Optimization the Hydropower-reservoir and Multi-reservoir Operating using the Gravity Search Algorithm

Rivers discharge variations, variable rainfall regimes and drought are important reasons for using the water resource management tools in multi reservoir operation. Heuristic optimization methods can be used with different fitness functions; they can be applied for a wide range of water resource management problems specially reservoirs operation systems. Gravitational search algorithm (GSA) is an evolutionary optimization algorithm based on the law of gravity and mass interactions. In this paper, the ability of this algorithm is investigated for solving the well-known benchmark functions, hydropower-reservoir and ten-reservoir operation system.

For the verification of new evolutionary algorithm, three well-known benchmarks of Bukin6, Rosenbrock, and Sphere were optimized with gravity search algorithm and the results were compared with the outcome of well-developed genetic algorithm (GA) and global optima solutions. Then, hydropower-reservoir operation of Karon4 reservoir was optimized with GSA and compared with the results of GA and global solutions. The global solution was obtained from linear programing solving method by using Lingo software. Finally, the ability of GSA was investigated in large scale water resource management problems. In this regard a ten-reservoir system operation was optimized with both GSA and GA and their results were compared with the global solution. It should be noted that the results were reported in different ten runs for three types of problems to ensure that the results are true. Also the function evaluation values of GSA and GA were equal for all optimization problems.

The ability of GSA in optimizing of different types of problems are demonstrated with showing the solving results of well-known benchmark functions. The results of Bukin6, Rosenbrock and Sphere problems were close to global optima solutions compared with the outcome of the well-developed genetic algorithm results (GA). In single-reservoir hydropower operation, the average values of the objective function were equal 1.218 and 1.746 with the GSA and GA, respectively. The global solution equals to 1.213. Over all, the mean optimum solutions in GSA are better than that of obtained for GA in hydropower-reservoir and ten-reservoir operation problems about 44% and 8% respectively.

The results demonstrated the applicability and efficiency of the proposed algorithm in solving the well-known benchmark functions and water-resource optimization problems such as hydropower-reservoir and ten-reservoir operation systems. It is indicated that GSA solutions in different runs are close to the global optima and the algorithm is converged more rapidly than the genetic algorithm.