Constrained optimization model for the design of an adaptive (X)over-bar chart

An economic-statistical model is developed for variable parameters (VP) (X) over bar charts in which all design parameters vary adaptively, that is, each of the design parameters (sample size, sampling interval and control-limit width) vary as a function of the most recent process information. The cost function due to controlling the process quality through a VP (X) over bar chart is derived. During the optimization of the cost function, constraints are imposed on the expected times to signal when the process is in and out of control. In this way, required statistical properties can be assured. Through a numerical example, the proposed economic-statistical design approach for VP (X) over bar charts is compared to the economic design for VP (X) over bar charts and to the economic-statistical and economic designs for fixed parameters (FP) (X) over bar charts in terms of the operating cost and the expected times to signal. From this example, it is possible to assess the benefits provided by the proposed model. Varying some input parameters, their effect on the optimal cost and on the optimal values of the design parameters was analysed.

A barrier method for constrained nonlinear optimization using a modified Hopfield network

The ability of neural networks to realize some complex nonlinear function makes them attractive for system identification. This paper describes a novel barrier method using artificial neural networks to solve robust parameter estimation problems for nonlinear model with unknown-but-bounded errors and uncertainties. This problem can be represented by a typical constrained optimization problem. More specifically, a modified Hopfield network is developed and its internal parameters are computed using the valid-subspace technique. These parameters guarantee the network convergence to the equilibrium points. A solution for the robust estimation problem with unknown-but-bounded error corresponds to an equilibrium point of the network. Simulation results are presented as an illustration of the proposed approach.

Bound constrained smooth optimization for solving variational inequalities and related problems

Variational inequalities and related problems may be solved via smooth bound constrained optimization. A comprehensive discussion of the important features involved with this strategy is presented. Complementarity problems and mathematical programming problems with equilibrium constraints are included in this report. Numerical experiments are commented. Conclusions and directions of future research are indicated.

Design and analysis of an efficient neural network model for solving nonlinear optimization problems

This paper presents an efficient approach based on a recurrent neural network for solving constrained nonlinear optimization. More specifically, a modified Hopfield network is developed, and its internal parameters are computed using the valid-subspace technique. These parameters guarantee the convergence of the network to the equilibrium points that represent an optimal feasible solution. The main advantage of the developed network is that it handles optimization and constraint terms in different stages with no interference from each other. Moreover, the proposed approach does not require specification for penalty and weighting parameters for its initialization. A study of the modified Hopfield model is also developed to analyse its stability and convergence. Simulation results are provided to demonstrate the performance of the proposed neural network.

Efficient parametric adjustment of fuzzy inference system using unconstrained optimization

This paper presents a new methodology for the adjustment of fuzzy inference systems, which uses technique based on error back-propagation method. The free parameters of the fuzzy inference system, such as its intrinsic parameters of the membership function and the weights of the inference rules, are automatically adjusted. This methodology is interesting, not only for the results presented and obtained through computer simulations, but also for its generality concerning to the kind of fuzzy inference system used. Therefore, this methodology is expandable either to the Mandani architecture or also to that suggested by Takagi-Sugeno. The validation of the presented methodology is accomplished through estimation of time series and by a mathematical modeling problem. More specifically, the Mackey-Glass chaotic time series is used for the validation of the proposed methodology. © Springer-Verlag Berlin Heidelberg 2007.

Market-driven security-constrained transmission network expansion planning

This paper presents a Bi-level Programming (BP) approach to solve the Transmission Network Expansion Planning (TNEP) problem. The proposed model is envisaged under a market environment and considers security constraints. The upper-level of the BP problem corresponds to the transmission planner which procures the minimization of the total investment and load shedding cost. This upper-level problem is constrained by a single lower-level optimization problem which models a market clearing mechanism that includes security constraints. Results on the Garver's 6-bus and IEEE 24-bus RTS test systems are presented and discussed. Finally, some conclusions are drawn. © 2011 IEEE.

Uma abordagem usando redes neurais artificiais para resolução de problemas de otimização restrita

Sistemas baseados em redes neurais artificiais fornecem altas taxas de computação devido ao uso de um número massivo de elementos processadores simples. Redes neurais com conexões realimentadas fornecem um modelo computacional capaz de resolver uma rica classe de problemas de otimização. Este artigo apresenta uma nova abordagem para resolver problemas de otimização restrita utilizando redes neurais artificiais. Mais especificamente, uma rede de Hopfield modificada é desenvolvida cujos parâmetros internos são calculados usando a técnica de subespaço válido de soluções. A partir da obtenção destes parâmetros a rede tende a convergir aos pontos de equilíbrio que representam as possíveis soluções para o problema. Exemplos de simulação são apresentados para justificar a validade da abordagem proposta.

On the solution of the extended linear complementarity problem

The extended linear complementarity problem (XLCP) has been introduced in a recent paper by Mangasarian and Pang. In the present research, minimization problems with simple bounds associated to this problem are defined. When the XLCP is solvable, their solutions are global minimizers of the associated problems. Sufficient conditions that guarantee that stationary points of the associated problems are solutions of the XLCP will be proved. These theoretical results support the conjecture that local methods for box constrained optimization applied to the associated problems could be efficient tools for solving the XLCP. (C) 1998 Elsevier B.V. All rights reserved.

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.

On the solution of mathematical programming problems with equilibrium constraints

Mathematical programming problems with equilibrium constraints (MPEC) are nonlinear programming problems where the constraints have a form that is analogous to first-order optimality conditions of constrained optimization. We prove that, under reasonable sufficient conditions, stationary points of the sum of squares of the constraints are feasible points of the MPEC. In usual formulations of MPEC all the feasible points are nonregular in the sense that they do not satisfy the Mangasarian-Fromovitz constraint qualification of nonlinear programming. Therefore, all the feasible points satisfy the classical Fritz-John necessary optimality conditions. In principle, this can cause serious difficulties for nonlinear programming algorithms applied to MPEC. However, we show that most feasible points do not satisfy a recently introduced stronger optimality condition for nonlinear programming. This is the reason why, in general, nonlinear programming algorithms are successful when applied to MPEC.

Multiarea optimal power flow using multiobjective evolutionary algorithm

In this work the multiarea optimal power flow (OPF) problem is decoupled into areas creating a set of regional OPF subproblems. The objective is to solve the optimal dispatch of active and reactive power for a determined area, without interfering in the neighboring areas. The regional OPF subproblems are modeled as a large-scale nonlinear constrained optimization problem, with both continuous and discrete variables. Constraints violated are handled as objective functions of the problem. In this way the original problem is converted to a multiobjective optimization problem, and a specifically-designed multiobjective evolutionary algorithm is proposed for solving the regional OPF subproblems. The proposed approach has been examined and tested on the RTS-96 and IEEE 354-bus test systems. Good quality suboptimal solutions were obtained, proving the effectiveness and robustness of the proposed approach. ©2009 IEEE.

Algoritmo genético especializado na resolução de problemas com variáveis contínuas e altamente restritos

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

A novel approach for solving constrained nonlinear optimization problems using neurofuzzy systems

A neural network model for solving constrained nonlinear optimization problems with bounded variables is presented in this paper. More specifically, a modified Hopfield network is developed and its internal parameters are completed using the valid-subspace technique. These parameters guarantee the convergence of the network to the equilibrium points. The network is shown to be completely stable and globally convergent to the solutions of constrained nonlinear optimization problems. A fuzzy logic controller is incorporated in the network to minimize convergence time. Simulation results are presented to validate the proposed approach.

A neural system to robust Nonlinear optimization subject to disjoint and constrained sets

The ability of neural networks to realize some complex nonlinear function makes them attractive for system identification. This paper describes a novel method using artificial neural networks to solve robust parameter estimation problems for nonlinear models with unknown-but-bounded errors and uncertainties. More specifically, a modified Hopfield network is developed and its internal parameters are computed using the valid-subspace technique. These parameters guarantee the network convergence to the equilibrium points. A solution for the robust estimation problem with unknown-but-bounded error corresponds to an equilibrium point of the network. Simulation results are presented as an illustration of the proposed approach.

Nonlinear optimization using a modified Hopfield model

Systems based on artificial neural networks have high computational rates due to the use of a massive number of simple processing elements. Neural networks with feedback connections provide a computing model capable of solving a rich class of optimization problems. In this paper, a modified Hopfield network is developed for solving constrained nonlinear optimization problems. The internal parameters of the network are obtained using the valid-subspace technique. Simulated examples are presented as an illustration of the proposed approach.