An Early-Stage Set-Based Design Reduction Decision Support Framework Utilizing Design Space Mapping and a Graph Theoretic Markov Decision Process Formulation

Abstract

A novel set reduction decision support framework for large-scale, team-based design efforts is presented. The framework provides a design manager with valuable and easy-to-understand information that is used to make better informed reduction decisions within a set-based design (SBD) environment. SBD is a convergent design method that uses dominance and infeasibility to consider multiple design alternatives in parallel while accommodating separate groups of specialists within a concurrent engineering approach. Based on the limitations of current SBD research and the completion of extensive design experiments, three major set reduction considerations are identified: time-dependent design relationships, the impact of reduction decisions, and identifying robust reduction decisions. Design relationships change as the fidelity of analysis increases, variable set-ranges are reduced, or requirement changes are instituted. Due to these changing conditions, the impact of reduction decisions can be difficult to determine. Although SBD has proven resilient to changing circumstances, the reduction process can still be impact the design process to the point of potential failure. Identifying robust reduction decisions avoids situations where changes lead to a design failure.

Each of the three considerations set forth is addressed by a specific component of the overall decision support framework used to analyze a specific function of interest. Design space mapping is used to determine relationships between variable and function spaces. The Longest Path Problem (LPP) formulated as a Markov Decision Process (MDP) is used as a structure for the reduction decision-making process and the identification of optimal decision paths. Through simulation, robust decision paths are identified. Since the developed LPP MDP formulation has never been used to analyze set reduction problems, multiple metrics and representations are developed using the MDP and simulation results.

Based on a series of studies, the MDP LPP framework is able to better handle situations with changing conditions, as well as better accommodate constrained problems, compared to a method based solely on current in-state knowledge. As part of a ship design case study, the framework’s ability to handle multiple and more complicated functions is shown. Also, how the framework fits into a more realistic reduction scenario is presented.