Solving a Network Flow Decision Problem with Sampled Nonlinearities

Abstract

The tensor product B-spline is applied in global solution of approximated mixed integer nonlinear programs, exploiting the special structure of the B-spline to create convex relaxations in a Branch-and-Bound framework. The main application considered is the short-term oil production optimization problem, were one of the fundamental challenges is to replace the nonlinear simulator models with more conveniently manipulated approximations. Representing the network structure analytically allows for a decoupling of large simulator models into smaller, manageable components that can be replaced individually. The suggested method is applied to a real production case and a classic academic problem. The results presented are of both theoretical and practical interest and indicate that the method has potential and is worthy of further investigation.