Optimization of Multireservoir Systems Operation Using Modified Direct Search Genetic Algorithm

A direct search method using genetic algorithms (DSGA), which seeks to directly find optimal parameters for prescribed operating policies, is utilized for optimization of multireservoir operational problems and several modifications are presented. The problems presented consist of 3, 7, and 16 reservoirs, respectively, from the Greater Karoon system in Iran. For the three-reservoir problem, the DSGA method is used to obtain optimal linear operating policies and has proven to be very effective in both objective function values and computational time in comparison to the more traditional optimization models based on dynamic programming. However, the model must be modified to optimize larger problems successfully. The first set of proposed modifications is primarily for enhancing the efficiency of the genetic algorithm (GA) used in the model and reducing its sensitivity to GA parameters such as the probability of mutations and size of generations. The more robust modified DSGA is then applied to the seven-reservoir problem to obtain optimal linear policies as well as two forms of piecewise linear ones, which achieves better objective values. The other modifications applied to the model are a Fourier series approximation which defines the seasonal variation of policy parameters and a stepwise GA, which employs varying lengths of simulations for fitness evaluations in different generations. These modifications reduce the time of computations significantly. As a final point, the fine-tuned modified DSGA model optimizes the 16-reservoir problem in less than $20\mathrm{h}$ , which is a significant time period. Computational time is estimated to increase geometrically (second order) with the number of reservoirs.