A Generalized Global Optimization Algorithm for Dual Response Systems

During exploration of an industrial process, the engineer/experimenter must take into account both the mean and variance of the system in order to seek the appropriate parameter settings for better production outputs. This situation leads to the problem of determining optimal operating conditions for one response function while keeping a desirable target on the other response, the so-called dual response (DR) system. The purpose of this paper is to present an ANSI FORTRAN implementation of a comprehensive algorithm for the global (or near-global) optimization of DR systems within a radial region of experimentation. The algorithm, DR2, is a new computational procedure that guarantees a global optimal solution for nondegenerate problems and returns a near-global one for degenerate problems. Three degenerate problems published in the response surface methodology literature are provided which compare the performance of DR2 with that of other algorithms. In one of these examples, the Taguchi’s “target is best” case is used to illustrate an important application of DR2. In the final parts of the paper, DR2 is tested against an implementation of sequential quadratic programming (SQP)-MINOS. Computational results based on large simulations show that DR2 is more effective at locating optimal operating conditions (near global optima) even if the DR system is degenerate.