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

Branch and bound based coordinate search filter algorithm for nonsmooth nonconvex mixed-integer nonlinear programming problems

Publicado em "Computational science and its applications – ICCSA 2014...", ISBN 978-3-319-09128-0. Series "Lecture notes in computer science", ISSN 0302-9743, vol. 8580.A mixed-integer nonlinear programming problem (MINLP) is a problem with continuous and integer variables and at least, one nonlinear function. This kind of problem appears in a wide range of real applications and is very difficult to solve. The difficulties are due to the nonlinearities of the functions in the problem and the integrality restrictions on some variables. When they are nonconvex then they are the most difficult to solve above all. We present a methodology to solve nonsmooth nonconvex MINLP problems based on a branch and bound paradigm and a stochastic strategy. To solve the relaxed subproblems at each node of the branch and bound tree search, an algorithm based on a multistart strategy with a coordinate search filter methodology is implemented. The produced numerical results show the robustness of the proposed methodology.This work has been supported by FCT (Fundação para a Ciência e aTecnologia) in the scope of the projects: PEst-OE/MAT/UI0013/2014 and PEst-OE/EEI/UI0319/2014

Neural Network and Multi - Parametric Programming Based Approximation Techniques for Process Optimisation

In this thesis two approximation techniques are proposed: Artificial Neural Networks (ANN) and Multi – Parametric Programming. The usefulness of these techniques is demonstrated through process optimisation case studies. The oil refining industry mainly uses Linear Programming (LP) for refinery optimization and planning purposes, on a daily basis. LPs are attractive from the computational time point of view; however it has limitations such as the nonlinearity of the refinery processes is not taken into account. The main aim of this work is to develop approximate models to replace the rigorous ones providing a good accuracy without compromising the computational time, for refinery optimization. The data for deriving approximate models is generated from rigorous process models from a commercial software, which is extensively used in the refining industry. In this work we present three model reduction techniques. The first approach is based upon deriving an optimal configuration of artificial neural networks (ANN) for approximating the refinery models. The basic idea is to formulate the existence or not of the nodes and interconnections in the network using binary variables. This results in a Mixed Integer Nonlinear Programming formulation for Artificial Neural Networks (MIPANN). The second approach is concerned with dealing with complexity associated with large amounts of data that is usually available in the refineries; a disagg regation¬aggregation based approach is presented to address the complexity. The data is split (disagg reg ation) into smaller subsets and reduced ANN models are obtained for each of the subset. These ANN models are then combined (aggregation) to obtain an ANN model which represents the whole of the original data. The disagg reg ation step can be carried out within a parallel computing platform. The third approach consists of combining the MIPA NN and the disagg reg ation¬aggregation reduction methods to handle medium and large scale training data using a neural network that has already been reduced through nodes and interconnections optimization. Refinery optimization studies are carried out to demonstrate the applicability and the usefulness of these proposed model reduction approaches. Process synthesis and MIPANN problems are usually formulated as Mixed Integer Nonlinear programming (MINLP) problems requiring efficient algorithm for their solution. An approximate multi-parametric programming Branch and Bound (mpBB) algorithm is proposed. An approximate parametric solution at the root node and other fractional nodes of the Branch and Bound (BB) tree are obtained and used to estimate the solution at the terminal nodes in different sections of the tree. These estimates are then used to guide the search in the BB tree, resulting in fewer nodes being evaluated and reduction in the computational effort. Problems from the literature are solved using the proposed algorithm and compared with the other currently available algorithms for solving MINLP problems