Multiresponse Optimization and Pareto Frontiers

Abstract

Methods that can capture evenly distributed solutions along the Pareto frontier are useful for multiresponse optimization problems because they provide a large variety of alternative solutions to the decision maker from among a set of nondominated solutions. However, methods often used for optimizing dual and multiple dual response problems have been rarely evaluated in terms of their ability to capture those solutions. This article provides this information by evaluating a global criterion–based method and the popular weighted mean square error method. Convex and nonconvex response surfaces were considered, and results of the methods were compared with those of a lexicographic approach on the basis of two examples from the literature. Regarding the results, it is shown that the user can be successful in capturing Pareto solutions in convex and nonconvex regions using the global criterion–based method. Moreover, it is shown that the starting point affects the distribution of solutions along the Pareto frontier but is not pivotal to obtain a complete representation of the Pareto frontier. For this purpose, it is necessary to decrease the weight increment and to compute for more solutions. Copyright © 2011 John Wiley & Sons, Ltd.