Inverse Graphical Method for Global Optimization and Application to Design Centering Problem

Consider the problem of finding an optimal value of some objective functional subject to constraints over numerical domain. This type of problem arises frequently in practical engineering tasks. Nowdays almost all general methods for solving such a problem are based on user-supplied routines computing the objective value at some points. We study another approach called inverse relying on some procedure to estimate the set of points instead having objective values bounded by a specified constant. In particular, we present an inverse optimization algorithm derived from the bisection of the objective range. In case of seeking a proven global optimal solution inherently requiring many computations, and a problem with some kind of coherency utilized in estimation procedure, the inverse scheme is much more efficient than conventional ones. An example of such a problem, namely the design centering, is studied to compare the approaches

On finding large empty convex bodies in 3D scenes of polygonal models.

This paper presents a method for finding large empty convex bodies within a 3D scene of polygonal models. The convex bodies we pack are discrete orientation polytopes (k-dops) with a small number of facets. The algorithm searches for a large empty k-dop within the scene, using a combination of random sampling and physical simulation, allowing the body to grow and interact (via rotation, translation, and scaling) with the environment when collisions are detected. We pack multiple empty k-dops in a 3D scene using a greedy incremental approach, attempting to maximize the volume of each new body found. We demonstrate the practicality of our method experimentally, showing that it is fast and that it does an effective job of packing on a variety of models.