A General Approach to Constrained Optimal Design Based on Symbolic Mathematics

Abstract

Abstract This paper presents a new method of optimal design that combines ideas and techniques from both the Method of Optimal Design (MOD) and monotonicity analysis. This new method, while presently limited to constrained monotonic problems, has been automated. The problem is first reduced in size and reformulated using ideas from MOD. The reduced problem is then repeatedly reformulated to develop state and design equations in terms of all possible variable partitions. The complete set of candidate optimal solution points is extracted by monotonicity analysis applied to the trivial constraint sets on the design equations from every possible formulation of the problem. These candidate solution points can then be numerically sorted to determine the optimal solution for a particular numerical case. The new method and its automation are illustrated with two example problems from the literature.