Multi-reservoir system operation is a challenging and complex task, because of the curse of uncertainties, nonlinearities, dimensionalities and conflicts among the various contradictory objectives. Contemporaneous optimization of such competing objectives needs improving the capability of existing optimization algorithms. This study reports the first application of the recently-introduced multi-objective moth swarm algorithm (MOMSA) in optimization of long-term operation of the large Karun multi-purpose multi-reservoir system. In this algorithm, the decision variables were defined in such a way that the algorithm synchronization capability has improved. Furthermore, a robust mechanism (crowding distance mechanism) with high exploratory capability was employed to select the most efficient solutions within the population. To evaluate the algorithm's efficiency, the results of MOMSA were compared with two well-known multi-objective algorithms of the non-dominated sorting genetic algorithm-II (NSGA-II) and the strength Pareto evolutionary algorithm-II (SPEA-II). To compare the capability of these algorithms, a set of statistical indices including the generational distance (GD), the spacing (S), the spread (Δ), and the maximum spread (MS), along with four reservoir's performance evaluation indicators of the reliability (Rel), the vulnerability (Vul), the resiliency (Res), and the sustainability index were employed. The results demonstrated the superior performance of the MOMSA in solving the Karun multi-reservoir system problem with GD = 259.64, S = 3574.69, Δ = 0.755 and MS = 18420.8. The MOMSA, with the optimized average annual energy production of 15669.7 GW, outperformed the NSGA-II (7569.1 GW) and SPEA-II (9026.3 GW) algorithms. Furthermore, the developed algorithm could supply the downstream demands with a sustainability index of 86.73%, while the corresponding values for the NSGA-II, the SPEA-II and the real operating conditions were 22.73%, 46.09% and 78.87%, respectively. In addition, among the utilized algorithms, the MOMSA demonstrated the best results for flood control purpose. The superior performance of MOMSA will ensure it as a robust algorithm in the optimization of complex and large-scale problems.