The Method of Alternate Formulations, an Automated Strategy for Optimal Design

Abstract

The Method of Alternate Formulations (MAF) is a new method of global information extraction for constrained, nonlinear optimization problems. MAF automatically generates the complete set of candidate solution points for these optimization problems using a symbolic mathematics computer package. MAF uses ideas and techniques from both the Method of Optimal Design and Monotonicity Analysis to reduce and formulate the problem. The reduced problem is repeatedly reformulated to develop state equations and objective functions in terms of all possible variable partitions. Trend analysis on the decision variables in the objective functions yields global information about constraint activity at possible solution points. Trend analysis on all of the possible formulations of the objective functions yields the complete set of candidate solutions. The state equations in each partition of the variables are used to test the feasibility of these candidate solutions, and the best feasible point is selected as the optimum solution. MAF can be used as a preprocessor for standard numerical optimization techniques and can be extended to nonmonotonic problems.