A Branch-and-Estimate Heuristic Procedure for Solving Nonconvex Integer Optimization Problems

We present a method for solving nonconvex mixed-integer nonlinear programs using a branch-and-bound framework. At each node in the search tree, we solve the continuous nonlinear relaxation multiple times using an existing non-linear solver. Since the relaxation we create is in general not convex, this method may not find an optimal solution. In order to mitigate this difficulty, we solve the relaxation multiple times in parallel starting from different initial points. Our preliminary computational experiments show that this approach gives optimal or near-optimal solutions on benchmark problems, and that the method benefits well from parallelism.