Ability of Objective Functions to Generate Points on Nonconvex Pareto Frontiers
Achille Messac, Glynn J. Sundararaj, Ravindra V. Tappeta, John E. Renaud · AIAA Journal · 2000
New ground is broken in our understanding of objective functions' ability to capture Pareto solutions for multi-objective design optimization problems. It is explained why widely used objective functions fail to capture Pareto solutions when the Pareto frontier is not convex in objective space, and the means to avoid this limitation, when possible, is provided. These conditions are developed and presented in the general context ofn-dimensional objective space, and numerical examples are provided. An important point is that most objective function structures can be made to generate nonconvex Pareto frontier solutions if the curvature of the objective function can be varied by setting one or more parameters. Because the occurrence of nonconvex efficient frontiers is common in practice, the results are of direct practical usefulness.