRAM strategy to control the amount of approximation error and efficiently manage the convergence to a Karush Kuhn Tucker solution.