Optimal operation of multi-purpose multi-reservoir dams is a challenging problem for dams’ stakeholders and decision-makers. Optimization algorithms are able to present reliable solutions for such complex problems. This study compared the capability of 20 state-of-the-art robust meta-heuristic algorithms for determining the optimal operating policy of Halilrood multi-reservoir system under the three competing operational objectives of water supply, flood control, and hydropower generation. Before that, the performance of the algorithms in solving two benchmark problems (the Schaffer problem and the MMF1 problem from the CEC suite) was evaluated. Four metrics of generational distance (GD), spacing (S), spread (Δ), and maximum spread (MS) were used to compare the algorithms’ performance in solving the benchmark problems. In addition, four reservoirs performance evaluation indicators of reliability (Rel), resiliency (Res), vulnerability (Vul), and sustainability index (SI) were used to ass the algorithms’ performance in solving the real-case Halilrood problem. The results showed that although the solving capability of each algorithm depends on the nature of the problem, some algorithms were always superior in solving all three problems (2 benchmark problems and one real case). For the Schaffer benchmark problem, the MOAHA algorithm with the performance metrics of (GD = 0.00095, S = 0.58155, Δ = 0.20375, MS = 4.0002) had the best Pareto front in terms of coverage and diversity, and so it was placed at the first rank. In this problem, the MOCryStAl algorithm with (GD = 0.00141, S = 0.48395, Δ = 1.49467, MS = 3.94799) placed at the lowest rank. For the MMF1 problem, the MOMA (GD = 0.00751, S = 0.07516, Δ = 0.29519, MS = 0.99826) followed by the MOAHA (GD = 0.00833, S = 0.07660, Δ = 0.17832, MS = 1.00) had the best performance, respectively, and the MOFA algorithms was the worst. For the Halilrood real-case problem, the MOGWO algorithm (with Rel = 83.41, Res = 67.57, Vul = 22.07 and SI = 76.01) followed by the MOAHA algorithm (Rel = 84.57, Res = 64.71, Vul = 33.60, and SI = 71.41) and the MOMA algorithm (Rel = 79.82, Res = 66.67, Vul = 21.65, and SI = 74.70) obtained the best ranks in terms of reservoir's performance evaluation indicators. They could successfully minimize all three objectives of the total deficit, the flood control and electricity generation indicating the highest performance of these algorithms in the optimization problem. The Pareto front obtained by these algorithms had better distribution and was closer to the origin of coordinates compared to the other utilized algorithms. They could favorably supply the total water demand in the Halilrood basin while increasing the hydropower energy generation up to the power plant capacity at the Jiroft dam. The results of this study can be applied to the optimal operation of any other multi-reservoir system with conflict in water demands.

多用途多水库大坝的优化运行是大坝利益相关者和决策者面临的一个具有挑战性的问题。优化算法能够为此类复杂问题提供可靠的解决方案。本研究比较了 20 种最先进的鲁棒元启发式算法在供水、防洪和水力发电三个相互竞争的运行目标下确定 Halilrood 多水库系统的最佳运行策略的能力。在此之前，评估了算法在解决两个基准问题（Schaffer 问题和 CEC 套件中的 MMF1 问题）中的性能。代际距离（GD）、间距（S）、散布（Δ）和最大散布（MS ）的四个度量) 用于比较算法在解决基准问题中的性能。此外，采用可靠性（Rel）、弹性（Res）、脆弱性（Vul）和可持续性指数（SI）四个油藏性能评价指标来评估算法在解决真实案例Halilrood问题中的性能。结果表明，尽管每种算法的求解能力取决于问题的性质，但有些算法在解决所有三个问题（2 个基准问题和一个真实案例）方面总是表现出色。对于 Schaffer 基准问题，MOAHA 算法的性能指标为 ( GD  = 0.00095, S  = 0.58155, Δ = 0.20375, MS = 4.0002）在覆盖率和多样性方面具有最好的帕累托前沿，因此它被排在第一名。在这个问题中，具有 ( GD  = 0.00141, S  = 0.48395, Δ  = 1.49467, MS  = 3.94799) 的 MOCryStAl 算法排名最低。对于 MMF1 问题，MOMA ( GD  = 0.00751, S  = 0.07516, Δ  = 0.29519, MS  = 0.99826) 其次是 MOAHA ( GD  = 0.00833, S  = 0.07660, Δ  = 0.17832, MS = 1.00) 分别表现最好，MOFA 算法最差。对于 Halilrood 真实案例问题，MOGWO 算法（Rel  = 83.41，Res  = 67.57，Vul  = 22.07 和SI  = 76.01）然后是 MOAHA 算法（Rel  = 84.57，Res  = 64.71，Vul  = 33.60，SI  = 71.41）和 MOMA 算法（Rel  = 79.82，Res  = 66.67，Vul  = 21.65，SI = 74.70）在油藏动态评价指标中排名第一。他们可以成功地最小化总赤字、防洪和发电这三个目标，表明这些算法在优化问题中的最高性能。与其他算法相比，这些算法得到的帕累托前沿分布更好，更接近坐标原点。它们可以有利地满足哈利鲁德盆地的总用水需求，同时将水力发电量增加到 Jiroft 大坝的发电厂容量。这项研究的结果可以应用于任何其他存在用水需求冲突的多水库系统的优化运行。