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

Spatial planning with constraints on translational distances between geometric objects

The main constraint on relative position of geometric objects, used in spatial planning for computing the C-space maps (for example, in robotics, CAD, and packaging), is the relative non-overlapping of objects. This is the simplest constraint in which the minimum translational distance between objects is greater than zero, or more generally, than some positive value. We present a technique, based on the Minkowski operations, for generating the translational C-space maps for spatial planning with more general and more complex constraints on the relative position of geometric objects, such as constraints on various types (not only on the minimum) of the translational distances between objects. The developed technique can also be used, respectively, for spatial planning with constraints on translational distances in a given direction, and rotational distances between geometric objects, as well as for spatial planning with given dynamic geometric situation of moving objects