Sine cosine algorithm (SCA) is an emerging meta-heuristic method for the complicated global optimization problems, but still suffers from the premature convergence problem due to the loss of swarm diversity. To improve the SCA performance, this paper develops a modified sine cosine algorithm coupled with three improvement strategies, where the quasi-opposition learning strategy is used to balance global exploration and local exploitation; the random weighting agent produced by multiple leader solutions is integrated into the agent’s evolution equation to improve the convergence rate; the adaptive mutation strategy is designed to increase the swarm diversity. The proposed method is compared with several famous evolutionary methods on 12 classical test functions, 24 CEC2005 composite functions and 30 CEC2017 benchmark functions. The results show that the proposed method outperforms several control methods in both solution quality and convergence rate. Then, the long-term operation optimization of multiple hydropower reservoirs in China is chosen to testify the engineering practicality of the developed method. The simulation results indicate that in different scenarios, the proposed method can produce satisfying scheduling schemes with better objective values compared with several existing evolutionary methods. Hence, a novel optimizer is provided to handle the complicated engineering optimization problem.