Biogeography-Based Optimization Algorithm for Optimal Operation of Reservoir Systems

Abstract

The optimal operation of reservoir systems to meet water demand is a complex and nonlinear problem. This paper applies the biogeography-based optimization (BBO) algorithm to solve reservoir operation problems. The BBO algorithm is first verified with the minimization of three mathematical benchmark functions (Sphere, Rosenbrock, and Bukin6). In addition, the BBO algorithm was applied to a single reservoir system and a four-reservoir system. The performance of the BBO algorithm was compared with that of the genetic algorithm (GA) in solving the three optimization problems. The results show that the BBO algorithm minimized the benchmark functions accurately, and outperformed the GA in this respect. In the case of the single-reservoir hydropower optimization problem the BBO reached a near-optimal solution. The values of the objective function averaged 1.228 and 1.746 with the BBO and GA, respectively. The global solution of this problem with the nonlinear programming method equals 1.213. In the four-reservoir system application the BBO converged to 99.94% of the optimal solution in its best-performing history, whereas the GA converged to 97.46% of the optimal solution. The results from the three test problems demonstrated the superior capacity of the BBO to optimize general mathematical problems and the operation of reservoir systems.