Optimal operation of cascade hydropower reservoirs is a complex high-dimensional engineering problem. Developing an appropriate model to solve such problems requires an efficient search method proportional to the dimensions of the problem. Accordingly, this research employed the new fitness-distance-balance (FDB) selection method in the moth swarm algorithm (MSA) to achieve promoted FDB-MSA with a high performance in solving complex large-scale problems. To ensure the efficiency of the developed algorithm, five benchmark functions of Shekel, Six-Hump Camel, McCormick, Goldstein-Price and Rosenbrock were used. Then, the FDB-MSA was used for optimization of hydropower generation of a real five-reservoir system along Karun River at Iran. This is the largest cascade reservoir system in Iran, which supplies more than 90% of the country’s hydropower demand. The results of the developed algorithm were compared with those of genetic algorithm (GA) and particle swarm optimization (PSO) algorithm. It was found that the FDB-MSA could successfully increase the hydropower generation by 59.5% (6724 GW) compared to the actual generation of energy over a 180-months operational period. The corresponding values for PSO and GA algorithms were 54.3% and 9.2% respectively. In addition, the results revealed the superiority of FDB-MSA to GA and PSO, so that, it demonstrated the smallest difference (3.41%) between nominal and optimal power generation compared to the PSO (6.58%) and GA (33.89%).

梯级水库的优化运行是一个复杂的高维工程问题。开发适当的模型来解决此类问题需要一种与问题的大小成比例的有效搜索方法。因此，本研究在蛾群算法（MSA）中采用了新的适应度-距离-平衡（FDB）选择方法，以实现具有高性能的改进的FDB-MSA，可以解决复杂的大规模问题。为了确保所开发算法的效率，使用了Shekel，六峰驼峰，麦考密克，Goldstein-Price和Rosenbrock的五个基准功能。然后，FDB-MSA被用于优化伊朗卡伦河沿岸的一个真正的五水库系统的水力发电。这是伊朗最大的梯级水库系统，它满足了该国90％以上的水电需求。将该算法与遗传算法和粒子群优化算法的结果进行了比较。研究发现，与180个月的运营期间的实际发电量相比，FDB-MSA可以成功地将水力发电量增加59.5％（6724 GW）。PSO和GA算法的相应值分别为54.3％和9.2％。此外，结果显示了FDB-MSA优于GA和PSO，因此，与PSO（6.58％）和GA（33.89％）相比，它显示了额定发电量和最佳发电量之间的最小差异（3.41％）。研究发现，与180个月的运营期间的实际发电量相比，FDB-MSA可以成功地将水力发电量增加59.5％（6724 GW）。PSO和GA算法的相应值分别为54.3％和9.2％。此外，结果显示了FDB-MSA优于GA和PSO，因此，与PSO（6.58％）和GA（33.89％）相比，它显示了额定发电量和最佳发电量之间的最小差异（3.41％）。研究发现，与180个月的运营期间的实际发电量相比，FDB-MSA可以成功地将水力发电量增加59.5％（6724 GW）。PSO和GA算法的相应值分别为54.3％和9.2％。此外，结果显示了FDB-MSA优于GA和PSO，因此，与PSO（6.58％）和GA（33.89％）相比，它显示了额定发电量和最佳发电量之间的最小差异（3.41％）。