Comprehensive assessment of 20 state-of-the-art multi-objective meta-heuristic algorithms for multi-reservoir system operation

•20 meta-heuristics were compared for optimization of multi-reservoir operation.•Two multi-objective benchmark problems and one real case problem were investigated.•Most of the algorithms could reasonably optimize the objective functions.•The MOAHA algorithm had significant performance in optimizing of all problems. 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 =