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PubMed2003

Optimization of beam orientations and beam weights for conformal radiotherapy using mixed integer programming.

An algorithm for optimizing beam orientations and beam weights for conformal radiotherapy has been developed. The algorithm models the optimization of beam orientations and beam weights as a problem of mixed integer linear programming (MILP), and optimizes the beam orientations and beam weights simultaneously. The application process of the algorithm has four steps: (a) prepare a pool of beam orientation candidates with the consideration of avoiding any patient-gantry collision and avoiding direct irradiation of organs at risk with quite low tolerances (e.g., eyes). (b) Represent each beam orientation candidate with a binary variable, and each beam weight with a continuous variable. (c) Set up an optimization problem according to dose prescriptions and the maximum allowed number of beam orientations. (d) Solve the optimization problem with a ready-to-use MILP solver. After optimization, the candidates with unity binary variables remain in the final beam configuration. The performance of the algorithm was tested with clinical cases. Compared with standard treatment plans, the beam-orientation-optimized plans had better dose distributions in terms of target coverage and avoidance of critical structures. The optimization processes took less than 1 h on a PC with a Pentium IV 2.4 GHz processor.

Algorithms↗
PubMed1989

Allocating blood to hospitals.

A method is proposed for the allocation of units of blood from a regional blood transfusion centre to the hospitals of its area, taking into consideration the characteristics of the individual hospitals, such as the transfusion activity, the demand of each hospital and the regional blood transfusion service policy concerning the allocation of units of blood expressed through a utility function. The problem is formulated as a stochastic programming problem but reduces to a linear programming problem and therefore is easily applicable. The method is suitable for application in systems with a National Health Service system, such as the British. Finally the results are given of an application to the despatches of units of blood in the Regional Blood Transfusion Service of Glasgow and West of Scotland.

Blood Banks↗
PubMed1987

Direct comparison of muscle force predictions using linear and nonlinear programming.

Estimating forces in muscles and joints during locomotion requires formulations consistent with available methods of solving the indeterminate problem. Direct comparisons of results between differing optimization methods proposed in the literature have been difficult owing to widely varying model formulations, algorithms, input data, and other factors. We present an application of a new optimization program which includes linear and nonlinear techniques allowing a variety of cost functions and greater flexibility in problem formulation. Unified solution methods such as the one demonstrated here, offer direct evaluations of such factors as optimization criteria and constraints. This unified method demonstrates that nonlinear formulations (of the sort reported) allow more synergistic activity and in contrast to linear formulations, allow antagonistic activity. Concurrence of EMG activity and predicted forces is better with nonlinear predictions than linear predictions. The prediction of synergistic and antagonistic activity expectedly leads to higher joint force predictions. Relaxation of the requirement that muscles resolve the entire intersegmental moment maintains muscle synergism in the nonlinear formulation while relieving muscle antagonism and reducing the predicted joint contact force. Such unified methods allow more possibilities for exploring new optimization formulations, and in comparing the solutions to previously reported formulations.

Algorithms↗
PubMed1999

Scaling of program fitness spaces.

We investigate the distribution of fitness of programs concentrating on those represented as parse trees and, particularly, how such distributions scale with respect to changes in the size of the programs. By using a combination of enumeration and Monte Carlo sampling on a large number of problems from three very different areas, we suggest that, in general, once some minimum size threshold has been exceeded, the distribution of performance is approximately independent of program length. We proof this for both linear programs and simple side effect free parse trees. We give the density of solutions to the parity problems in program trees which are composed of XOR building blocks. Limited experiments with programs including side effects and iteration suggest a similar result may also hold for this wider class of programs.

Algorithms↗
PubMedDate not supplied

NL-FIT: a microcomputer program for non-linear fitting.

A program for a microcomputer (HP 85) has been written using BASIC language. Given the analytical form of a model y: R leads to R the program computes the optimal parameters for non-linear least-squares fitting and gives information for its statistical evaluation. The program uses the Gauss-Newton algorithm with Marquardt's modification and other tricks. During the run a message is displayed if there is a high correlation between one or more couples of parameters to establish an interactive dialogue with the user on critical problems. The authors' aim was to make the program sufficiently quick and easy to use, efficient for a wide class of models and robust enough to deal with bad starting parameters.

Computers↗
PubMed2004

Constructing sequence alignments from a Markov decision model with estimated parameter values.

Current methods for aligning biological sequences are based on dynamic programming algorithms. If large numbers of sequences or a number of long sequences are to be aligned, the required computations are expensive in memory and central processing unit (CPU) time. In an attempt to bring the tools of large-scale linear programming (LP) methods to bear on this problem, we formulate the alignment process as a controlled Markov chain and construct a suggested alignment based on policies that minimise the expected total cost of the alignment. We discuss the LP associated with the total expected discounted cost and show the results of a solution of the problem based on a primal-dual interior point method. Model parameters, estimated from aligned sequences, along with cost function parameters are used to construct the objective and constraint conditions of the LP problem. This article concludes with a discussion of some alignments obtained from the LP solutions of problems with various cost function parameter values.

Algorithms↗
PubMed1983

Breeding programs of dairymen selecting Holstein sires by computer.

A computerized linear program (MAXBULL) selects groups of sires to attain or exceed goals of dairymen and maximize weighted average Predicted Difference for milk. Goals for 196 dairymen with Holsteins in the spring of 1982 averaged -.05 Predicted Difference fat percent, .85 Difference type, $17.52 per unit, and percents net superiority 29, 35, 36, 27, 33, and 46 for descriptive traits udder support, rear udder, fore udder, teats, hind legs, and feet. Percent net superiority is the percentage of units from sires having a significant number of superior daughters in a trait, reduced by the percentage of units from sires having a significant number of inferior daughters. Associated Predicted Difference milk, fat, and dollars were 789 kg, 25 kg, and $215. All goals exceeded averages of artificial insemination sires available, and Predicted Difference dollars exceeded Virginia service sire averages by $44 and the 90th percentile sire by $6. Predicted Difference fat percent was the most frequently binding production trait, whereas udder support was the most frequently binding type trait. Predicted Difference fat percent and price were most influential on maximum Predicted Difference milk. Breeding programs of dairymen using bulls from on organization differed from those using bulls from several organizations.

Animals↗
PubMedDate not supplied

A free derivative program for non-linear regression analysis of enzyme kinetics to be used on small computers.

A non-linear regression program, written in BASIC, is described. The program uses the Marquardt 's algorithm as modified by Reich et al. (Eur. J. Biochem., 26 (1972) pp. 368-379). The user only supplies the expression to fit, since the program uses numerical differentiation. It is possible to fit models of 1 substrate, 2 substrates, 1 substrate and 1 inhibitor, and 2 substrates and 1 inhibitor. Likewise, several weighting patterns, as well as a simple or robust regression, can be selected.

Computers↗
PubMed1982

Simultaneous electron capture detection of chlorpyrifos and 3, 5, 6-trichloro-2-pyridinol residues in peach and bahia grass field samples following gel permeation cleanup.

A recently published method involving the simultaneous extraction, gel permeation cleanup, and electron capture gas chromatographic detection of residues of the insecticide and acaricide chlorpyrifos and its principal metabolite 3,5,6-trichloro-2-pyridinol is successfully applied to Lorsban-treated peach and Bahia samples. Previous quantitation of these compounds has required 2 separate analytical procedures. Multilevel temperature programming and manipulation of the gel permeation column effluent rate are the only adjustments of experimental parameters necessary to avoid large amounts of gas chromatographic interferences. Chromatographic peaks are more clearly defined and easier to integrate with the multilevel program than they are with 2-step or linear programs. This is one reason that recovery data are improved over those reported for the method as applied in the pea vine work. Residue analysis conducted on field-treated peaches and Bahia grass show the newly published procedure to be sensitive and effective.

Chlorpyrifos↗
PubMed2003

Biomechanical modeling and optimal control of human posture.

The present work describes the biomechanical modeling of human postural mechanics in the saggital plane and the use of optimal control to generate open-loop raising-up movements from a squatting position. The biomechanical model comprises 10 equivalent musculotendon actuators, based on a 40 muscles model, and three links (shank, thigh and HAT-Head, Arms and Trunk). Optimal control solutions are achieved through algorithms based on the Consistent Approximations Theory (Schwartz and Polak, 1996), where the continuous non-linear dynamics is represented in a discrete space by means of a Runge-Kutta integration and the control signals in a spline-coefficient functional space. This leads to non-linear programming problems solved by a sequential quadratic programming (SQP) method. Due to the highly non-linear and unstable nature of the posture dynamics, numerical convergence is difficult, and specific strategies must be implemented in order to allow convergence. Results for control (muscular excitations) and angular trajectories are shown using two final simulation times, as well as specific control strategies are discussed.

Algorithms↗
PubMed1999

Treatment planning for brachytherapy: an integer programming model, two computational approaches and experiments with permanent prostate implant planning.

An integer linear programming model is proposed as a framework for optimizing seed placement and dose distribution in brachytherapy treatment planning. The basic model involves using 0/1 indicator variables to describe the placement or non-placement of seeds in a prespecified three-dimensional grid of potential locations. The dose delivered to each point in a discretized representation of the diseased organ and neighbouring healthy tissue can then be modelled as a linear combination of the indicator variables. A system of linear constraints is imposed to attempt to keep the dose level at each point to within specified target bounds. Since it is physically impossible to satisfy all constraints simultaneously, each constraint uses a variable to either record when the target dose level is achieved, or to record the deviation from the desired level. These additional variables are embedded into an objective function to be optimized. Variations on this model are discussed and two computational approaches--a branch-and-bound algorithm and a genetic algorithm--for finding 'optimal' seed placements are described. Results of computational experiments on a collection of prostate cancer cases are reported. The results indicate that both optimization algorithms are capable of producing good solutions within 5 to 15 min, and that small variations in model parameters can have a measurable effect on the dose distribution of the resulting plans.

Algorithms↗
PubMed2006

Two mathematical programming models of cheese manufacture.

The standardization problem faced by cheese makers is formulated as a nonlinear programming problem using the assumptions of the Van Slyke cheese yield formula. The objective function of the model is to minimize the net cost of producing a given quantity of cheese subject to a set of production constraints. An approximation of the standardization problem formulated as a linear programming problem is also presented. Two different approaches to finding a solution are provided. The model is implemented in Microsoft Excel and solved with the standard add-in solver available in that program. An example is provided to contrast the difference between the nonlinear programming and its linear approximation, and a second example is used to illustrate the yield implications of ultrafiltered milk protein products in Cheddar cheese production. Additionally, a method for pricing inputs using the sensitivity analysis generated by the solver is demonstrated.

Caseins↗
PubMed2001

Linear and quadratic models of the southern Murray-Darling basin.

Linear programming (LP), a well-established technique for modelling agricultural and other systems, has been extensively used to model irrigation systems in Australia. The models constructed have been used to assess the effects of changing water charges on farm incomes, water use, and the effects of trade in water allocations. An LP model that reflects actual farm behaviour requires a large amount of data. Moreover, demand and supply functions estimated with LP models are necessarily stepped rather than smooth. Howitt has suggested a way of escaping from these problems of LP models. His positive programming approach replaces an LP model with a simpler quadratic programming model. In this paper, Howitt's approach is used to develop a quadratic programming model from an existing LP model of irrigated agriculture in the southern Murray-Darling basin of Australia. A comparison of the quadratic and linear models indicates that the quadratic programming model is smaller and simpler to specify and that it produces similar results to the linear model, in terms of cropping, trade, and demand for irrigation water. The choice of modelling technique depends on the problem and the available resources. Positive programming can be a valuable addition to the farm modellers' arsenal.

Agriculture↗
PubMedDate not supplied

Benchmarking of linear and nonlinear approaches for quantitative structure-property relationship studies of metal complexation with ionophores.

A benchmark of several popular methods, Associative Neural Networks (ANN), Support Vector Machines (SVM), k Nearest Neighbors (kNN), Maximal Margin Linear Programming (MMLP), Radial Basis Function Neural Network (RBFNN), and Multiple Linear Regression (MLR), is reported for quantitative-structure property relationships (QSPR) of stability constants logK1 for the 1:1 (M:L) and logbeta2 for 1:2 complexes of metal cations Ag+ and Eu3+ with diverse sets of organic molecules in water at 298 K and ionic strength 0.1 M. The methods were tested on three types of descriptors: molecular descriptors including E-state values, counts of atoms determined for E-state atom types, and substructural molecular fragments (SMF). Comparison of the models was performed using a 5-fold external cross-validation procedure. Robust statistical tests (bootstrap and Kolmogorov-Smirnov statistics) were employed to evaluate the significance of calculated models. The Wilcoxon signed-rank test was used to compare the performance of methods. Individual structure-complexation property models obtained with nonlinear methods demonstrated a significantly better performance than the models built using multilinear regression analysis (MLRA). However, the averaging of several MLRA models based on SMF descriptors provided as good of a prediction as the most efficient nonlinear techniques. Support Vector Machines and Associative Neural Networks contributed in the largest number of significant models. Models based on fragments (SMF descriptors and E-state counts) had higher prediction ability than those based on E-state indices. The use of SMF descriptors and E-state counts provided similar results, whereas E-state indices lead to less significant models. The current study illustrates the difficulties of quantitative comparison of different methods: conclusions based only on one data set without appropriate statistical tests could be wrong.

Algorithms↗
PubMed2005

Molecular solutions to the binary integer programming problem based on DNA computation.

Binary optimization is a widely investigated topic in integer linear programming. This study proposes a DNA-based computing algorithm for solving the significantly large binary integer programming (BIP) problem. The proposed approach is based upon Adleman and Lipton's DNA operations to solve the BIP problem. The potential of DNA computation for the BIP problem is promising given the operational time complexity of O(nxk).

Algorithms↗
PubMed1986

The use of a microcomputer for non-linear optimisation of doses in external radiotherapy.

The study presents software for a microcomputer designed to determine the optimum dose distribution in external radiotherapy, either by calculating the doses delivered and the field width (in linear programming) or, in addition, by calculating the beam geometry (non-linear optimisation). Various optimisation criteria can be selected, namely the homogeneity, the concentration on the target and the total dose in a sensitive area. The article outlines an example.

Humans↗
PubMed1991

The use of integer programming in dairy sire selection.

A computerized sire selection integer program, IPSIRE, was developed to test the optimality of solutions obtained by using MAXBULL, a popular computerized sire selection aid. The IPSIRE program uses an optimization software package and a compatible spreadsheet; MAXBULL uses linear programming techniques. The computer programs were compared using large and small data sets. Multiple combinations were run, varying the levels requested for PD fat percentage, PD type, and price paid per unit of semen. All other constraints were held constant. The objective function for all combinations maximized PD milk. The IPSIRE program exceeded MAXBULL by an average of $2.5 for PD dollars and 7.3 kg (16.1 lb) for PD milk using the small bull data base. Sire averages for traits PD type, PD fat percentage, and price paid were not different between the two programs. Similar trends were seen using the large bull data base. The IPSIRE program exceeded MAXBULL by an average of $1.2 for PD dollars and 4.1 kg (9.0 lb) for PD milk, whereas sire averages for PD fat percentage, PD type, and price paid were not different between programs. The goal for PD type had the least influence of the three goals on sire averages for PD milk. The goal for price paid had the greatest impact on realized PD milk; higher goals for price paid produced solutions with higher values for realized PD milk. The IPSIRE program required longer computational times for finding solutions that maximized PD milk than MAXBULL.

Animals↗
PubMed2006

Convergence of neural networks for programming problems via a nonsmooth Lojasiewicz inequality.

This paper considers a class of neural networks (NNs) for solving linear programming (LP) problems, convex quadratic programming (QP) problems, and nonconvex QP problems where an indefinite quadratic objective function is subject to a set of affine constraints. The NNs are characterized by constraint neurons modeled by ideal diodes with vertical segments in their characteristic, which enable to implement an exact penalty method. A new method is exploited to address convergence of trajectories, which is based on a nonsmooth Lojasiewicz inequality for the generalized gradient vector field describing the NN dynamics. The method permits to prove that each forward trajectory of the NN has finite length, and as a consequence it converges toward a singleton. Furthermore, by means of a quantitative evaluation of the Lojasiewicz exponent at the equilibrium points, the following results on convergence rate of trajectories are established: (1) for nonconvex QP problems, each trajectory is either exponentially convergent, or convergent in finite time, toward a singleton belonging to the set of constrained critical points; (2) for convex QP problems, the same result as in (1) holds; moreover, the singleton belongs to the set of global minimizers; and (3) for LP problems, each trajectory converges in finite time to a singleton belonging to the set of global minimizers. These results, which improve previous results obtained via the Lyapunov approach, are true independently of the nature of the set of equilibrium points, and in particular they hold even when the NN possesses infinitely many nonisolated equilibrium points.

Algorithms↗