Sequential Cooperative Robust Optimization (SCRO) for Multi-Objective Design Under Uncertainty

The optimal design of systems under uncertainty is a critical challenge faced by design engineers. Robust optimization is a well-studied and widely used technique for the design of engineering systems that possess uncertainty, and numerous robust optimization techniques have been presented in recent years. The majority of the robust optimization techniques presented in the literature suffer from a computational efficiency challenge, either due to the expense of obtaining objective or constraint function uncertainty information, or due to the fact that many robust optimization approaches (with a few notable exceptions) require that a potentially expensive uncertainty analysis calculation (e.g. Monte-Carlo simulation) be nested within an already potentially expensive optimization solver (e.g. a genetic algorithm). Additionally, many robust optimization approaches focus solely on design problems that possess a single design objective, and the robust techniques that do consider problems with multiple design objectives often require various simplifying assumptions or are even more computationally expensive to implement. Clearly there are opportunities for improvement in the area of robust optimization, and this paper presents a new robust design Optimization approach called Sequential Cooperative Robust Optimization (SCRO), which uses both a sequential approach and multi-objective optimization techniques in an effort to decouple the deterministic system optimization problem from the associated uncertainty analysis problem. The SCRO approach first fits surrogate models to the system objective and constraint functions, in addition to system sensitivity functions, using as few function calls as possible in order to improve computational efficiency. The approach then performs a series of sequential multi-objective optimizations using the developed surrogate models. These optimizations work to find points in the design space that are optimal with respect to deterministic performance and both objective and feasibility robustness metrics based on predicted system sensitivities. The SCRO approach has the potential to find solutions not available to other robust optimization approaches, and can be more efficient than other more traditional robust optimization techniques due to its use of surrogate approximation and a sequential framework.