Verification of FPA and PSO algorithms for rule curve extraction and optimization of single- and multi-reservoir systems' operations considering their specific purposes

Abstract

Abstract The optimal operation of reservoirs is known as a complex issue in water resources management, which requires consideration of numerous variables (such as downstream water demand and power generation). For this optimization, researchers have used evolutionary and meta-heuristic algorithms, which are generally inspired by nature. These algorithms have been developed to achieve optimal/near-optimal solutions by a smaller number of function evaluations with less calculation time. In this research, the flower pollination algorithm (FPA) was used to optimize: (1) Aidoghmoush single-reservoir system operation for agricultural water supply, (2) Bazoft single-reservoir system operation for hydropower generation, (3) multi-reservoir system operation of Karun 5, Karun 4, and Bazoft, and (4) Bazoft single-reservoir system for rule curve extraction. To demonstrate the effectiveness of the FPA, it was first applied to solve the mathematical test functions, and then used to determine optimal operations of the reservoir systems with the purposes of downstream water supply and hydropower generation. In addition, the FPA was compared with the particle swarm optimization (PSO) algorithm and the non-linear programming (NLP) method. The results for the Aidoghmoush single-reservoir system showed that the best FPA solution was similar to the NLP solution, while the best PSO solution was about 0.2% different from the NLP solution. The best values of the objective function of the PSO were approximately 3.5 times, 28%, and 43% worse than those of the FPA for the Bazoft single-reservoir system for hydropower generation, the multi-reservoir system, and the Bazoft single-reservoir system for rule curve extraction, respectively. The FPA outperformed the PSO in finding the optimal solutions. Overall, FPA is one of the new evolutionary algorithms, which is capable of determining better (closer to the ideal solution) objective functions, decreasing the calculation time, simplifying the problem, and providing better solutions for decision makers.