Economic dispatch by the combination of HNN and the Lagrange method

In this work, we are going to solve the ED (economic dispatch) problem by the use of an HNN (Hopfield neural networks) model combined with the Lagrange method noted LHNN. In contrary to the techniques that use the linear function of the total inputs to neurons, we are going to use it at the non-linear form that allows the parameters of NN to contain all information of the original problem, so the HNN become able to reach exactly the solutions. At the end, simulations will be presented, with promising results, of a multi-objective economic environmental problem.