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.
