Mixed Integer Optimization With NURBs HyPerModels

The challenge of determining the best design in a multimodal design space with multiple local optimal solutions often challenges the best available optimization techniques. By casting the objective function of the optimization problem in the form of a Non-Uniform Rational B-spline (NURBs) metamodel, known as a HyPerModel, significant optimization advantages can be achieved, including the ability to efficiently find the global metamodel optimum solution with less computational expense than traditional approaches. This optimization strategy, defined by the HyPerOp algorithm, uses the underlying structure of a HyPerModel to intelligently select starting points for optimization runs and to identify regions of the design space that do not contain locations for the global metamodel optimum location. This paper describes the application of the HyPerOp algorithm to mixed integer programming problems and demonstrates its use with two example applications. The algorithm works with design spaces composed of continuous and integer design variables and provides a complementary approach for improved optimization capabilities.