Optimization Strategies Based on Sequential Quadratic Programming Applied for a Fermentation Process for Butanol Production

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

On an approximate analytical solution to a nonlinear vibrating problem, excited by a nonideal motor

This paper analyzes through Multiple Scales Method a response of a simplified nonideal and nonlinear vibrating system. Here, one verifies the interactions between the dynamics of the DC motor (excitation) and the dynamics of the foundation (spring, damper, and mass). We remarked that we consider cubic nonlinearity (spring) and quadratic nonlinearity (DC motor) of the same order of magnitude according to experimental results. Both analytical and numerical results that we have obtained had good agreement.

On the resolution of the generalized nonlinear complementarity problem

Minimization of a differentiable function subject to box constraints is proposed as a strategy to solve the generalized nonlinear complementarity problem (GNCP) defined on a polyhedral cone. It is not necessary to calculate projections that complicate and sometimes even disable the implementation of algorithms for solving these kinds of problems. Theoretical results that relate stationary points of the function that is minimized to the solutions of the GNCP are presented. Perturbations of the GNCP are also considered, and results are obtained related to the resolution of GNCPs with very general assumptions on the data. These theoretical results show that local methods for box-constrained optimization applied to the associated problem are efficient tools for solving the GNCP. Numerical experiments are presented that encourage the use of this approach.

Penalty-based nonlinear solver for optimal reactive power dispatch with discrete controls

The optimal reactive dispatch problem is a nonlinear programming problem containing continuous and discrete control variables. Owing to the difficulty caused by discrete variables, this problem is usually solved assuming all variables as continuous variables, therefore the original discrete variables are rounded off to the closest discrete value. This approach may provide solutions far from optimal or even unfeasible solutions. This paper presents an efficient handling of discrete variables by penalty function so that the problem becomes continuous and differentiable. Simulations with the IEEE test systems were performed showing the efficiency of the proposed approach. © 1969-2012 IEEE.

A Modified Branch and Bound Algorithm to Solve the Transmission Expansion Planning Problem

In this paper a novel Branch and Bound (B&B) algorithm to solve the transmission expansion planning which is a non-convex mixed integer nonlinear programming problem (MINLP) is presented. Based on defining the options of the separating variables and makes a search in breadth, we call this algorithm a B&BML algorithm. The proposed algorithm is implemented in AMPL and an open source Ipopt solver is used to solve the nonlinear programming (NLP) problems of all candidates in the B&B tree. Strategies have been developed to address the problem of non-linearity and non-convexity of the search region. The proposed algorithm is applied to the problem of long-term transmission expansion planning modeled as an MINLP problem. The proposed algorithm has carried out on five commonly used test systems such as Garver 6-Bus, IEEE 24-Bus, 46-Bus South Brazilian test systems, Bolivian 57-Bus, and Colombian 93-Bus. Results show that the proposed methodology not only can find the best known solution but it also yields a large reduction between 24% to 77.6% in the number of NLP problems regarding to the size of the systems.

The use of nonlinear programming as a tool for maximum profit feed formulation of broilers

The purpose of this study was to compare linear and nonlinear programming models for feed formulation, for maximum profit, considering the real variation in the prices of the corn, soybean meal and broilers during the period from January of 2008 to October of 2009, in the São Paulo State, Brazil. For the nonlinear formulation model, it was considered the following scenarios of prices: a) the minimum broiler price and the maximum prices of the corn and soybean meal during the period, b) the mean prices of the broiler, corn and soybean meal in the period and c) the maximum broiler price and the minimum prices of the corn and soybean meal, in the considered period; while for the linear formulation model, it was considered just the prices of the corn and the soybean. It was used the Practical Program for Feed Formulation 2.0 for the diets establishment. A total of 300 Cobb male chicks were randomly assigned to the 4 dietary treatments with 5 replicate pens of 15 chicks each. The birds were fed with a starter diet until 21 d and a grower diet from 22 to 42 d of age, and they had ad libitum access to feed and water, on floor with wood shavings as litter. The broilers were raised in an environmentally-controlled house. Body weight, body weight gain, feed intake, feed conversion ratio and profitability (related to the prices variation of the broilers and ingredients) were obtained at 42 d of age. It was found that the broilers fed with the diet formulated with the linear model presented the lowest feed intake and feed conversion ratio as compared with the broilers fed with diets from nonlinear formulation models. There were no significant differences in body weight and body weight gain among the treatments. Nevertheless, the profitabilities of the diets from the nonlinear model were significantly higher than that one from the linear formulation model, when the corn and soybean meal prices were near or below their average values for the studied period, for any broiler chicken price.

A nonlinear elliptic problem with terms concentrating in the boundary

In this paper, we investigate the behavior of a family of steady-state solutions of a nonlinear reaction diffusion equation when some reaction and potential terms are concentrated in a e-neighborhood of a portion G of the boundary. We assume that this e-neighborhood shrinks to G as the small parameter e goes to zero. Also, we suppose the upper boundary of this e-strip presents a highly oscillatory behavior. Our main goal here was to show that this family of solutions converges to the solutions of a limit problem, a nonlinear elliptic equation that captures the oscillatory behavior. Indeed, the reaction term and concentrating potential are transformed into a flux condition and a potential on G, which depends on the oscillating neighborhood. Copyright (C) 2012 John Wiley & Sons, Ltd.

A modified Primal-Dual Logarithmic-Barrier Method for solving the Optimal Power Flow problem with discrete and continuous control variables

The aim of solving the Optimal Power Flow problem is to determine the optimal state of an electric power transmission system, that is, the voltage magnitude and phase angles and the tap ratios of the transformers that optimize the performance of a given system, while satisfying its physical and operating constraints. The Optimal Power Flow problem is modeled as a large-scale mixed-discrete nonlinear programming problem. This paper proposes a method for handling the discrete variables of the Optimal Power Flow problem. A penalty function is presented. Due to the inclusion of the penalty function into the objective function, a sequence of nonlinear programming problems with only continuous variables is obtained and the solutions of these problems converge to a solution of the mixed problem. The obtained nonlinear programming problems are solved by a Primal-Dual Logarithmic-Barrier Method. Numerical tests using the IEEE 14, 30, 118 and 300-Bus test systems indicate that the method is efficient. (C) 2012 Elsevier B.V. All rights reserved.

SOMS: SurrOgate MultiStart algorithm for use with nonlinear programming for global optimization

SOMS is a general surrogate-based multistart algorithm, which is used in combination with any local optimizer to find global optima for computationally expensive functions with multiple local minima. SOMS differs from previous multistart methods in that a surrogate approximation is used by the multistart algorithm to help reduce the number of function evaluations necessary to identify the most promising points from which to start each nonlinear programming local search. SOMS’s numerical results are compared with four well-known methods, namely, Multi-Level Single Linkage (MLSL), MATLAB’s MultiStart, MATLAB’s GlobalSearch, and GLOBAL. In addition, we propose a class of wavy test functions that mimic the wavy nature of objective functions arising in many black-box simulations. Extensive comparisons of algorithms on the wavy testfunctions and on earlier standard global-optimization test functions are done for a total of 19 different test problems. The numerical results indicate that SOMS performs favorably in comparison to alternative methods and does especially well on wavy functions when the number of function evaluations allowed is limited.

A nonlinear programming algorithm for an array computer /

"October 22, 1969."

On the nonlinear Neumann problem involving the critical Sobolev exponent on the boundary

in this paper we investigate the solvability of the Neumann problem (1.1) involving the critical Sobolev exponents on the right-hand side of the equation and in the boundary condition. It is assumed that the coefficients Q and P are smooth. We examine the common effect of the mean curvature of the boundary a deltaOhm and the shape of the graph of the coefficients Q and P on the existence of solutions of problem (1.1). (C) 2003 Published by Elsevier Inc.

A meshless method for an inverse two-phase one-dimensional nonlinear Stefan problem

We extend a meshless method of fundamental solutions recently proposed by the authors for the one-dimensional two-phase inverse linear Stefan problem, to the nonlinear case. In this latter situation the free surface is also considered unknown which is more realistic from the practical point of view. Building on the earlier work, the solution is approximated in each phase by a linear combination of fundamental solutions to the heat equation. The implementation and analysis are more complicated in the present situation since one needs to deal with a nonlinear minimization problem to identify the free surface. Furthermore, the inverse problem is ill-posed since small errors in the input measured data can cause large deviations in the desired solution. Therefore, regularization needs to be incorporated in the objective function which is minimized in order to obtain a stable solution. Numerical results are presented and discussed. © 2014 IMACS.

Funções penalidade para o tratamento das variáveis discretas do problema de fluxo de potência ótimo reativo

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Um método eficiente para resolução do problema de Despacho Ótimo de Reativos com controle discreto do TAP dos transformadores

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)