New Adaptive Move-Limit Management Strategy for Approximate Optimization, Part 2

Abstract

Approximations play an important role in multidisciplinary design optimization 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. To ensure convergence of the sequence of approximate optimizations to a Karush-Kuhn-Tucker solution a move-limit management strategy is required. In a companion paper, issues of move-limit management are reviewed and a new adaptive strategy for move-limit management is developed (Wujek, B. A., and Renaud, J. E., New Adaptive Move-Limit Management Strategy for Approximate Optimization, Part 1,' AIAA Journal, Vol. 36, No. 10, 1998, pp. 1911-1921). With its basis in the provably convergent trust region methodology, the trust region ratio approximation method (TRAM) 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 TRAM strategy is successfully implemented in application to several multidisciplinary design optimization test problems. In addition, a comprehensive study comparing the performance of the TRAM strategy to existing move-limit strategies is conducted. Results indicate that application of the TRAM strategy results in increased efficiency for approximate optimization processes. 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.