Voronoi Diagram Based Blending of Quadratic Response Surfaces for Cumulative Global Optimization

This paper proposes a Voronoi diagram based blending scheme of local response surfaces for cumulative global optimization. In the scheme, after sample points are distributed over the design space and local function expressions are generated as quadratic polynomials for the subspaces around respective sample points, they are blended into the global approximation by using superposable function approximation based on geometric structure that is represented by Voronoi diagram, a technique of computational geometry. Under its superposability, it has an ability of cumulative function approximation, in which sample points are adaptively added based on tentative optimization results and approximation fidelity is cumulatively enhanced. Numerical examples of cumulative global optimization are given to ascertain the effectiveness and validity of the proposed blending scheme.