A transformation system for interactive reformulation of design optimization strategies

Abstract

Automatic design optimization is highly sensitive to problem formulation. The choice of objective function, constraints and design parameters can dramatically impact on the computational cost of optimization and the quality of the resulting design. The best formulation varies from one application to another. A design engineer will usually not know the best formulation in advance. To address this problem, we have developed a system that supports interactive formulation, testing and reformulation of design optimization strategies. Our system includes an executable, data-flow language for representing optimization strategies. The language allows an engineer to define multiple stages of optimization, each using different approximations of the objective and constraints or different abstractions of the design space. We have also developed a set of transformations that reformulate strategies represented in our language. The transformations can approximate objective and constraint functions, abstract or reparameterize search spaces, or divide an optimization process into multiple stages. The system is applicable in principle to any design problem that can be expressed in terms of constrained optimization; however, we expect the system to be most useful when the design artifact is governed by algebraic and ordinary differential equations. We have tested the system on problems of racing yacht design and jet engine nozzle design. We report experimental results demonstrating that our reformulation techniques can significantly improve the performance of automatic design optimization. Our research demonstrates the viability of a reformulation methodology that combines symbolic program transformation with numerical experimentation. It is an important first step in a research program aimed at automating the entire strategy formulation process.