Augmented Lagrange-Hopfield Network for Economic Load Dispatch with Combined Heat and Power

This article proposes an augmented Lagrange-Hopfield network for the combined heat and power economic dispatch problem. The augmented Lagrange-Hopfield network method is the continuous Hopfield neural network with its energy function based on augmented Lagrangian relaxation. In the proposed augmented Lagrange-Hopfield network, the energy function is augmented by Hopfield terms from the Hopfield neural network and penalty factors from the augmented Lagrangian function to damp out oscillation of the Hopfield network during the convergence process, leading to a fast convergence. The proposed augmented Lagrange-Hopfield network has been tested on various systems and compared to Lagrangian relaxation, the genetic algorithm, the improved ant colony search algorithm, evolutionary programming, the improved genetic algorithm with multiplier updating, and the harmony search algorithm. Test results indicate that the proposed neural network is better than the other methods due to a lower total cost and faster computational time, especially for large-scale combined heat and power economic dispatch problems.