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At least 19 recordsLinked to original sources
PubMedDate not supplied

Treatment plan optimization using linear programming.

Linear programming is a versatile mathematical tool for optimizing radiation therapy treatment plans. For planning purposes, dose constraint points, possible treatment beams, and an objective function are defined. Dose constraint points are specified in and about the target volume and normal structures with minimum and maximum dose values assigned to each point. A linear objective function is designed that defines the goal of optimization. A list of potential treatment beams is defined by energy, angle, and wedge selection. Then, linear programming calculates the relative weights of all the potential beams such that the objective function is optimized and doses to all constraint points are within the prescribed limits. Historically, linear programming has been used to improve conventional treatment techniques. It can also be used to create sophisticated, complex treatment plans suitable for delivery by computer-controlled therapy techniques.

Humans↗
PubMed1994

Laying hen production responses to least cost rations formulated with stochastic programming or linear programming with a margin of safety.

An experiment with 480 DeKalb DK laying hens was conducted to study the effect of rations formulated with stochastic programming (STCH) or linear programming with a margin of safety (LPMS) over 12, 28-d periods. Rations were formulated to guarantee the requirement of methionine and lysine > or = 69%, in all rations, and Ca and P > or = either 69 or 90%. The four rations were: LPMS69 with Ca and P > or = 69%, LPMS90 with Ca and P > or = 90%, STCH69 with Ca and P > or = 69%, and STCH90 with Ca and P > or = 90%. Rations formulated with STCH were lower in cost than LPMS rations for respective probability levels. Costs per metric ton for LPMS69, LPMS90, STCH69, and STCH90 were $155.70, $157.71, $155.00, and $156.30, respectively. Compared to STCH rations, LPMS rations were overformulated in nutrients. There was no difference (P > .05) in performance for hen-housed egg production, hen-day egg production, feed per dozen eggs, mortality, egg weight, or eggshell percentage.

Animals↗
PubMed2001

Seriation of asymmetric matrices using integer linear programming.

Integer linear programming approaches for seriation of asymmetric n x n proximity matrices have generally been perceived as intractable for problems of practical size. However, to date, no computational evidence has been provided regarding the effectiveness (or ineffectiveness) of such approaches. This paper presents an evaluation of an integer linear programming method for asymmetric seriation using five moderately sized matrices (15 < or = n < or = 36) from the psychological literature, as well as 80 synthetic matrices (20 < or = n < or = 30). The solution to the linear programming relaxation of the integer-programming model was integer-optimal for each of the five empirical matrices and many of the synthetic matrices. In such instances, branch-and-bound integer programming was not required and optimal orderings were obtained within a few seconds. In all cases where the solution to the linear programming relaxation was not integer-optimal, branch-and-bound integer programming was able to find an optimal seriation in 18 minutes or less. A pragmatic solution strategy for larger matrices (n > 30) is also presented. This approach exploits the fact that, in many instances, only a modest percentage of all possible transitivity constraints are required to obtain an optimal solution.

Humans↗
PubMed1996

Consideration in selecting crops for the human-rated life support system: a Linear Programming model.

A Linear Programming model has been constructed which aids in selecting appropriate crops for CELSS (Controlled Environment Life Support System) food production. A team of Controlled Environment Agriculture (CEA) faculty, staff, graduate students and invited experts representing more than a dozen disciplines, provided a wide range of expertise in developing the model and the crop production program. The model incorporates nutritional content and controlled-environment based production yields of carefully chosen crops into a framework where a crop mix can be constructed to suit the astronauts' needs. The crew's nutritional requirements can be adequately satisfied with only a few crops (assuming vitamin mineral supplements are provided) but this will not be satisfactory from a culinary standpoint. This model is flexible enough that taste and variety driven food choices can be built into the model.

Crops, Agricultural↗
PubMed2003

RAPTOR: optimal protein threading by linear programming.

This paper presents a novel linear programming approach to do protein 3-dimensional (3D) structure prediction via threading. Based on the contact map graph of the protein 3D structure template, the protein threading problem is formulated as a large scale integer programming (IP) problem. The IP formulation is then relaxed to a linear programming (LP) problem, and then solved by the canonical branch-and-bound method. The final solution is globally optimal with respect to energy functions. In particular, our energy function includes pairwise interaction preferences and allowing variable gaps which are two key factors in making the protein threading problem NP-hard. A surprising result is that, most of the time, the relaxed linear programs generate integral solutions directly. Our algorithm has been implemented as a software package RAPTOR-RApid Protein Threading by Operation Research technique. Large scale benchmark test for fold recognition shows that RAPTOR significantly outperforms other programs at the fold similarity level. The CAFASP3 evaluation, a blind and public test by the protein structure prediction community, ranks RAPTOR as top 1, among individual prediction servers, in terms of the recognition capability and alignment accuracy for Fold Recognition (FR) family targets. RAPTOR also performs very well in recognizing the hard Homology Modeling (HM) targets. RAPTOR was implemented at the University of Waterloo and it can be accessed at http://www.cs.uwaterloo.ca/~j3xu/RAPTOR_form.htm.

Algorithms↗
PubMed1978

Clark's Theorem on linear programs holds for convex programs.

Given a linear minimization program, then there is an associated linear maximization program termed the dual. F. E. Clark proved the following theorem. "If the set of feasible points of one program is bounded, then the set of feasible points of the other program is unbounded." A convex program is the minimization of a convex function subject to the constraint that a number of other convex functions be nonpositive. As is well known, a dual maximization problem can be defined in terms of the Lagrange function. The dual objection function is the infimum of the Lagrange function. The feasible Lagrange multipliers are those satisfying: (i) the multipliers are nonnegative and (ii) the dual objective function is not negative infinity. It is found that Clark's Theorem applies unchanged to dual convex programs. Moreover, the programs have equal values.

Journal Article↗
PubMed2005

Sparse nonnegative solution of underdetermined linear equations by linear programming.

Consider an underdetermined system of linear equations y = Ax with known y and d x n matrix A. We seek the nonnegative x with the fewest nonzeros satisfying y = Ax. In general, this problem is NP-hard. However, for many matrices A there is a threshold phenomenon: if the sparsest solution is sufficiently sparse, it can be found by linear programming. We explain this by the theory of convex polytopes. Let a(j) denote the jth column of A, 1 < or = j < or = n, let a0 = 0 and P denote the convex hull of the a(j). We say the polytope P is outwardly k-neighborly if every subset of k vertices not including 0 spans a face of P. We show that outward k-neighborliness is equivalent to the statement that, whenever y = Ax has a nonnegative solution with at most k nonzeros, it is the nonnegative solution to y = Ax having minimal sum. We also consider weak neighborliness, where the overwhelming majority of k-sets of a(j)s not containing 0 span a face of P. This implies that most nonnegative vectors x with k nonzeros are uniquely recoverable from y = Ax by linear programming. Numerous corollaries follow by invoking neighborliness results. For example, for most large n by 2n underdetermined systems having a solution with fewer nonzeros than roughly half the number of equations, the sparsest solution can be found by linear programming.

Journal Article↗
PubMed2004

A web portal for classification of expression data using maximal margin linear programming.

The Maximal Margin (MAMA) linear programming classification algorithm has recently been proposed and tested for cancer classification based on expression data. It demonstrated sound performance on publicly available expression datasets. We developed a web interface to allow potential users easy access to the MAMA classification tool. Basic and advanced options provide flexibility in exploitation. The input data format is the same as that used in most publicly available datasets. This makes the web resource particularly convenient for non-expert machine learning users working in the field of expression data analysis.

Algorithms↗
PubMed2006

A binary linear programming formulation of the graph edit distance.

A binary linear programming formulation of the graph edit distance for unweighted, undirected graphs with vertex attributes is derived and applied to a graph recognition problem. A general formulation for editing graphs is used to derive a graph edit distance that is proven to be a metric, provided the cost function for individual edit operations is a metric. Then, a binary linear program is developed for computing this graph edit distance, and polynomial time methods for determining upper and lower bounds on the solution of the binary program are derived by applying solution methods for standard linear programming and the assignment problem. A recognition problem of comparing a sample input graph to a database of known prototype graphs in the context of a chemical information system is presented as an application of the new method. The costs associated with various edit operations are chosen by using a minimum normalized variance criterion applied to pairwise distances between nearest neighbors in the database of prototypes. The new metric is shown to perform quite well in comparison to existing metrics when applied to a database of chemical graphs.

Algorithms↗
PubMed1988

Biomechanical model calculation of muscle contraction forces: a double linear programming method.

This paper presents a novel scheme for the use of linear programming to calculate muscle contraction forces in models describing musculoskeletal system biomechanics. Models of this kind are frequently found in the biomechanics literature. In most cases they involve muscle contraction force calculations that are statically indeterminate, and hence use optimization techniques to make those calculations. We present a linear programming optimization technique that solves a two-objective problem with two sequential linear programs. We use the technique here to minimize muscle intensity and joint compression force, since those are commonly used objectives. The two linear program model has the advantages of low computation cost, ready implementation on a micro-computer, and stable solutions. We show how to solve the model analytically in simple cases. We also discuss the use of the dual problem of linear programming to gain understanding of the solution it provides.

Biomechanical Phenomena↗
PubMed2005

Linear programming to optimize performance in a department of surgery.

BACKGROUND: Linear programming is an analytic method that can be used to develop models for health care that optimize distribution of resources through mathematical means. STUDY DESIGN: The linear programming model contained objective, decision, and constraint elements. The objective was to optimize financial outcomes for both the hospital and physicians in the Department of Surgery. The decision concerns procedure mix or the number of each type of surgical procedure. Constraints apply to resources that are consumed during the course of the patient's surgical encounter. RESULTS: The optimal solution produced an increase in professional payments of 3.6% and an increase in hospital total margin of 16.1%. This solution favored surgical procedures that require inpatient care; these patients had greater comorbidity, reflected in a higher case-mix index of 3.74 compared to 2.97. Substantial differences were noted in use of general care and ICU days, and in consumption of preoperative, intraoperative, and recovery room time. CONCLUSIONS: Aligning quality surgical care with optimal financial performance may be assisted by mathematical models such as linear programming.

Comorbidity↗
PubMed2006

An inexact two-stage mixed integer linear programming method for solid waste management in the City of Regina.

In this study, an interval-parameter two-stage mixed integer linear programming (ITMILP) model is developed for supporting long-term planning of waste management activities in the City of Regina. In the ITMILP, both two-stage stochastic programming and interval linear programming are introduced into a general mixed integer linear programming framework. Uncertainties expressed as not only probability density functions but also discrete intervals can be reflected. The model can help tackle the dynamic, interactive and uncertain characteristics of the solid waste management system in the City, and can address issues concerning plans for cost-effective waste diversion and landfill prolongation. Three scenarios are considered based on different waste management policies. The results indicate that reasonable solutions have been generated. They are valuable for supporting the adjustment or justification of the existing waste flow allocation patterns, the long-term capacity planning of the City's waste management system, and the formulation of local policies and regulations regarding waste generation and management.

Canada↗
PubMedDate not supplied

Dose-volume considerations with linear programming optimization.

A method of incorporating dose-volume considerations within the framework of conventional linear programming is presented. This method is suitable for the optimization of beam weights and angles using a conformal treatment philosophy (i.e., tailoring the high-dose region to the target volume only). Dose-volume constraints are introduced using the concept that volumes of normal tissue nearer the target volume will be allowed higher dose constraints than volumes of normal tissue distal to the target volume. Each involved normal structure is divided into high-dose and low-dose volumes. These two volume partitions are represented by constraint points with either high-dose or low-dose constraints, respectively. Optimized treatment plans for three clinical sites demonstrate that this technique meets or surpasses the original dose-volume constraints for a conformal-type treatment plan using straightforward linear programming in a time frame that is comparable to other linear programming problems.

Humans↗
PubMed1986

Linear programming analysis of VA/Q distributions: limits on central moments.

Linear programming examines the boundaries of infinite sets. We used this method with the multiple-inert gas-elimination technique to examine the central moments and arterial blood gases of the infinite family of ventilation perfusion (VA/Q) distributions that are compatible with a measured inert gas-retention set. A linear program was applied with Monte-Carlo error simulation to theoretical retention data, and 95% confidence intervals were constructed for the first three moments (mean, dispersion, and skew) and the arterial PO2 and PCO2 of all compatible blood flow distributions. Six typical cases were studied. Results demonstrate narrow confidence intervals for both the lower moments and predicted arterial blood gases of all test cases, which widen as moment number or error increase. We conclude that the blood gas composition and basic structure of all compatible VA/Q distributions are tightly constrained and that even subtle changes in this structure, as may occur experimentally, can be identified.

Biometry↗
PubMed1976

A rumen linear programming model for evaluation of concepts of rumen microbial function.

A linear programming model provides for analysis of general input-output relationships in the rumen, for evaluation of competitive relationships among rumen microbes, and for computation of optimal relationships in the rumen. Eight rumen microbial groups defined on the bases of substrate specificity, nutrient requirements for growth, fermentation products, and relative metabolic activities comprise the central core of the model. Relative metabolic rates of microbial groups calculated from their cell sized were used as coefficients in the objective function. The model was used to evaluate effects of different amounts of protein from feed and various carbohydrates upon microbial population and fermentation patterns as accommodated by current concepts. During the several solutions of the model, considerable simplification of the rumen microflora occurred. This implies that current data and concepts, and the hypothesis regarding relative metabolic rate, as represented in the model, do not accommodate adequately competitions among the several rumen microbial species and, thus, that additional data and concepts regarding rumen microbial interactions are required. Also evaluated were effects of ingestion of bacteria by protozoa upon over-all rumen function, absolute microbial cell yields, cell yields per mole of adenosine triphosphate, and factors affecting these.

Adenosine Triphosphate↗