AN AUTOMATED MODELING AND REFORMULATION SYSTEM FOR DESIGN OPTIMIZATION

Many optimization problems in engineering rely on the use of computer algorithms for solving nonlinear programming (NLP), mixed-integer linear programming (MILP) and mixed-integer nonlinear programming (MINLP) models. Although a number of powerful optimization packages are currently available, it is still far from trivial for design engineers to properly formulate optimization models. Since a qualitative knowledge base does exist for expert modelling of optimization problems. there is an incentive to develop computer systems that can encode this knowledge. In this work we develop some of this qualitative knowledge and describe a knowledge-based implementation for automatic model reformulation. The resulting program, REFORM, symbolically reformulates nonlinear and mixed-integer models to increase the robustness and efficiency of the respective algorithms. Models specified in GAMS input files are automatically preprocessed by REFORM to generate a new, well-formulated model. Moreover, its capabilities include constraint reformulation to induce linearity and convexity, tightening of bounds, problem scaling and fixing binary (0-1) variables a priori. While some of these represent common knowledge in the area of optimization, the tight bounding procedure is a novel method that exploits monotonicity in the linear and nonlinear equations. and has applications for fixing binary variables. Computational results are presented to illustrate how the implementation of qualitative knowledge-based problem reformulation can improve the solution of poorly developed models.