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PubMed1999

Neural networks and linear programming for the satisfiability problem.

First a Linear Programming formulation is considered for the satisfiability problem, in particular for the satisfaction of a Conjunctive Normal Form in the Propositional Calculus and the Simplex algorithm for solving the optimization problem. The use of Recurrent Neural Networks is then described for choosing the best pivot positions and greatly improving the algorithm performance. The result of hard cases testing is reported and shows that the technique can be useful even if it requires a huge amount of size for the constraint array and Neural Network Data Input.

Algorithms↗
PubMed2003

Waste load allocation for water quality management of a heavily polluted river using linear programming.

A waste load allocation model using linear programming has been developed for economic water quality management. A modified Qual2e model was used for water quality calculations and transfer coefficients were derived from the calculated water quality. This allocation model was applied to the heavily polluted Gyungan River, located in South Korea. For water quality management of the river, two scenarios were proposed. Scenario 1 proposed to minimise the total waste load reduction in the river basin. Scenario 2 proposed to minimise waste load reduction considering regional equity. Waste loads, which have to be reduced at each sub-basin and WWTP, were determined to meet the water quality goal of the river. Application results of the allocation model indicate that advanced treatment is required for most of the existing WWTPs in the river basin and construction of new WWTPs and capacity expansion of existing plants are necessary. Distribution characteristics of pollution sources and pollutant loads in the river basin was analysed using Arc/View GIS.

Environmental Monitoring↗
PubMed2002

Characterization of electrostatic binding sites of extracellular polymers by linear programming analysis of titration data.

Electrostatic binding sites of extracellular polymeric substances (EPS) were characterized from titration data using linear programming analysis. Test results for three synthetic solutions of given solutes comprising amino, carboxyl, and phenolic groups indicated that this method was able to identify the electrostatic binding sites. For the six sites with pK(a) between 3 and 10, the estimated pK(a) deviated 0.11 +/- 0.09 from the theoretical values, and the estimated concentrations deviated 3.0% +/- 0.9% from the actual concentrations. Two EPS samples were then extracted from a hydrogen-producing sludge (HPS) and a sulfate-reducing biofilm (SRB). Analysis of charge excess data in titration from pH 3 to 11 indicated that the EPS of HPS comprised of five electrostatic binding sites with pK(a) ranging from 3 to 11. The pK(a) values of these binding sites and the possible corresponding functional groups were pK(a) 4.8 (carboxyl), pK(a) 6.0 (carboxyl/phosphoric), pK(a) 7.0 (phosphoric), pK(a) 9.8 (amine/phenolic), and pK(a) 11.0 (hydroxyl). EPS of the SRB comprised five of similar binding sites (with corresponding pK(a) values of 4.4, 6.0, 7.4, 9.4, and 11.0), plus one extra site at pK(a) 8.2, which was likely corresponding to the sulfhydryl group. The total electrostatic binding site concentration of EPS extracted from HPS were 10.88 mmol/g-EPS, of which the highest concentration was from the site of pK(a) 11.0. The corresponding values for the EPS extracted from SRB were 16.44 mmol/g-EPS and pK(a) 4.4. The total concentrations of electrostatic binding sites found in this study were 20- to 30-fold of those reported for bacterial cell surface, implying that EPS might be more crucial in biosorption of metals than bacterial cell surface in wastewater treatment and in bioremediation.

Bacteria↗
PubMed2002

An application of linear programming discriminant analysis to classifying and predicting the symptomatic status of HIV/AIDS patients.

This study presents an application of linear programming discriminant analysis (LPDA) to classify and to predict the symptomatic status of HIV/AIDS patients. We applied LPDA as well as several traditional discriminant analysis methods to the AIDS Cost and Services Utilization Survey data set in order to demonstrate the use of LPDA to classify the symptomatic status of HIV/AIDS patients. The potential benefit of LPDA in terms of the classification accuracy was also analyzed.

Diagnosis, Computer-Assisted↗
PubMed2002

A cost constraint alone has adverse effects on food selection and nutrient density: an analysis of human diets by linear programming.

Economic constraints may contribute to the unhealthy food choices observed among low socioeconomic groups in industrialized countries. The objective of the present study was to predict the food choices a rational individual would make to reduce his or her food budget, while retaining a diet as close as possible to the average population diet. Isoenergetic diets were modeled by linear programming. To ensure these diets were consistent with habitual food consumption patterns, departure from the average French diet was minimized and constraints that limited portion size and the amount of energy from food groups were introduced into the models. A cost constraint was introduced and progressively strengthened to assess the effect of cost on the selection of foods by the program. Strengthening the cost constraint reduced the proportion of energy contributed by fruits and vegetables, meat and dairy products and increased the proportion from cereals, sweets and added fats, a pattern similar to that observed among low socioeconomic groups. This decreased the nutritional quality of modeled diets, notably the lowest cost linear programming diets had lower vitamin C and beta-carotene densities than the mean French adult diet (i.e., <25% and 10% of the mean density, respectively). These results indicate that a simple cost constraint can decrease the nutrient densities of diets and influence food selection in ways that reproduce the food intake patterns observed among low socioeconomic groups. They suggest that economic measures will be needed to effectively improve the nutritional quality of diets consumed by these populations.

Costs and Cost Analysis↗
PubMed2005

Image reconstruction by linear programming.

One way of image denoising is to project a noisy image to the subspace of admissible images derived, for instance, by PCA. However, a major drawback of this method is that all pixels are updated by the projection, even when only a few pixels are corrupted by noise or occlusion. We propose a new method to identify the noisy pixels by l1-norm penalization and to update the identified pixels only. The identification and updating of noisy pixels are formulated as one linear program which can be efficiently solved. In particular, one can apply the upsilon trick to directly specify the fraction of pixels to be reconstructed. Moreover, we extend the linear program to be able to exploit prior knowledge that occlusions often appear in contiguous blocks (e.g., sunglasses on faces). The basic idea is to penalize boundary points and interior points of the occluded area differently. We are also able to show the upsilon property for this extended LP leading to a method which is easy to use. Experimental results demonstrate the power of our approach.

Algorithms↗
PubMed2000

Linear programming based on neural networks for radiotherapy treatment planning.

In this paper, we propose a neural network model for linear programming that is designed to optimize radiotherapy treatment planning (RTP). This kind of neural network can be easily implemented by using a kind of 'neural' electronic system in order to obtain an optimization solution in real time. We first give an introduction to the RTP problem and construct a non-constraint objective function for the neural network model. We adopt a gradient algorithm to minimize the objective function and design the structure of the neural network for RTP. Compared to traditional linear programming methods, this neural network model can reduce the time needed for convergence, the size of problems (i.e., the number of variables to be searched) and the number of extra slack and surplus variables needed. We obtained a set of optimized beam weights that result in a better dose distribution as compared to that obtained using the simplex algorithm under the same initial condition. The example presented in this paper shows that this model is feasible in three-dimensional RTP.

Algorithms↗
PubMedDate not supplied

Correct bond order assignment in a molecular framework using integer linear programming with application to molecules where only non-hydrogen atom coordinates are available.

We describe a method based on linear programming, for deducing the correct bond orders in small molecules, which only needs the sigma bonds connectivity and atom symbols as input. The procedure checks whether the current structure can be written as a valid Lewis structure by assigning double and triple bonds by translating the octet equations into an integer linear program that is solved by an external solver. The procedure was intensively tested on some ligands from the protein data bank as well as some other exotic molecules, for which first the hydrogen topology is generated by a standard procedure from literature. The most stable Lewis structure is retained for which hydrogen coordinates are generated.

Databases, Protein↗
PubMed2003

Linear programming: a mathematical tool for analyzing and optimizing children's diets during the complementary feeding period.

During the complementary feeding period, children require a nutrient-dense diet to meet their high nutritional requirements. International interest exists in the promotion of affordable, nutritionally adequate complementary feeding diets based on locally available foods. In this context, two questions are often asked: 1) is it possible to design a diet suitable for the complementary feeding period using locally available food? and 2) if this is possible, what is the lowest-cost, nutritionally adequate diet available? These questions are usually answered using a "trial and error" approach. However, a more efficient and rigorous technique, based on linear programming, is also available. It has become more readily accessible with the advent of powerful personal computers. The purpose of this review, therefore, is to inform pediatricians and public health professionals about this tool. In this review, the basic principles of linear programming are briefly examined and some practical applications for formulating sound food-based nutritional recommendations in different contexts are explained. This review should facilitate the adoption of this technique by international health professionals.

Diet↗
PubMed2003

Analysis of metabolic networks using a pathway distance metric through linear programming.

The solution of the shortest path problem in biochemical systems constitutes an important step for studies of their evolution. In this paper, a linear programming (LP) algorithm for calculating minimal pathway distances in metabolic networks is studied. Minimal pathway distances are identified as the smallest number of metabolic steps separating two enzymes in metabolic pathways. The algorithm deals effectively with circularity and reaction directionality. The applicability of the algorithm is illustrated by calculating the minimal pathway distances for Escherichia coli small molecule metabolism enzymes, and then considering their correlations with genome distance (distance separating two genes on a chromosome) and enzyme function (as characterised by enzyme commission number). The results illustrate the effectiveness of the LP model. In addition, the data confirm that propinquity of genes on the genome implies similarity in function (as determined by co-involvement in the same region of the metabolic network), but suggest that no correlation exists between pathway distance and enzyme function. These findings offer insight into the probable mechanism of pathway evolution.

Algorithms↗
PubMed2003

The use of linear programming in optimization of HDR implant dose distributions.

The introduction of high dose rate brachytherapy enabled optimization of dose distributions to be used on a routine basis. The objective of optimization is to homogenize the dose distribution within the implant while simultaneously satisfying dose constraints on certain points. This is accomplished by varying the time the source dwells at different locations. As the dose at any point is a linear function of the dwell times, a linear programming approach seems to be a natural choice. The dose constraints are inherently linear inequalities. Homogeneity requirements are linearized by minimizing the maximum deviation of the doses at points inside the implant from a prescribed dose. The revised simplex method was applied for the solution of this linear programming problem. In the homogenization process the possible source locations were chosen as optimization points. To avoid the problem of the singular value of the dose at a source location from the source itself we define the "self-contribution" as the dose at a small distance from the source. The effect of varying this distance is discussed. Test cases were optimized for planar, biplanar and cylindrical implants. A semi-irregular, fan-like implant with diverging needles was also investigated. Mean central dose calculation based on 3D Delaunay-triangulation of the source locations was used to evaluate the dose distributions. The optimization method resulted in homogeneous distributions (for brachytherapy). Additional dose constraints--when applied--were satisfied. The method is flexible enough to include other linear constraints such as the inclusion of the centroids of the Delaunay-triangulation for homogenization, or limiting the maximum allowable dwell time.

Brachytherapy↗
PubMed1979

Application of linear programming to dose optimization in intracavitary implant therapy.

Linear programming can be used to optimize intracavitary brachytherapy for carcinoma of the cervix. A method has been developed which gives meaningful output and is described. A set of reference points were necessary in addition to the standard reference points. Point A as well as an array of points for adjacent radiation sensitive normal structures were used in order to obtain isodose curves conforming to those commonly used for therapy. In addition, arbitrary upper and lower limits of dose at selected points were needed and were set to conform to systems commonly used clinically for intracavitary therapy. It was immediately evident that a wide variety of loadings can be used that deliver appropriate or improved doses to reference points while minimizing normal tissue dose. The loadings represent arrangements which are not commonly used in many clinics but offer potential for clinical use.

Brachytherapy↗
PubMed1988

Three-dimensional reconstruction of myocardial contrast perfusion from biplane cineangiograms by means of linear programming techniques.

The assessment of coronary flow reserve from the instantaneous distribution of the contrast agent within the coronary vessels and myocardial muscle at the control state and at maximal flow has been limited by the superimposition of myocardial regions of interest in the two-dimensional images. To overcome these limitations, we are in the process of developing a three-dimensional (3D) reconstruction technique to compute the contrast distribution in cross sections of the myocardial muscle from two orthogonal cineangiograms. To limit the number of feasible solutions in the 3D-reconstruction space, the 3D-geometry of the endo- and epicardial boundaries of the myocardium must be determined. For the geometric reconstruction of the epicardium, the centerlines of the left coronary arterial tree are manually or automatically traced in the biplane views. Next, the bifurcations are detected automatically and matched in these two views, allowing a 3D-representation of the coronary tree. Finally, the circumference of the left ventricular myocardium in a selected cross section can be computed from the intersection points of this cross section with the 3D coronary tree using B-splines. For the geometric reconstruction of the left ventricular cavity, we envision to apply the elliptical approximation technique using the LV boundaries defined in the two orthogonal views, or by applying more complex 3D-reconstruction techniques including densitometry. The actual 3D-reconstruction of the contrast distribution in the myocardium is based on a linear programming technique (Transportation model) using cost coefficient matrices. Such a cost coefficient matrix must contain a maximum amount of a priori information, provided by a computer generated model and updated with actual data from the angiographic views. We have only begun to solve this complex problem. However, based on our first experimental results we expect that the linear programming approach with advanced cost coefficient matrices and computed model will lead to acceptable solutions in the 3D-reconstruction of the myocardial contrast distribution from biplane cineangiograms.

Cineangiography↗
PubMed2004

Food-based dietary guidelines can be developed and tested using linear programming analysis.

Effective food-based dietary guidelines (FBDGs) are required to combat micronutrient deficiencies. This study aimed to develop a rigorous approach for designing population-specific FBDGs. A 4-phase approach based on linear programming analysis was used to design, test, and refine the FBDGs. This was illustrated for Malawian children. In phase I, the objective function minimized the difference in the energy contributed by different food groups between modeled and observed diets for 16 observed diet types, while preferentially selecting foods most often consumed. Constraints ensured nutrient adequacy and diet palatability. In phase II, the meal/snack patterns of the phase I modeled diets were examined to develop season-specific FBDGs. In phase III, the robustness of these FBDGs, for ensuring a nutritionally adequate diet, was tested. The objective function, in this analysis, minimized selected nutrient levels in the modeled diets (i.e., chose the "worst-case scenario"), while respecting the FBDGs, palatability, and energy constraints. The FBDGs were refined in phase IV. In the Malawian example used to illustrate our approach, the FBDGs promoted daily consumption of maize flour, small dry fish (>or=20 g), leaf relish, and 2-3 snacks. The last mentioned included mangoes, in the food-shortage season, and pumpkin in the food-plenty season. In addition, legume relish was recommended in the food-shortage season. The approach presented here can be used to design and then test the robustness of FBDGs for meeting nutrient recommendations.

Animals↗
PubMed1984

[Elaboration, by linear programming, of new products from cereals and legumes].

The differing contents of essential amino acids in cereals and legumes bring about an overall increase in protein quality when these foods are consumed together. This study describes a least cost formulation method for preparing products based on cereals and legumes using linear programming. The mixture was formulated under different constraints; from a nutritional standpoint, a given amino acid pattern, and another one on a technological feasibility constraint, which depends on the type of product to be elaborated. From the formulation based on wheat, chick-pea, sorghum, and soybean flours, three products were developed: bread, tortillas and cookies; from these, bread was selected for further evaluation. The product was chemically evaluated by proximate analysis composition, and amino acids were determined by HPLC. Biological evaluation was performed by the PER and RPV methods, obtaining a PER of 1.69 for the developed bread product, and of 0.68 for the control bread. The RPV for the developed product was 64.31% of lactoalbumin and 23% for the control bread, which represents an increase of 41%. The sensory evaluation results did not indicate significant differences in taste, texture, color or overall acceptability of the developed bread product as compared to the control.

Amino Acids, Essential↗
PubMed2006

Linking linear programming and spatial simulation models to predict landscape effects of forest management alternatives.

Forest management planners require analytical tools to assess the effects of alternative strategies on the sometimes disparate benefits from forests such as timber production and wildlife habitat. We assessed the spatial patterns of alternative management strategies by linking two models that were developed for different purposes. We used a linear programming model (Spectrum) to optimize timber harvest schedules, then a simulation model (HARVEST) to project those schedules in a spatially explicit way and produce maps from which the spatial pattern of habitat could be calculated. We demonstrated the power of this approach by evaluating alternative plans developed for a national forest plan revision in Wisconsin, USA. The amount of forest interior habitat was inversely related to the amount of timber cut, and increased under the alternatives compared to the current plan. The amount of edge habitat was positively related to the amount of timber cut, and increased under all alternatives. The amount of mature northern hardwood interior and edge habitat increased for all alternatives, but mature pine habitat area varied. Mature age classes of all forest types increased, and young classes decreased under all alternatives. The average size of patches (defined by age class) generally decreased. These results are consistent with the design goals of each of the alternatives, but reveal that the spatial differences among the alternatives are modest. These complementary models are valuable for quantifying and comparing the spatial effects of alternative management strategies.

Computer Simulation↗
PubMedDate not supplied

Computing the minimum recombinant haplotype configuration from incomplete genotype data on a pedigree by integer linear programming.

We study the problem of reconstructing haplotype configurations from genotypes on pedigree data with missing alleles under the Mendelian law of inheritance and the minimum-recombination principle, which is important for the construction of haplotype maps and genetic linkage/association analyses. Our previous results show that the problem of finding a minimum-recombinant haplotype configuration (MRHC) is in general NP-hard. This paper presents an effective integer linear programming (ILP) formulation of the MRHC problem with missing data and a branch-and-bound strategy that utilizes a partial order relationship and some other special relationships among variables to decide the branching order. Nontrivial lower and upper bounds on the optimal number of recombinants are introduced at each branching node to effectively prune the search tree. When multiple solutions exist, a best haplotype configuration is selected based on a maximum likelihood approach. The paper also shows for the first time how to incorporate marker interval distance into a rule-based haplotyping algorithm. Our results on simulated data show that the algorithm could recover haplotypes with 50 loci from a pedigree of size 29 in seconds on a Pentium IV computer. Its accuracy is more than 99.8% for data with no missing alleles and 98.3% for data with 20% missing alleles in terms of correctly recovered phase information at each marker locus. A comparison with a statistical approach SimWalk2 on simulated data shows that the ILP algorithm runs much faster than SimWalk2 and reports better or comparable haplotypes on average than the first and second runs of SimWalk2. As an application of the algorithm to real data, we present some test results on reconstructing haplotypes from a genome-scale SNP dataset consisting of 12 pedigrees that have 0.8% to 14.5% missing alleles.

Algorithms↗
PubMed1991

Multivariable optimization of mechanical ventilation. A linear programming approach.

The proposed method aims at improved ventilatory care with reduced morbidity. It combines two important aspects of mechanical ventilation: gas exchange and lung mechanics. A single criterion was selected as optimization index of lung trauma: peak respiratory power (PRP) defined as the maximum product of pressure times flow during inspiration. Arterial blood gases reflect gas exchange and constitute the constraints of the problem. The constraints as well as the optimization index are expressed as linear functions of the input variables (frequency of breathing, tidal volume, and positive end expiratory pressure). A linear programming approach can therefore be used to determine the values of input variables that minimize PRP and at the same time keep arterial blood gases within the prescribed limits. The coefficients of the constraints and the optimization index equation are found by manipulating input variables in order to obtain four different values of PaO2, PaCO2 and PRP (there are four coefficients in each equation). The coefficients can then be calculated and the optimization procedure run. In a pilot study 5 patients suffering from diseases of varying pulmonary pathology were investigated with this method. In 4 out of 5 the ventilator treatment improved in terms of blood gas values (mean increase in PaO2 was 4.7%) and reduction of mechanical load on the lungs (mean PRP reduction was 20%). Lower PRP is accompanied by lower mean power and pressure values, which results in increased cardiac output. Presently, the main problem is the time it takes to determine the patient coefficients (approx one hour), a procedure that needs to be simplified.

Acute Disease↗