Design Optimization Problem Reformulation Using Singular Value Decomposition

This paper presents a design optimization problem reformulation method based on singular value decomposition, dimensionality reduction, and unsupervised clustering. The method calculates linear approximations of associative patterns of symbol co-occurrences in a design problem representation to induce implicit coupling strengths between variables and constraints. Unsupervised clustering of these approximations is used to heuristically identify useful reformulations. In contrast to knowledge-rich Artificial Intelligence methods, this method derives from a knowledge-lean, unsupervised pattern recognition perspective. We explain the method on an analytically formulated decomposition problem, and apply it to various analytic and nonanalytic problem forms to demonstrate design decomposition and design "case" identification. A single method is used to demonstrate multiple design reformulation tasks. 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 manner.