Design and management optimization of trickle irrigation systems using non-linear programming

A non-linear model is presented which optimizes the lay-out, as well as the design and management of trickle irrigation systems, to achieve maximum net benefit. The model consists of an objective function that maximizes profit at the farm level, subject to appropriate geometric and hydraulic constraints. It can be applied to rectangular shaped fields, with uniform or zero slope. The software used is the Gams-Minos package. The basic inputs are the crop-water-production function, the cost function and cost of system components, and design variables. The main outputs are the annual net benefit and pipe diameters and lengths. To illustrate the capability of the model, a sensitivity analysis of the annual net benefit for a citrus field is evaluated with respect to irrigated area, ground slope, micro-sprinkler discharge and shape of the field. The sensitivity analysis suggests that the greatest benefit is obtained with the smallest microsprinkler discharge, the greatest area, a square field and zero ground slope. The costs of the investment and energy are the components of the objective function that had the greatest effect in the 120 situations evaluated. (C) 1996 Academic Press Limited

Efficient linear programming algorithm for the transmission network expansion planning problem

The transmission network planning problem is a non-linear integer mixed programming problem (NLIMP). Most of the algorithms used to solve this problem use a linear programming subroutine (LP) to solve LP problems resulting from planning algorithms. Sometimes the resolution of these LPs represents a major computational effort. The particularity of these LPs in the optimal solution is that only some inequality constraints are binding. This task transforms the LP into an equivalent problem with only one equality constraint (the power flow equation) and many inequality constraints, and uses a dual simplex algorithm and a relaxation strategy to solve the LPs. The optimisation process is started with only one equality constraint and, in each step, the most unfeasible constraint is added. The logic used is similar to a proposal for electric systems operation planning. The results show a higher performance of the algorithm when compared to primal simplex methods.

Robust linear mixed models with normal/independent distributions and Bayesian MCMC implementation

Linear mixed effects models have been widely used in analysis of data where responses are clustered around some random effects, so it is not reasonable to assume independence between observations in the same cluster. In most biological applications, it is assumed that the distributions of the random effects and of the residuals are Gaussian. This makes inferences vulnerable to the presence of outliers. Here, linear mixed effects models with normal/independent residual distributions for robust inferences are described. Specific distributions examined include univariate and multivariate versions of the Student-t, the slash and the contaminated normal. A Bayesian framework is adopted and Markov chain Monte Carlo is used to carry out the posterior analysis. The procedures are illustrated using birth weight data on rats in a texicological experiment. Results from the Gaussian and robust models are contrasted, and it is shown how the implementation can be used for outlier detection. The thick-tailed distributions provide an appealing robust alternative to the Gaussian process in linear mixed models, and they are easily implemented using data augmentation and MCMC techniques.

A mixed-integer linear programming approach for optimal type, size and allocation of distributed generation in radial distribution systems

This paper presents a mixed-integer linear programming approach to solving the problem of optimal type, size and allocation of distributed generators (DGs) in radial distribution systems. In the proposed formulation, (a) the steady-state operation of the radial distribution system, considering different load levels, is modeled through linear expressions; (b) different types of DGs are represented by their capability curves; (c) the short-circuit current capacity of the circuits is modeled through linear expressions; and (d) different topologies of the radial distribution system are considered. The objective function minimizes the annualized investment and operation costs. The use of a mixed-integer linear formulation guarantees convergence to optimality using existing optimization software. The results of one test system are presented in order to show the accuracy as well as the efficiency of the proposed solution technique.© 2012 Elsevier B.V. All rights reserved.

Programação linear à criação de planejamentos otimizados em radioterapia

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Optimal fleet configuration in San Miguel Bay, Philippines: a simple linear programming approach

Includes bibliography

Modelos de programação linear inteira mista para resolver problemas de otimização de sistemas de distribuição de energia elétrica radiais

Pós-graduação em Engenharia Elétrica - FEIS

DESIGN OF MICROIRRIGATION SYSTEMS IN SLOPING LANDS USING LINEAR PROGRAMMING

Quando a área a ser irrigada apresenta um elevado gradiente de declive na direção das linhas de derivação, uma opção de dimensionamento é o uso de tubulações com vários diâmetros para economizar no custo e também para manter a variação de pressão dentro dos limites desejados. O objetivo deste trabalho foi desenvolver um modelo de programação linear para dimensionar sistemas de irrigação por microaspersão com linhas de derivação com mais de um diâmetro e operando em declive, visando a minimização do custo anualizado da rede hidráulica e do custo anual com energia elétrica, além de assegurar que a máxima variação de carga hidráulica na linha será respeitada. Os dados de entrada são: configuração da rede hidráulica do sistema de irrigação, custo de todos os componentes da rede hidráulica e custo da energia. Os dados de saída são: custo anual total, diâmetro da tubulação em cada linha do sistema, carga hidráulica em cada ponto de derivação e altura manométrica total. Para ilustrar a potencialidade do modelo desenvolvido, ele foi aplicado em um pomar de citros no Estado de São Paulo, Brasil. O modelo demonstrou ser eficiente no dimensionamento do sistema de irrigação quanto à obtenção da uniformidade de emissão desejada. O custo anual com bombeamento deve ser considerado no dimensionamento de sistemas de irrigação por microaspersão porque ele gera menores valores de custo anual total quando comparado com a mesma alternativa que não considera aquele custo.

Method validation using weighted linear regression models for quantification of UV filters in water samples

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Short-term expansion planning of radial electrical distribution systems using mixed-integer linear programming

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Applications of Linear Programming to Coding Theory

Maximum-likelihood decoding is often the optimal decoding rule one can use, but it is very costly to implement in a general setting. Much effort has therefore been dedicated to find efficient decoding algorithms that either achieve or approximate the error-correcting performance of the maximum-likelihood decoder. This dissertation examines two approaches to this problem. In 2003 Feldman and his collaborators defined the linear programming decoder, which operates by solving a linear programming relaxation of the maximum-likelihood decoding problem. As with many modern decoding algorithms, is possible for the linear programming decoder to output vectors that do not correspond to codewords; such vectors are known as pseudocodewords. In this work, we completely classify the set of linear programming pseudocodewords for the family of cycle codes. For the case of the binary symmetric channel, another approximation of maximum-likelihood decoding was introduced by Omura in 1972. This decoder employs an iterative algorithm whose behavior closely mimics that of the simplex algorithm. We generalize Omura's decoder to operate on any binary-input memoryless channel, thus obtaining a soft-decision decoding algorithm. Further, we prove that the probability of the generalized algorithm returning the maximum-likelihood codeword approaches 1 as the number of iterations goes to infinity.

Local power properties of some asymptotic tests in symmetric linear regression models

In this paper we obtain asymptotic expansions, up to order n(-1/2) and under a sequence of Pitman alternatives, for the nonnull distribution functions of the likelihood ratio, Wald, score and gradient test statistics in the class of symmetric linear regression models. This is a wide class of models which encompasses the t model and several other symmetric distributions with longer-than normal tails. The asymptotic distributions of all four statistics are obtained for testing a subset of regression parameters. Furthermore, in order to compare the finite-sample performance of these tests in this class of models, Monte Carlo simulations are presented. An empirical application to a real data set is considered for illustrative purposes. (C) 2011 Elsevier B.V. All rights reserved.

An integer linear programming approach for bilinear integer programming

We introduce a new Integer Linear Programming (ILP) approach for solving Integer Programming (IP) problems with bilinear objectives and linear constraints. The approach relies on a series of ILP approximations of the bilinear P. We compare this approach with standard linearization techniques on random instances and a set of real-world product bundling problems. (C) 2011 Elsevier B.V. All rights reserved.

The concept of quasi-integrability for modified non-linear Schrodinger models

We consider modifications of the nonlinear Schrodinger model (NLS) to look at the recently introduced concept of quasi-integrability. We show that such models possess an in finite number of quasi-conserved charges which present intriguing properties in relation to very specific space-time parity transformations. For the case of two-soliton solutions where the fields are eigenstates of this parity, those charges are asymptotically conserved in the scattering process of the solitons. Even though the charges vary in time their values in the far past and the far future are the same. Such results are obtained through analytical and numerical methods, and employ adaptations of algebraic techniques used in integrable field theories. Our findings may have important consequences on the applications of these models in several areas of non-linear science. We make a detailed numerical study of the modified NLS potential of the form V similar to (vertical bar psi vertical bar(2))(2+epsilon), with epsilon being a perturbation parameter. We perform numerical simulations of the scattering of solitons for this model and find a good agreement with the results predicted by the analytical considerations. Our paper shows that the quasi-integrability concepts recently proposed in the context of modifications of the sine-Gordon model remain valid for perturbations of the NLS model.

Application-oriented Mixed Integer Non-Linear Programming

In the most recent years there is a renovate interest for Mixed Integer Non-Linear Programming (MINLP) problems. This can be explained for different reasons: (i) the performance of solvers handling non-linear constraints was largely improved; (ii) the awareness that most of the applications from the real-world can be modeled as an MINLP problem; (iii) the challenging nature of this very general class of problems. It is well-known that MINLP problems are NP-hard because they are the generalization of MILP problems, which are NP-hard themselves. However, MINLPs are, in general, also hard to solve in practice. We address to non-convex MINLPs, i.e. having non-convex continuous relaxations: the presence of non-convexities in the model makes these problems usually even harder to solve. The aim of this Ph.D. thesis is to give a flavor of different possible approaches that one can study to attack MINLP problems with non-convexities, with a special attention to real-world problems. In Part 1 of the thesis we introduce the problem and present three special cases of general MINLPs and the most common methods used to solve them. These techniques play a fundamental role in the resolution of general MINLP problems. Then we describe algorithms addressing general MINLPs. Parts 2 and 3 contain the main contributions of the Ph.D. thesis. In particular, in Part 2 four different methods aimed at solving different classes of MINLP problems are presented. Part 3 of the thesis is devoted to real-world applications: two different problems and approaches to MINLPs are presented, namely Scheduling and Unit Commitment for Hydro-Plants and Water Network Design problems. The results show that each of these different methods has advantages and disadvantages. Thus, typically the method to be adopted to solve a real-world problem should be tailored on the characteristics, structure and size of the problem. Part 4 of the thesis consists of a brief review on tools commonly used for general MINLP problems, constituted an integral part of the development of this Ph.D. thesis (especially the use and development of open-source software). We present the main characteristics of solvers for each special case of MINLP.