These results emphasize the importance of using appropriate algorithms and provide further insights into the choice of algorithms for the optimization of hydropower systems. Based on the comprehensive evaluation, NSGA-III seems to be more appropriate for more than two objectives. NSGA-II is more suitable for solving the optimization operation problem with two objectives. The results show that for the two-objective model, the non-dominant size generation rate (NDSGR) of NSGA-II is 1.66 and 4.01 times that of NSGA-III and RVEA, respectively. Numerical experiments were conducted to evaluate the performance of these three algorithms for the optimization of a cascaded reservoir system. In this study, three representative MOGAs were selected, namely the Non-dominated Sorting Genetic Algorithm II (NSGA-II), Non-Dominated Sorting Genetic Algorithm III (NSGA-III), and Reference Vector Guided Evolutionary Algorithm (RVEA), and three multi-objective optimization models were then developed accordingly. suitable and efficient multi-objective algorithm for multi-reservoir system optimization. However, the computational cost grows exponentially with the expansion of multi-reservoir systems and the increased dimensions of optimization problems, posing a great challenge to multi-reservoir operations. Multi-objective genetic algorithms (MOGAs) are widely used for multi-reservoir systems’ optimization due to their high efficiency and fast convergence. The results of solving the model problem showed the effectiveness of the proposed algorithm. The algorithm makes it possible to reduce the number of iterations by several orders of magnitude compared to the gradient descent algorithm currently used and to obtain the accuracy of the solution, which is practically unattainable by the gradient descent algorithm. We used the fast algorithm proposed by the authors for training networks of radial basis functions by the Levenberg-Marquardt method with analytical calculation of the Jacobi matrix. This removes the restrictions on the use of radial basis functions and allows the use of radial basis functions with both unlimited and limited definition areas.
The proposed algorithm is based on solving individual problems for each area with different properties of the medium and using a common error functional that takes into account errors at the interface between the media. The solution of boundary value problems describing piecewise-homogeneous media on networks of radial basis functions is considered.
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