Optimal Design of Single Output Process System by Max-Sensitive Method

Abstract

A new optimization technique called the max-sensitive method has been developed for a class of single output optimization problems, that is, to obtain the optimal solution A^* which minimizes g (A) subject to A_i≥0 (i=1, 2, …, n) when one system output X_out (A) =f (A) has been specified. Initially, the family of problems is formulated in which the original problem is imbedded. “Maximize X_out (A) =f (A) subject to A_i≥0 (i=1, 2, …, n), and g (A) ≥t, where t is increased from a lower bound t₀ to an upper bound, t_f.”
The optimal solutions of this family of problems form an equi-sensitive line on which the sensitivities S_i= (∂f/∂A_i) / (∂g/∂A_i) become equal to each other. A new algorithm for following the equi-sensitive line is presented, and the optimal solution of the original problem is then easily obtained. As well as the theoretical aspects of the method, numerical considerations of practical design problems are included. By applying this method to the design of complex heat exchanger systems, it has been shown to have many distinct advantages.