The Application of GA, SMPSO and HGAPSO in Optimal Reservoirs Operation

The reservoir operation is a multi-objective optimization problem with large-scale which consider reliability and the needs of hydrology, energy, agriculture and the environment. There were not the any algorithms with this ability which consider all the above-mentioned demands until now. Almost the existing algorithms usually solve a simple form of the problem for their limitations. In the recent decay the application of meta-heuristic algorithms were introduced into the water resources problem to overcome on some complexity, such as non-linear, non-convex and description of these problems which limited the mathematical optimization methods. In this paper presented a Simple Modified Particle Swarm Optimization Algorithm (SMPSO) with applying a new factor in Particle Swarm Optimization (PSO) algorithm. Then a new suggested hybrid method which called HGAPSO developed based on combining with Genetic algorithm (GA). In the end, the performance of GA, MPSO and HGAPSO algorithms on the reservoir operation problem is investigated with considering water supplying as objective function in a period of 60 months according to inflow data.
The GA is one of the newer programming methods which use of the theory of evolution and survival in biology and genetics principles. GA has been developed as an effective method in optimization problems which doesn’t have the limitation of classical methods. The SMPSO algorithm is the member of swarm intelligence methods that a solution is a population of birds which know as a particle. In this collection, the birds have the individual artificial intelligence and develop the social behavior and their coordinate movement toward a specific destination. The goal of this process is the communication between individual intelligence with social interaction. The new modify factor in SMPSO makes to improve the speed of convergence in optimal answer. The HGAPSO is a suggested combination of GA and SMPSO to remove the limitation of GA and SMPSO. In this paper the initial population which caused randomly in all metha-heuristic algorithms consider fixing for the three mentioned algorithms because the elimination of random effect in initial population may make increase or decrease the convergence speed. The objective function is the minimum sum of the difference between the downstream demand reservoir and system release in the period time. Also the constrains problem is continuity equation, minimum and maximum of reservoir storage and system release.
The performance of GA, SMPSO and HGAPSO evaluated based on the objective function for Dez reservoir in the south east of Iran. In this study the programming of GA, SMPSO and HGAPSO was written in Matlab software and then was run for the time period with a maximum of 400 iterations. The minimum of the objective function for GA, SMPSO and HGAPSO was obtained 1.19, 1.05 and 0.9 respectively, and the maximum of objective function was calculated 1.66, 1.26 and 1.10 respectively. The results showed that the minimum of the objective function by HGAPSO was estimated 32 and 16 percent lower than the counts which calculated by GA and SMPSO. The standard deviation of SMPSO and HGAPSO were near to each other and less than GA which shows the diversity between solutions for SMPSO and HGAPSO are much less than GA. Also the HGAPSO had the better performance rather than previous method in terms of minimum, maximum, average and standard deviation. The convergence speed of HGAPSO for finding the optimal solution is much faster of GA and SMPSO. The difference graphs between system release and monthly demand in HGAPSO is much less than GA and SMPSO. Also the storage calculated in HGAPSO and SMPSO is highly close to each other but in GA method the storage calculated more in the first and second years.
The convergence speed in finding the optimal solution in SMPSO in more than GA but in other hand the probability of caughting in local optima for SMPSO is great whereas GA can make the diverse optimal solutions. For this reason, in this paper was trying to improve the performance of the GA and SMPSO and remove their disadvantage based on combining them and presenting a new hybrid method. The results showed the HGAPSO method which presented in this paper to use without any complexity and additional operator to GA and SMPSO has the ability to use for reservoir operation with large-scale. In addition it is suggested which the HGAPSO apply to other water resources engineering problems.