Automatic Dantzig–Wolfe reformulation of mixed integer programs

Mathematical Programming - Dantzig–Wolfe decomposition (or reformulation) is well-known to provide strong dual bounds for specially structured mixed integer programs (MIPs). However, the...     

Nachweis und Bestimmung des Chroms

Ohne Zusammenfassung     

The systematics of nuclear single-particle states (II). the region A < 35

The energies of single-particle states in nuclei with A < 35 are obtained as eigenvalues of a local Saxon-Woods potential with depth depending linearly on A and on the nuclear symmetry parameter.     

HPLC-F analysis of melatonin and resveratrol isomers in wine using an SPE procedure

An original analytical method has been developed for the determination of the antioxidants trans-resveratrol (t-RSV) and cis-resveratrol (c-RSV) and of melatonin (MLT) in red and white wine. The method is based on HPLC coupled to fluorescence detection. Separation was obtained by using a RP column (C8, 150 mm x 4.6 mm id, 5 mum) and a mobile phase composed of 79% aqueous phosphate buffer at pH 3.0 and 21% ACN. Fluorescence intensity was monitored at lambda = 386 nm while exciting at lambda = 298 nm, mirtazapine was used as the internal standard. A careful pretreatment of wine samples was developed, using SPE with C18 cartridges (100 mg, 1 mL). The calibration curves were linear over the following concentration ranges: 0.03-5.00 ng/mL for MLT, 3-500 ng/mL for t-RSV and 1-150 ng/mL for c-RSV. The LOD values were 0.01 ng/mL for MLT, 1 ng/mL for t-RSV and 0.3 ng/mL for c-RSV. Precision data, as well as extraction yield and sample purification results, were satisfactory. Thus, the method seems to be suitable for the analysis of MLT and resveratrol isomers in wine samples. Moreover, wine total polyphenol content and antioxidant activity were evaluated.     

A column generation heuristic for the two-dimensional two-staged guillotine cutting stock problem with multiple stock size

We consider a two-dimensional cutting stock problem where stock of different sizes is available, and a set of rectangular items has to be obtained through two-staged guillotine cuts. We propose a heuristic algorithm, based on column generation, which requires as its subproblem the solution of a two-dimensional knapsack problem with two-staged guillotines cuts. A further contribution of the paper consists in the definition of a mixed integer linear programming model for the solution of this knapsack problem, as well as a heuristic procedure based on dynamic programming. Computational experiments show the effectiveness of the proposed approach, which obtains very small optimality gaps and outperforms the heuristic algorithm proposed by Cintra et al. [3].     

Tailored design of WDM filters in BCB embedded PhC membranes

We propose a design strategy for wavelength division multiplexing (WDM) filters in BCB embedded photonic crystal membranes. Due to the weaker vertical confinement determined by the material embedding the whole structure, accurate tailoring of the resonant cavity and of both bus and drop waveguides is necessary, in order to guarantee the required performance of the filter for WDM applications.     

Models and heuristic algorithms for a weighted vertex coloring problem

We consider a weighted version of the well-known Vertex Coloring Problem (VCP) in which each vertex i of a graph G has associated a positive weight w _i . Like in VCP, one is required to assign a color to each vertex in such a way that colors on adjacent vertices are different, and the objective is to minimize the sum of the costs of the colors used. While in VCP the cost of each color is equal to one, in the Weighted Vertex Coloring Problem (WVCP) the cost of each color depends on the weights of the vertices assigned to that color, and it equals the maximum of these weights. WVCP is known to be NP-hard and arises in practical scheduling applications, where it is also known as Scheduling on a Batch Machine with Job Compatibilities. We propose three alternative Integer Linear Programming (ILP) formulations for WVCP: one is used to derive, dropping integrality requirement for the variables, a tight lower bound on the solution value, while a second one is used to derive a 2-phase heuristic algorithm, also embedding fast refinement procedures aimed at improving the quality of the solutions found. Computational results on a large set of instances from the literature are reported.     

Test-assignment: a quadratic coloring problem

We consider the problem of assigning the test variants of a written exam to the desks of a classroom in such a way that desks that are close-by receive different variants. The problem is a generalization of the Vertex Coloring and we model it as a binary quadratic problem. Exact solution methods based on reformulating the problem in a convex way and applying a general-purpose solver are discussed as well as a Tabu Search algorithm. The methods are extensively evaluated through computational experiments on real-world instances. The problem arises from a real need at the Faculty of Engineering of the University of Bologna where the solution method is now implemented.     

An evolutionary approach for bandwidth multicoloring problems

In this paper we consider some generalizations of the vertex coloring problem, where distance constraints are imposed between adjacent vertices (bandwidth coloring problem) and each vertex has to be colored with more than one color (bandwidth multicoloring problem). We propose an evolutionary metaheuristic approach for the first problem, combining an effective tabu search algorithm with population management procedures. The approach can be applied to the second problem as well, after a simple transformation. Computational results on instances from the literature show that the overall algorithm is able to produce high quality solutions in a reasonable amount of time, outperforming the most effective algorithms proposed for the bandwidth coloring problem, and improving the best known solution of many instances of the bandwidth multicoloring problem.