Approximate multi-parametric programming based B&B algorithm for MINLPs

In this work an improved B&B algorithm for MINLPs is proposed. The basic idea of the proposed algorithm is to treat binary variables as parameters and obtain the solution of the resulting multi-parametric NLP (mp-NLP) as a function of the binary variables, relaxed as continuous variables, at the root node of the search tree. It is recognized that solving the mp-NLP at the root node can be more computationally expensive than exhaustively enumerating all the terminal nodes of the tree. Therefore, only a local approximate parametric solution, and not a complete map of the parametric solution, is obtained and it is then used to guide the search in the tree.