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Slime mould algorithm (SMA) is extensively used in engineering applications such as the parameter estimation of photovoltaic models, image segmentation, economic emission dispatch, etc. To improve SMA's inherent search stagnation, slow convergence speed and poor transition ability when transferring from exploration to exploitation, especially for optimization problems with high dimensions and many local optimal values, a multi-strategy improved slime mould algorithm (MSMA) is proposed in this paper. The elite chaotic search strategy (ECSS) is adopted to improve the ability of the algorithm to explore near the elite individuals. Moreover, the z parameter of SMA, which originally is a constant, is substituted by a nonlinear convergence factor with chaotic disturbance to enhance the algorithm's transition ability between exploration and exploitation. MSMA is compared with other 9 classical or advanced metaheuristic algorithms by optimizing 12 benchmark functions, and the comparative results show that MSMA has better performance in solving accuracy, convergence speed and robustness. Finally, to verify the effectiveness of MSMA, MSMA and the other 9 algorithms are applied to a real cascade hydropower reservoirs system along Dadu River in China to maximize the annual power generation. The numerical simulation results show that with the proposed MSMA, the average power generation in the wet year, the normal year and the dry year are 1.11%–19.22%, 0.35%–13.21% and 0.84%–12.85% more than with other algorithms respectively, which verifies the superiority and effectiveness of MSMA for cascade reservoirs operation problem. [ABSTRACT FROM AUTHOR]