Reply to “Comment on ‘A hybrid multi-objective cultural algorithm for short-term environmental/economic hydrothermal scheduling’ by Youlin Lu et al. [Energy Convers. Manage. 52 (2011) 2121–2134]”

In the manuscript “Comment on ‘A hybrid multi-objective cultural algorithm for short-term environmental/economic hydrothermal scheduling’ by Youlin Lu et al. [Energy Convers. Manage. 52 (2011) 2121–2134]”, Abdollah Ahmad et al. reported that there were some inaccuracies made by Youlin Lu et al. in the paper [Energy Convers. Manage. 52 (2011) 2121–2134] while presenting the solutions. By detailed analysis and checking, the different results in the two papers are caused by taking the storage volume at different moments of one period during hydro generation calculation. Abdollah Ahmad et al. take the final storage volume of the period when doing the calculating, while Youlin Lu et al. take the initial storage volume of the period. The checking results indicate that the schemes in the two papers are correct and reasonable only they are obtained by taking different storage volumes. These schemes have less fuel cost and emission while satisfying various constraints. Moreover, the key references cited in the original paper also take the initial storage volume of the period to calculate hydro generation, which are suitable for the comparison of the optimal results. Finally, few inaccurate expressions in the original paper [Energy Convers. Manage. 52 (2011) 2121–2134] are modified.