Using interval techniques to solve a parametric multi-objective optimization problem

Abstract

A system that solves a parametric multi-objective optimization problem in a combined design space and parameter space using interval techniques is described. The design space contains design-space variables fixed for a selected design; the parameter space contains variable parameters for the selected design. Multiple-objective functions are specified for optimization. The system initializes a design-variable box spanning the design space and performs interval optimization process on the parameter space by subdividing the design-variable box into design-variable sub-boxes, and iteratively: (1) determining parametric Pareto fronts for a design-variable sub-box using an interval optimization technique; (2) comparing parametric Pareto fronts associated with a set of design-variable sub-boxes and determining the parametric Pareto fronts certainly dominated by other parametric Pareto fronts; (3) eliminating the design-variable sub-boxes associated with the certainly dominated Pareto fronts; and (4) subdividing remaining design-variable sub-boxes. An optimized solution is produced from the remaining design-variable sub-boxes and the associated parametric Pareto fronts.