The constrained compartmentalized knapsack problem: mathematical models and solution methods

The constrained compartmentalized knapsack problem can be seen as an extension of the constrained knapsack problem. However, the items are grouped into different classes so that the overall knapsack has to be divided into compartments, and each compartment is loaded with items from the same class. Moreover, building a compartment incurs a fixed cost and a fixed loss of the capacity in the original knapsack, and the compartments are lower and upper bounded. The objective is to maximize the total value of the items loaded in the overall knapsack minus the cost of the compartments. This problem has been formulated as an integer non-linear program, and in this paper, we reformulate the non-linear model as an integer linear master problem with a large number of variables. Some heuristics based on the solution of the restricted master problem are investigated. A new and more compact integer linear model is also presented, which can be solved by a branch-and-bound commercial solver that found most of the optimal solutions for the constrained compartmentalized knapsack problem. On the other hand, heuristics provide good solutions with low computational effort.     

An inexact bundle variant suited to column generation

We give a bundle method for constrained convex optimization. Instead of using penalty functions, it shifts iterates towards feasibility, by way of a Slater point, assumed to be known. Besides, the method accepts an oracle delivering function and subgradient values with unknown accuracy. Our approach is motivated by a number of applications in column generation, in which constraints are positively homogeneous—so that zero is a natural Slater point—and an exact oracle may be time consuming. Finally, our convergence analysis employs arguments which have been little used so far in the bundle community. The method is illustrated on a number of cutting-stock problems. Research supported by INRIA New Investigation Grant “Convex Optimization and Dantzig–Wolfe Decomposition”.     

Lifetime maximization in wireless directional sensor network

This paper addresses two versions of a lifetime maximization problem for target coverage with wireless directional sensor networks. The sensors used in these networks have a maximum sensing range and a limited sensing angle. In the first problem version, predefined sensing directions are assumed to be given, whereas sensing directions can be freely devised in the second problem version. In that case, a polynomial-time algorithm is provided for building sensing directions that allow to maximize the network lifetime. A column generation algorithm is proposed for both problem versions, the subproblem being addressed with a hybrid approach based on a genetic algorithm, and an integer linear programming formulation. Numerical results show that addressing the second problem version allows for significant improvements in terms of network lifetime while the computational effort is comparable for both problem versions.     

An improved method for assay of vitamin C in fish feed and tissues

Summary A method was devised to assay four forms of vitamin C: L-ascorbic acid (AA), dehydroascorbic acid (DHA), ascorbate-2-mono- and polyphosphate (AMP, APP), as well as ascorbate-2-monosulphate (AMS), in sample series of different fish tissues and feed. Direct and indirect detection were combined. Sample extractions were carried out with 0.2 mol L⁻¹ sodium acetate buffer (pH 4.8) and extracts were deproteinized after different chemical or enzymatic reactions, with perchloric acid. The DHA was reduced to AA with dithioerythritol (DTE). Ascorbate oxidase enzyme was used for the detection of background and an acidic phosphatase enzyme for the hydrolysis of different phosphate esters. Ascorbate-2-sulphate was detected directly with help of coinjection of the compound. Chromatographic analysis was carried out with a single column isocratic reverse phase method. The mobile phase was an aqueous buffer of 0.04 M sodium-acetate, 0.05 mM EDTA, 0.5 mM tetrabutylammonium dihydrogen phosphate (TBA) adjusted to pH 3.76 with 85% H₃PO₄ and with 24 mL methanol added to 1000 mL. C-18 columns were used with 0.6 mL min⁻¹ flow rate at 23°C. The vitamin C forms were detected by UV absorption at 250 nm. The determination limit was 1.0–5.0 μg g⁻¹ in AA equivalent. The standard deviations were between 1–6% and depended on the concentrations of vitamin C forms and tissues. Recoveries were between 90–96% in samples. Presented at: Balaton Symposium on High-Performance Separation Methods, Siófok, Hungary, September 3–5, 1997     

HPLC separations of meropenem and selected pharmaceuticals using a polar endcapped octadecylsilane narrow bore column

Summary Stability indicating high performance liquid chromatography methods have been developed for the assay of meropenem in combination with either dopamine (A), aminophylline (B), metoclopramide (C) or ranitidine (D) in intravenous fluid mixtures. Separations B, C and D were performed on a polar endcapped ODS column (150×2 mm) with aqueous, pH 3.0—acetonitrile (89∶11, 88∶12, and 92∶8) eluent and detection at 270, 290, 317 nm respectively. Meropenem was linear over the concentration ranges 126.88–507.50, 131.25–525, and 131.25–525 gmg mL⁻¹. Aminophylline, metoclopramide and ranitidine were linear over the concentration ranges 13–52, 37.5–150, and 25–100 μg mL⁻¹. Separation A was performed on a conventional ODS column (150×2.1 mm) with aqueous, pH 3.0—acetonitrile (85∶15) eluent and detection at 280 nm. Meropenem and dopamine were linear in the 61.25–245 and 10–40 μg mL⁻¹ ranges, respectively. Accuracy and precision for all methods were 0.20–3.30% and 0.10–1.58%, respectively. Accelerated stability studies have been carried out on each drug by exposure to acid, base, H₂O₂, and heat for different time periods.     

Liquid chromatographic separation of fluoroquinolone antibacterials used as veterinary drugs

Summary A liquid chromatographic method has been developed to separate a series of quinolones which are widely used as veterinary drugs: danofloxacin, difloxacin, enrofloxacin (and its metabolite ciprofloxacin), marbofloxacin, norfloxacin and sarafloxacin. Separation was performed by using an end-capped high-purity silica-based C₈ column and a mobile phase consisting of acetonitrile-aqueous oxalic acid buffer solution. In order to establish the optimal conditions for an isocratic separation, a three-factor Doehlert experimental design was applied. Gradient elution was applied which reduced analysis time. Figures of merit of the method proposed, with fluorimetric detection, were evaluated.     

Calculation of amino acid hydrophilicity indices for retention of peptides on amide, diol and silica columns in normal-phase liquid chromatography

Summary A set of hydrophilicity parameters in a normal-phase liquid chromatography of peptides is presented in order to clarify the contribution of individual amino acid residues to peptide retention and to predict retention times. The retention of 100 peptides was studied using normal-phase liquid chromatography on amide, diol and silica columns. An acetonitrile-water mixed solution containing 0.2% trifluoroacetic acid +0.2% triethylamine was used as the mobile phase in a linear gradient elution system. The contribution of each residue upon retention was calculated by linear multiple regression analysis. This paper described the contribution values as “hydrophilicity retention coefficients”. Using these hydrophilicity retention coefficients, retention times could be predicted for peptides of known amino acid content and sequence. A set of hydrophilicity retention coefficients on each column was successfully explained by contributions to the degree of retention.     

Enantioselective liquid-solid extraction for screening of structurally related chiral stationary phases

Summary An enantioselective liquid-solid batch extraction method is described for the screening of novel chiral stationary phases (CSPs) during optimization studies of chiral selectors derived form a common lead structure. Extraction enantioselectivity (α) values can be calculated from the enantiomeric excess ee-values of the selectand, which are measured in the liquid phase by enantioselective HPLC. Extraction α-values have been correlated with chromatographic α-values. The influence was studied of several experimental parameters of the assay (pH_a, buffer concentration, temperature, selector/selectand and phase ratio) on the enantiomeric excess (ee) values of the selectands and the enantioselectivity of the CSPs, respectively. The derived statistically significant model has then been implemented to predict chromatographic α-values of novel CSPs. For example, an ee of 89.3% for DNB-Leu as selectand could be achieved in batch extraction for a novel synthesized but mechanistically similarly-acting CSP derived form quinine. This corresponds to a calculated extraction α-value of 17.7. Based on this α_extraction a chromatographic α-value of 28.8 was predicted by the linear correlation model; the experimental HPLC α-value of 31.7 was in good agreement and demonstrated the validity of the proposed screening method. The method is particularly helpful in SO optimization studies.     

Simultaneous determination of tetrahydro-β-carbolines and β-carbolines

Summary Reversed-phase ion-pair HPLC with fluorimetric detectors connected in series was studied for the simultaneous determination of two tetrahydro--carbolines and two -carbolines. After additon of internal standards the samples were reacted with fluorescamine, and then subjected to serial extractions to remove their precursor (tryptamine) from the analytical system. This treatment not only suppressed the artefactual formation of tetrahydro--carbolines and -carbolines during analysis, but also effectively purified them. Under optimum conditions, using trifluoroacetic acid as counter ion, all analytes were separated within 14 min and without major interfering peaks. The quantitative ranges were 0.25–80.0 ng mL^–1 for both tetrahydro--carbolines and 0.1–30.0 ng mL^–1 for both -carbolines. Replicate spiking experiments showed that recovery from most of the samples tested was over 90% and the relative standard deviation ranged from 0.7 to 10.4% within and between assays. The proposed method was applicable to various materials such as soy sauce, vinegar, ketchup, tabasco, beer, wine, sake, whisky, brandy, cows' milk, coffee, cocoa, cheese, cigarette smoke and urine.     

Directly Suspended Droplet Three Liquid Phase Microextraction of Diclofenac Prior to LC

Directly suspended droplet liquid–liquid–liquid microextraction (LLLME) has been used to determine residues of diclofenac (2-[2-(2,6-dichlorophenyl) aminophenyl] ethanoic acid), in environmental water samples. In this technique a free suspended droplet of an aqueous solvent is delivered to the top-center position of an immiscible organic solvent floating on the top of an aqueous sample while being agitated by a stirring bar placed on the bottom of the sample cell. Recently, diclofenac was found as an environmental contaminant in sewage, surface, ground and drinking water samples. In the present work, diclofenac was extracted from water samples by LLLME and analysed by HPLC with UV detection at 281 nm. Factors such as organic solvent, extraction and back extraction times, stirring rate and the pH of acceptor and donor phases were optimized. Enrichment factor and detection limit (LOD, n = 7) were 102 and 0.1 μg L⁻¹, respectively. The linearity ranged from 0.5 to 2,000 μg⁻¹ with a %RSD (n = 5) of 7.2 at S/N = 3. All experiments were carried out at room temperature (22 ± 0.5 °C).