Lagrangian relaxation neural network for unit commitment

This paper presents a novel method for unit commitment by synergistically combining Lagrangian relaxation for constraint handling with Hopfield-type recurrent neural networks for fast convergence to the minimum. The key idea is to set up a Hopfield-type network using the negative dual as its energy function. This network is connected to “neuron-based dynamic programming modules” that make full use of the DP structure to solve individual unit subproblems. The overall network is proved to be stable, and the difficulties in handling integer variables, subproblem constraints, and subproblem local minima plaguing current neural network methods are avoided. Unit commitment solutions are thus natural results of network convergence. Software simulation using data sets from Northeast Utilities demonstrates that the results are much better than what has been reported in the neural network literature, and the method can provide near-optimal solutions for practical problems. Furthermore, the method has the potential to be implemented in hardware with much improved quality and speed