Solving Minimum Distance Problems With Convex or Concave Bodies Using Combinatorial Global Optimization Algorithms

J.A. Carretero, M.A. Nahon
2005 IEEE Transactions on Systems Man and Cybernetics Part B (Cybernetics)  
Determining the minimum distance between convex objects is a problem that has been solved using many different approaches. On the other hand, computing the minimum distance between combinations of convex and concave objects is known to be a more complicated problem. Most methods propose to partition the concave object into convex sub-objects and then solve the convex problem between all possible sub-object combinations. This can add a large computational expense to the solution of the minimum
more » ... on of the minimum distance problem. In this paper an optimization-based approach is used to solve the concave problem without the need for partitioning the concave object into convex sub-objects. Since the optimization problem is no longer unimodal (i.e., has more than one local minimum point), global optimization techniques are used. Simulated Annealing and Genetic Algorithms are used to solve the concave minimum distance problem. In order to reduce the computational expense, it is proposed to replace the objects' geometry by a set of points on the surface of each body. This reduces the problem to an unconstrained combinatorial optimization problem where the combination of points (one on the surface of each body) that minimizes the distance will be the solution. Additionally, if the surface points are set as the nodes of a surface mesh, it is possible to accelerate the convergence of the global optimization algorithm by using a gradient-based local optimization algorithm. Some examples using these novel approaches are presented.
doi:10.1109/tsmcb.2005.850172 pmid:16366241 fatcat:5flonohyife27gacwpxhbxm24u