We propose methods for improving the relaxations obtained by the normalized multiparametric disaggregation technique (NMDT). These relaxations constitute a key component for some methods for solving nonconvex mixed-integer quadratically constrained quadratic programming (MIQCQP) problems. It is shown that these relaxations can be more efficiently formulated by significantly reducing the number of auxiliary variables (in particular, binary variables) and constraints. Moreover, a novel algorithm for solving MIQCQP problems is proposed. It can be applied using either its original NMDT or the proposed reformulation. Computational experiments are performed using both benchmark instances from the literature and randomly generated instances. The numerical results suggest that the proposed techniques can improve the quality of the relaxations.

Oil refining is one of the most complex activities in the chemical industry due to its nonlinear nature, which ruins the convexity properties and prevents any guarantees of the global optimality of solutions obtained by local nonlinear programming (NLP) algorithms. Moreover, using global optimization algorithms is often not feasible because they typically require large computational efforts. This paper proposes the use of convex relaxations based on McCormick envelopes for the Refinery Operations Planning Problem (ROPP) that can be used to generate both initial solutions for the ROPP and to estimate optimality gaps for the solutions obtained. The results obtained using data from a real-world refinery suggest that the proposed approach can provide reasonably good solutions for the ROPP, even for cases in which there was no solution available using traditional local NLP algorithms. Furthermore, compared with a global optimization solver, the proposed heuristic is capable of obtaining better solutions in less computational time.

This paper presents a novel technique to compute Lagrangian bounds for nonconvex mixed-integer quadratically constrained quadratic programming problems presenting a separable structure (i.e., a separable problems) such as those arising in deterministic equivalent representations of two-stage stochastic programming problems. In general, the nonconvex nature of these models still poses a challenge to the available solvers, which do not consistently perform well for larger-scale instances. Therefore, we propose an appealing alternative algorithm that allows for overcoming computational performance issues. Our novel technique, named the p-Lagrangian decomposition, is a decomposition method that combines Lagrangian decomposition with mixed-integer programming-based relaxations. These relaxations are obtained using the reformulated normalised multiparametric disaggregation technique and can be made arbitrarily precise by means of a precision parameter p. We provide a technical analysis showing the convergent behaviour of the approach as the approximation is made increasingly precise. We observe that the proposed method presents significant reductions in computational time when compared with a previously proposed techniques in the literature and the direct employment of a commercial solver. Moreover, our computational experiments show that the employment of a simple heuristic can recover solutions with small duality gaps.

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The treatment and preparation of a collection for a new destination after the closure of a library is a subject under explored in research and an activity for which there are no prepared instruments. This was the challenge of an action at the Nilza TavaresDias library of the Technical Assistance and Rural Extension Company of the State of Minas Gerais (EMATER-MG), in Brazil, deactivated in 2018. Since 2020, the inventory work for the proper disposal of the collection was started. For this purpose, it was necessary to develop the work methodology, as its base for recording and physical restructuring of the library for the activities’development. During the process, a large quantity/quality of EMATER publications produced since its creation was found, thus arising the need for a more depth study of these materials as an information, documentary and institutional memory source.