Optimal operation of reservoir systems is the most important issue in water resources management. It presents a large variety of multi-objective problems that require powerful optimization tools in order to fully characterize the existing trade-offs. Many optimization methods have been applied based on mathematical programming and evolutionary computation (especially heuristic methods) with various degrees of success more recently. This paper presents an implementation and comparison of multi-objective particle swarm optimization (MOPSO) and non-dominated sorting genetic algorithm II (NSGA-II) for the optimal operation of two reservoirs constructed on Ozan River catchment in order to maximize income from power generation and flood control capacity using MATLAB software. The alternative solutions were based on Pareto dominance. The results demonstrated superior capacity of the NSGA-II to optimize the operation of the reservoir system, and it provides better coverage of the true Pareto front than MOPSO.
In this paper, a multi-layer perceptron (MLP) neural network (NN) is put forward as an efficient tool for performing two tasks: 1) optimization of multi-objective problems and 2) solving a non-linear system of equations. In both cases, mathematical functions which are continuous and partially bounded are involved. Previously, these two tasks were performed by recurrent neural networks and also strong algorithms like evolutionary ones. In this study, multi-dimensional structure in the output layer of the MLP-NN, as an innovative method, is utilized to implicitly optimize the multivariate functions under the network energy optimization mechanism. To this end, the activation functions in the output layer are replaced with the multivariate functions intended to be optimized. The effective training parameters in the global search are surveyed. Also, it is demonstrated that the MLP-NN with proper dynamic learning rate is able to find globally optimal solutions. Finally, the efficiency of the MLP-NN in both aspects of speed and power is investigated by some well-known experimental examples. In some of these examples, the proposed method gives explicitly better globally optimal solutions compared to that of the other references and also shows completely satisfactory results in other experiments.