Design Optimization Problem Reformulation Using Singular Value Decomposition

This paper presents a design optimization problem reformulation method based on Singular Value Decomposition (SVD), dimensionality reduction, and unsupervised clustering. The method calculates linear approximations of the associative patterns of symbol co-occurrences in a design problem representation to infer induced interaction/coupling strengths between variables and constraints. Unsupervised clustering of these approximations is used to identify useful reformulations. These two components of the method automate a range of reformulation tasks that have traditionally required different solution algorithms. We explain the method using an analytic model-based decomposition problem, and apply the method to an analytic hydraulic cylinder design problem as an example of heuristic design “case” identification, and to non-analytic problems expressed in FDT and DSM forms as examples of design decomposition. An Aircraft Concept Sizing (ACS) problem is used to empirically validate the method’s performance. The results show that the method can be used to infer multiple well-formed reformulations starting from a single problem representation in a knowledge-lean and training lean manner.