10:30 AM - 10:55 AM
Global Optimization using Contractor Programming
Nowadays, the optimization problems are complex. But, despite the increasing number of solvers, the resolution is always a hard task to merge different kinds of constraints (linear, non-convex or black-box,...) and different kinds of variables (continuous, integer, optimal control,...). The Contractor Programming is a united framework which combines heterogeneous solvers. The principle is based on a Branch-and-Bound using Interval Analysis. Each algorithm is brought to an elementary operation which consists to contract or to prune a box.
10:55 AM - 11:20 AM
Heuristic Global Optimization via Quick Exploration of the Variable Space
Many heuristics for global optimization require numerous launches of an expensive local solver. We avoid this by using quick and computationally inexpensive methods (constraint consensus, clustering, simple search) to explore the variable space before choosing a small number of launch points for the local solver. Encouraging empirical results are given.
11:20 AM - 11:45 AM
Packing Unit Spheres into Three Dimensional Sphere Using VNS
The NP hard optimization problem of packing unit radii spheres into the three dimensional sphere is approximately solved using a variable neighborhood search (VNS) which identifies (near-) global optima by searching the neighborhoods of local minima. VNS obtains neighboring solutions by shaking one or more spheres. It alters the size of a neighborhood every time it fails to find an improving solution.
Keywords: variable neighborhood search, packing spheres in a cube, non-linear programming, three dimensional packing