The Smart Normal Constraint Method for Directly Generating a Smart Pareto Set

In design situations where a single solution must be selected, it is often desirable to present the designer with a smart Pareto set of solutions—a minimal set of nondominated solutions that sufficiently represents the tradeoff characteristics of the design space. These sets are generally created by finding many well-distributed solutions and then either filtering out the excess ones or searching more closely in those regions that appear to have significant tradeoff. Such methods suffer from the inherent inefficiency of creating numerous solutions that will never be presented to the designer. This paper introduces the Smart Normal Constraint (SNC) method—a Pareto set generation method capable of directly generating a smart Pareto set. Direct generation is achieved by iteratively updating an approximation of the design space geometry and searching only in those regions capable of yielding new smart Pareto solutions. This process is made possible through the use of a new, computationally benign calculation for identifying regions of high tradeoff in a design space. Examples are provided that show the SNC method performing significantly more efficiently than the predominant existing method for generating smart Pareto sets.