Assessment of Central Force Optimization (CFO) in optimal reservoir operation

The increasing growth of population and limited surface water resources, necessitate the proper management of the reservoirs of dams. Decision-making process in reservoir operation is influenced by many goals which many of them are not generally proportional to each other. Since the inflows to the reservoir and the storage volumes have uncertainties, the main challenge is to determine the best release of the reservoir and hydro system optimization.
Due to the presence of a variety of complexities and difficulties in solving optimization problems, extensive efforts have been made in order to use different algorithms in this field., Evolutionary and meta-heuristic algorithms are among these approximate methods. Rani and Moreira categorized different types of optimization models for reservoir operation, which are based on: 1. linear programming; 2. Non-linear programming; 3. dynamic programming; and 4. Collective intelligence algorithms. Collective intelligence algorithms have been regarded in recent years. Many of these algorithms have been inspired by the natural behaviors of organisms. Algorithms that have been presented, so far, solve the problem randomly, and in each time of running the program, they follow different paths to reach the solution. For years, researchers have dealt with solving the problems of reservoir operation using different algorithms. Wardlaw and Sharif applied the genetic algorithm as an alternative to dynamic programming in solving multi-reservoir problems. Kai et al. dealt with solving nonlinear problems in water resources, using genetic algorithms. Jalili and Afshar solved a single reservoir problem using ant colony optimization, and achieved better results in comparison with that of the genetic algorithm. Bozorg Haddad et al, and also Afshar et al applied honey-bee mating optimization for reservoir operation. But all these algorithms are stochastic, and will achieve the desired result after running the program, a few times.
Central force optimization (CFO) is an evolutionary and meta-heuristic algorithm, which was presented by Formatto for the first time in 2007. This algorithm is completely deterministic, unlike the previous algorithms. CFO performs its search through the flying of a group of probes whose paths are calculated using the two algebraic equations of motion (position and acceleration) in a series of discrete time steps (iterations). The CFO algorithm performs maximization, and to use this method in minimizing problems, the main function can be multiplied by minus one, thus the maximum of this function is the minimum of the main function. In fact, each probe is a feasible solution which has Nd coordinates in a Nd-dimensional problem. No reports have been given on the application of CFO in reservoir operation problems, yet. In the present study, in order to assess the central force optimization in water resources, the single-reservoir system of Dez Dam, in Khuzestan province located in southern Iran, is considered. This dam is supposed to meet the downstream agricultural demand. The aim of introducing this problem is to determine the most optimal monthly releases for 5 years of operation. Given that the intended problem is due to the non-linear programming, it can be solved using the Lingo software program. Lingo model has the ability to solve nonlinear models, and provides the global optimum in some cases such as the intended problem where the objective function is convex. Therefore, the solutions obtained from the CFO model were compared with that of obtained from the Lingo software program.
In the present study, by implementing the program several times, the optimal values of the constants were obtained. Frep and β were considered to be 0.5 and 2, respectively. During the implementation of the program, some of the obtained accelerations were very small, and the program was in trouble to find the optimum. This problem was solved by choosing a greater G, and the speed of convergence increased. On the other hand, choosing a greater G, α was affected too, and a smaller α presented the better results. α= 0.3 provides the best result; hence the values G= 500 and α= 0.3 were selected. The value of the objective function was calculated 0.7303, using Lingo software program; while it was equal to 0.73604 by using CFO algorithm. The values for the monthly release and reservoir storage obtained from both algorithms had very little difference, and the difference between the objective function and global optimum was 0.0057. Therefore, it can be concluded that, central force optimization (CFO) has high potential to be used in solving the complicated problems of multi-reservoir operation too.