A neural network approach for robust nonlinear parameter estimation in presence of unknown-but-bounded errors

Systems based on artificial neural networks have high computational rates due to the use of a massive number of simple processing elements and the high degree of connectivity between these elements. This paper presents a novel approach to solve robust parameter estimation problem for nonlinear model 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. Copyright (C) 2000 IFAC.

Stability and convergence analysis of a neural model applied in nonlinear systems optimization

A neural model for solving nonlinear optimization problems is presented in this paper. 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 network is shown to be completely stable and globally convergent to the solutions of nonlinear optimization problems. A study of the modified Hopfield model is also developed to analyze its stability and convergence. Simulation results are presented to validate the developed methodology.

An efficient Hopfield network to solve economic dispatch problems with transmission system representation

Economic dispatch (ED) problems have recently been solved by artificial neural network approaches. Systems based on artificial neural networks have high computational rates due to the use of a massive number of simple processing elements and the high degree of connectivity between these elements. The ability of neural networks to realize some complex non-linear function makes them attractive for system optimization. All ED models solved by neural approaches described in the literature fail to represent the transmission system. Therefore, such procedures may calculate dispatch policies, which do not take into account important active power constraints. Another drawback pointed out in the literature is that some of the neural approaches fail to converge efficiently toward feasible equilibrium points. A modified Hopfield approach designed to solve ED problems with transmission system representation is presented in this paper. The transmission system is represented through linear load flow equations and constraints on active power flows. The internal parameters of such modified Hopfield networks are computed using the valid-subspace technique. These parameters guarantee the network convergence to feasible equilibrium points, which represent the solution for the ED problem. Simulation results and a sensitivity analysis involving IEEE 14-bus test system are presented to illustrate efficiency of the proposed approach. (C) 2004 Elsevier Ltd. All rights reserved.

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.

Interior point algorithm for linear programming used in transmission network synthesis

This article presents a well-known interior point method (IPM) used to solve problems of linear programming that appear as sub-problems in the solution of the long-term transmission network expansion planning problem. The linear programming problem appears when the transportation model is used, and when there is the intention to solve the planning problem using a constructive heuristic algorithm (CHA), ora branch-and-bound algorithm. This paper shows the application of the IPM in a CHA. A good performance of the IPM was obtained, and then it can be used as tool inside algorithm, used to solve the planning problem. Illustrative tests are shown, using electrical systems known in the specialized literature. (C) 2005 Elsevier B.V. All rights reserved.

Multi-objective evolutionary particle swarm optimization in the assessment of the impact of distributed generation

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

Efficient method for AC transmission network expansion planning

A combinatorial mathematical model in tandem with a metaheuristic technique for solving transmission network expansion planning (TNEP) using an AC model associated with reactive power planning (RPP) is presented in this paper. AC-TNEP is handled through a prior DC model while additional lines as well as VAr-plants are used as reinforcements to cope with real network requirements. The solution of the reinforcement stage can be obtained by assuming all reactive demands are supplied locally to achieve a solution for AC-TNEP and by neglecting the local reactive sources, a reactive power planning (RPP) will be managed to find the minimum required reactive power sources. Binary GA as well as a real genetic algorithm (RCA) are employed as metaheuristic optimization techniques for solving this combinatorial TNEP as well as the RPP problem. High quality results related with lower investment costs through case studies on test systems show the usefulness of the proposal when working directly with the AC model in transmission network expansion planning, instead of relaxed models. (C) 2010 Elsevier B.V. All rights reserved.

Multiobjective 0-1 integer programming for the use of sugarcane residual biomass in energy cogeneration

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

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)

A common Tabu search algorithm for the global optimization of engineering problems

A novel common Tabu algorithm for global optimizations of engineering problems is presented. The robustness and efficiency of the presented method are evaluated by using standard mathematical functions and hy solving a practical engineering problem. The numerical results show that the proposed method is (i) superior to the conventional Tabu search algorithm in robustness, and (ii) superior to the simulated annealing algorithm in efficiency. (C) 2001 Elsevier B.V. B.V. All rights reserved.

Efficient robust optimization based on polynomial chaos and tabu search algorithm

The study of robust design methodologies and techniques has become a new topical area in design optimizations in nearly all engineering and applied science disciplines in the last 10 years due to inevitable and unavoidable imprecision or uncertainty which is existed in real word design problems. To develop a fast optimizer for robust designs, a methodology based on polynomial chaos and tabu search algorithm is proposed. In the methodology, the polynomial chaos is employed as a stochastic response surface model of the objective function to efficiently evaluate the robust performance parameter while a mechanism to assign expected fitness only to promising solutions is introduced in tabu search algorithm to minimize the requirement for determining robust metrics of intermediate solutions. The proposed methodology is applied to the robust design of a practical inverse problem with satisfactory results.

Short and long period optimization of drug doses in the treatment of AIDS

Técnicas de otimização numérica são úteis na solução de problemas de determinação da melhor entrada para sistemas descritos por modelos matemáticos e cujos objetivos podem ser expressos de uma maneira quantitativa. Este trabalho aborda o problema de otimizar as dosagens dos medicamentos no tratamento da AIDS em termos de um balanço entre a resposta terapêutica e os efeitos colaterais. Um modelo matemático para descrever a dinâmica do vírus HIV e células CD4 é utilizado para calcular a dosagem ótima do medicamento no tratamento a curto prazo de pacientes com AIDS por um método de otimização direta utilizando uma função custo do tipo Bolza. Os parâmetros do modelo foram ajustados com dados reais obtidos da literatura. Com o objetivo de simplificar os procedimentos numéricos, a lei de controle foi expressa em termos de uma expansão em séries que, após truncamento, permite obter controles sub-ótimos. Quando os pacientes atingem um estado clínico satisfatório, a técnica do Regulador Linear Quadrático (RLQ) é utilizada para determinar a dosagem permanente de longo período para os medicamentos. As dosagens calculadas utilizando a técnica RLQ , tendem a ser menores do que a equivalente terapia de dose constante em termos do expressivo aumento na contagem das células T+ CD4 e da redução da densidade de vírus livre durante um intervalo fixo de tempo.

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.

Tabu search algorithm for network synthesis

Large scale combinatorial problems such as the network expansion problem present an amazingly high number of alternative configurations with practically the same investment, but with substantially different structures (configurations obtained with different sets of circuit/transformer additions). The proposed parallel tabu search algorithm has shown to be effective in exploring this type of optimization landscape. The algorithm is a third generation tabu search procedure with several advanced features. This is the most comprehensive combinatorial optimization technique available for treating difficult problems such as the transmission expansion planning. The method includes features of a variety of other approaches such as heuristic search, simulated annealing and genetic algorithms. In all test cases studied there are new generation, load sites which can be connected to an existing main network: such connections may require more than one line, transformer addition, which makes the problem harder in the sense that more combinations have to be considered.

Parallel simulated annealing applied to long term transmission network expansion planning

The simulated annealing optimization technique has been successfully applied to a number of electrical engineering problems, including transmission system expansion planning. The method is general in the sense that it does not assume any particular property of the problem being solved, such as linearity or convexity. Moreover, it has the ability to provide solutions arbitrarily close to an optimum (i.e. it is asymptotically convergent) as the cooling process slows down. The drawback of the approach is the computational burden: finding optimal solutions may be extremely expensive in some cases. This paper presents a Parallel Simulated Annealing, PSA, algorithm for solving the long term transmission network expansion planning problem. A strategy that does not affect the basic convergence properties of the Sequential Simulated Annealing algorithm have been implementeded and tested. The paper investigates the conditions under which the parallel algorithm is most efficient. The parallel implementations have been tested on three example networks: a small 6-bus network, and two complex real-life networks. Excellent results are reported in the test section of the paper: in addition to reductions in computing times, the Parallel Simulated Annealing algorithm proposed in the paper has shown significant improvements in solution quality for the largest of the test networks.