Augmented Lagrange Hopfield Network for Combined Economic and Emission Dispatch with Fuel Constraint

Abstract

This chapter proposes an augmented Lagrange Hopfield network (ALHN) for solving combined economic and emission dispatch (CEED) problem with fuel constraint. In the proposed ALHN method, the augmented Lagrange function is directly used as the energy function of continuous Hopfield neural network (HNN), thus this method can properly handle constraints by both augmented Lagrange function and sigmoid function of continuous neurons in the HNN. For dealing with the bi-objective economic dispatch problem, the slope of sigmoid function in HNN is adjusted to find the Pareto-optimal front and then the best compromise solution for the problem will be determined by fuzzy-based mechanism. The proposed method has been tested on many cases and the obtained results are compared to those from other methods available the literature. The test results have shown that the proposed method can find good solutions compared to the others for the tested cases. Therefore, the proposed ALHN could be a favourable implementation for solving the CEED problem with fuel constraint.

An improved Hopfield Lagrange network with application on motor efficiency optimization

“…In recent years, Hopfield networks with Lagrange multipliers such as HLN were widely applied in optimization problems. 12,13 However, the Hopfield network is a deterministic gradient descent technique prone to fall into the first local minimum it encounters, 14 and HLN shares the same drawback. There are some recent innovations on nonconvex optimization: in, 15 an extremum-seeking-based approach was developed, whose convergence to a neighborhood of the global minimum was proved; in, 16 distributed stochastic gradient descent was proposed and proved to converge to global minima, yet the theoretical properties are based on certain assumptions, which may limit the application on real problems.…”

“…Later in, 11 the algorithm was named continuous Hopfield–Lagrange network (HLN) and the theoretical properties of HLN was deeply investigated. In recent years, Hopfield networks with Lagrange multipliers such as HLN were widely applied in optimization problems 12,13 …”