Research on Constraint Processing Method of High-dimensional Optimization Operation Problem of Cascade Reservoirs

With the expansion of operational scales and the refinement of time steps in optimizing cascade reservoirs, the dimensionality of decision variables in such problems can range from hundreds to thousands. In the operational optimization of cascaded reservoirs with high-dimensional decision variables, it is often essential to consider multiple complex constraints. Traditional optimization methods struggle to effectively identify feasible regions when addressing these challenges. The intelligent optimization algorithm is a multidimensional linkage random search, which boasts a vast optimization space but suffers from low optimization efficiency. Therefore, this study introduces a constraint processing approach that integrates a penalty function with nested DPSA–POA and intelligent algorithms and applies it to the optimal flood control operation problem of cascade reservoirs in the middle reaches of the Ganjiang River, with decision variables extending to 2196 dimensions. The results of the correlation analysis indicated that: 1) the nested DPSA–POA intelligent algorithm combined with a penalty function can address the high-dimensional optimization problem under varying water inflow conditions using three constraint processing methods; 2) Of the three constraint processing methods, method 2, which involves DE optimization after securing a feasible solution through nested optimization, achieves the highest convergence accuracy, though the computation time is approximately 10 h; method 3, which involves DPSA–POA optimization after securing a feasible solution through nested optimization, achieves the second highest convergence accuracy, with a computation time of about 1～3 h; 3) Existing SF, SR, PF, and EC constraint treatment strategies fail to consistently converge to a feasible solution under different water inflow conditions, and the convergence accuracy of the results, upon obtaining a feasible solution, is significantly lower than that of the method introduced in this study. Accordingly, the nested constraint processing method presented in this research can be an effective approach for high-dimensional optimization in the operation of cascade reservoirs. © 2024 Sichuan University. All rights reserved.