Using mathematical programming heuristics in a multicriteria network flow context

In this paper, we propose a local search procedure to test the robustness of a specific ‘satisfying point’ neighbourhood. It consists of the following steps: (1) build an indifference area around the satisfying point in the criteria space by using thresholds (this takes into account the possible uncertainty, vagueness and/or inaccuracy of data); (2) find some points in the satisfying point neighbourhood and the corresponding solutions in the decision variables space; (3) test the quality of these solutions from the point of view of user preference. The indifference area is defined by adding constraints to the network model. This approach, which allows us to verify the adequacy of the model, has been applied to a set of multicriteria network flow problems. A heuristic method, based on Lagrangian duality and subgradient techniques, exploits the combinatorial structure of network flow problems in order to find certain feasible points.     

Crystallization of KNbO3 in a B2O3 glass network

The ferroelectric material potassium niobate (KNbO₃) has a large number of exceptional electronic and optical properties with important technological applications. Due to the high preparation difficulties and costs of the single crystals, a considerable interest in the preparation of glass-ceramics with the KNbO₃ crystal phase exists. In this work we present the preparation of a glass, with the composition 40B₂O₃–40K₂O–20Nb₂O₅ (% mole), through the melt-quenching method and glass-ceramics obtained by controlled heat-treatments. The samples structure was analyzed using X-ray power diffraction (XRD), scanning electron microscopy (SEM) and Raman spectroscopy. KNbO₃ crystals were detected in the glass sample treated at 500 °C. For treatments at temperatures above 500 °C, other niobium-based crystal phases are present. The behavior of the heat-treatment temperature parameter, in the glass and glass ceramic structure, is discussed.