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The objective of jointly optimizing the dispatching of cascade hydropower stations in the basin is to maximize economic benefits while ensuring the safe and stable operation constraints of power grids and hydropower stations. The existing joint optimization scheduling algorithms include dynamic programming algorithms and intelligent optimization algorithms. Among them, the progressive optimization algorithm (POA) as a representative of dynamic programming methods can effectively solve complex nonlinear constraint optimization problems. However, while it effectively addresses the issue of "dimensional disaster" in traditional dynamic programming, it also faces the challenge of "local convergence". Although the intelligent optimization algorithm such as the differential evolutionary algorithm (DE) and the genetic algorithm (GA) can effectively handle large-scale complex constraint optimization problems, these algorithms rely on their own group evolution mechanism and lack a search strategy tailored to the mathematical mechanism of the joint scheduling model of cascade hydropower stations. Starting with the theoretical analysis of the two-stage problem of optimizing and dispatching cascade hydropower stations, this paper deduces the monotonicity principle of the two-stage optimization problem for power generation dispatch and proposes a local search strategy based on the monotonicity principle. By using the cascade reservoir group in the lower reaches of JinSha River as an example, the local search strategy for the two-stage optimization problem of power generation dispatch in cascade hydropower stations is validated. This strategy improves the convergence rate and solution accuracy of the algorithm, thereby achieving an efficient solution to the joint optimization dispatch problem of cascade hydropower stations. [ABSTRACT FROM AUTHOR]