A Learning and Inference Mechanism for Design Optimization Problem (Re)-Formulation Using Singular Value Decomposition

This paper presents a knowledge-lean learning and inference mechanism based on Singular Value Decomposition (SVD) for design optimization problem (re)-formulation at the problem modeling stage. The distinguishing feature of the mechanism is that it requires very few training cases to extract and generalize knowledge for large classes of problems sharing similar characteristics. The genesis of the mechanism is based on viewing problem (re)-formulation as a statistical pattern extraction problem. SVD is applied as a dimensionality reduction tool to extract semantic patterns from a syntactic formulation of the design problem. We explain and evaluate the mechanism on a model-based decomposition problem, a hydraulic cylinder design problem, and a medium-large scale Aircraft Concept Sizing problem. The results show that the method generalizes quickly and can be used to impute relations between variables, parameters, objective functions, and constraints when training data is provided in symbolic analytical form, and is likely to be extensible to forms when the representation is not in analytical functional form.