In this paper an optimization approach is used to solve the problem of finding the minimum distance between concave objects, without the need for partitioning the objects into convex sub-objects. Since the optimization problem is not unimodal (i.e., has more than one local minimum point), a global optimization technique, namely a Genetic Algorithm, is used to solve the concave problem. In order to reduce the computational expense of evaluating the constraints at runtime, the objects’ geometry is replaced by a set of points on the surface of the body. This reduces the problem to a combinatorial problem where the combination of points (one on each body) that minimizes the distance will be the solution. Additionally, niche formation is used to allow the minimum distance algorithm to track multiple minima rather than exclusively looking for the global minimum.
Approaching the Minimum Distance Problem by Algebraic Swarm-Based Optimizations
