Most engineering design problems involve optimizing a number of often conflicting performance measures in the presence of multiple constraints. Traditional vector optimization techniques approach these problems by generating a set of Pareto-optimal solutions, where any specific objective can be further improved only at the cost of degrading one or more other objectives. The solutions obtained in this manner, however, are only single points within the space of all possible Pareto-optimal solutions and generally do not indicate to designers how small deviations from predicted design parameters settings affect the performance of the product or the process under study.

In this paper we introduce a new approach to robust design based on the concept of inductive learning with regression trees. Given a set of training examples relating to a multiobjective design problem, we demonstrate how a multivariate regression tree can utilize an information-theoretic measure of covariance complexity to capture optimal, tradeoff design surfaces. The novelty of generating design surfaces as opposed to traditional points in the design space is that now designers are able to easily determine how the responses of a product or process vary as design parameters change. This ability is of paramount importance in situations where design parameter settings need to be modified during the lifetime of a product/process due to various economic or operational constraints. As a result, designers will be able to select optimal ranges for design parameters such that the product's performance indices exhibit minimal or tolerable deviations from their target values. To highlight the advantages of our methodology, we present a multiobjective example that deals with optimum design of an electric discharge machining (EDM) process.