Aiaa-2000-4919 Voronoi Diagram Based Cumulative Approximation for Engineering Optimization

This paper proposes a function approximation scheme based on Voronoi diagram, a technique of computational geometry, toward optimization cost saving in real engineering applications. The scheme consists of a blending function of local information over spatial structure among sample points that is topologically represented with Voronoi diagram, an estimation method of function gradients through the method of least squares along each Voronoi region, and an associated overall optimization algorithm. The scheme can locally establish and cumulatively update an approximation function based on the nature of Voronoi diagram, and this leads efficient and accurate accumulation of samples toward superior global fidelity in function approximation. Its validity and advantages are demonstrated through its application to a twodimensional example problem and a welded beam structure design problem.