Closure to Discussion of "Unit Commitment by Lagrangian Relaxation and Genetic Algorithms"

We would like to appreciate the discusser for his interest and valuable comments on our paper1 entitled “Unit Commitment by Lagrangian Relaxation and Genetic Algorithms.” In the following, we will address the points raised in the discussion. 1) In our paper, we apply the combination of Lagrangian Relaxation and Genetic Algorithms to solve the unit commitment problem. The basic idea of proposed LRGA is that Genetic Algorithm is incorporated into Lagrangian Relaxation method to update the Lagrangian multipliers and improve the performance of Lagrangian Relaxation method. Our paper present this method based on the approach proposed by Merlin and Sandrin [12]. The Reference [13] by F. Zhuang and F. D. Galiana is an interesting and excellent paper. The discusser presents the suggestion that Genetic Algorithm is incorporated into the Lagrangian Relaxation approach [13] to solve the unit commitment problem and compare the performance. This is a good idea and we will study and try the suggestion as far as possible in the future. 2) In step 6 of the LRGA algorithm presented, after setting the commitments variables to the solution of the problem solved in step 4, an economic dispatch procedure is run, provided there is sufficient generation committed that hour. If there is not enough generation committed, the total cost for that hour is set to a very large number. This means that the solution of the dual problem is uncertain of meeting the spinning reserve constrains. 3) We would like to thank the discusser for providing new techniques to update the Lagrangian multiplies in Reference [D6–D9]. These techniques are interesting and valuable. We will study and try these techniques for the unit commitment problem to compare the performance of our LRGA method to a LR approach as soon as possible in the future.