Ability of Objective Functions to Generate Points on Nonconvex Pareto Frontiers

Achille Messac, Glynn J. Sundararaj, Ravindra V. Tappeta, John E. Renaud
2000 AIAA Journal  
New ground is broken in our understanding of objective functions' ability to capture Pareto solutions for multiobjective 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 conditionsare developed and presented in the general context of n-dimensionalobjective space, and numerical examples are provided.
more » ... n 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 ef cient frontiers is common in practice, the results are of direct practical usefulness. Nomenclature J = aggregate objective function (a scalar) v i = i th entry of a generic vector v w = vector of numerical weights, used in forming the aggregate objective function x = n-dimensional design parameter vector µ = m-dimensional design metric vector (also referred to as design criteria or design objectives vector)
doi:10.2514/2.1071 fatcat:n2gnvevxrvdujmsavu5mhom5we