To aid in faster and better decision making it is interesting to couple advanced simulators with optimization tools.Most simulators however does not offer gradients, therefore derivative-free methods must be used. In this thesis optimization of and oil and gas field with free routing is considered. By embedding the structural information in the optimization problem and approximating the simulators by polynomials a MINLP problem is formed which can be solved by gradient based solvers. This approach requires that the polynomial models are updated frequently to fit the simulators. Each update requires several simulations and creates a trade-off between robustness and computation time. Different updating strategies for the models are considered in this thesis. By solving a separate optimization problem to update the models the MINLP problem can be formulated as a convex problem which is solved in a branch and bound framework and with an interior-point. Two approaches to updating the models in respect to the branch and bound method are explored, and it is found to be more robust to update the models for each node of the branch and bound tree, ensuring a local fit before branching.