Design Space Covering for Uncertainty: Exploration of a New Methodology for Decision Making in Early Stage Design

Abstract

Decisions made in early-stage design are of vital importance as they significantly impact the quality of the final design. Despite recent developments in design theory for early-stage design, designers of large complex systems still lack sufficient tools to make robust and reliable preliminary design decisions that do not have a lasting negative impact on the final design. Much of the struggle stems from uncertainty in early-stage design due to loosely defined problems and unknown parameters. Existing methods to handle this uncertainty in point-based design provide feasible, but often suboptimal, solutions that cover the range of uncertainty. Robust Optimization and Reliability Based Design Optimization are examples of point-based design methods that handle uncertainty. To maintain feasibility over the range of uncertainty, these methods accept suboptimal designs resulting in a design margin. In set-based design, design decisions are delayed preventing suboptimal final designs but at the expense of computational efficiency. This work proposes a method that evaluates a compromise between these two methodologies by evaluating the trade off of the induced regret and computational cost of keeping a larger design space. The design space covering for uncertainty (DSC-U) problem defines the metrics regret, which measures suboptimality, and space remaining, which quantifies the design space size after it is reduced. Solution methods for the DSC-U problem explore the trade space between these two metrics. When there is uncertainty in a problem, and the design space is reduced, there is the possibility that the optimal solution for the realized values of the uncertainty parameters has been eliminated; but without performing the design space reduction, it is computationally expensive to properly explore the original design space. Because of this, smart design space reductions need to be made to avoid the elimination of the optimal solution. To make smart design space reductions, designers need information regarding the design space and the trade-offs between the computational efficiency of a smaller subspace and the expected regret, or suboptimality, of the final design. As part of the DSC-U defitition, two separate spaces for the design variables and the uncertain parameters are defined. Two algorithms are presented here that solve the DSC-U problem as it is defined. A nested optimizer algorithm using a single objective optimization problem, nested in a multi-objective optimization problem is capable of finding the Pareto front in the regret-space remaining trade space for small problems. The nested optimizer algorithm is used to solve a box girder design and a cantilever tube design problems. The level set covering (LSC) algorithm solves for the Pareto front by solving the set covering problem with level sets corresponding to allowable regret levels. The LSC is used to solve a 7-variable Rosenbrock problem and a midship design problem. The presented solutions show that the DSC-U problem is a valid approach for handling uncertainty in early-stage design.