Heriot-Watt University
Introduction
Reservoir operating rules are used for managing reservoir systems to achieve satisfactory performance in meeting the demands placed on them. To this end, various optimisation schemes have been used to derive optimal rule curves based on minimisation of water-shortage related objective functions (Senthil Kumar et al., 2012). In particular, evolutionary genetic algorithms (GA) optimisation has long been recognized, and widely applied, to provide the optimal solutions when deriving reservoir operating policies. The main challenge in GA optimisation, however, is establishing the optimum boundary of the feasible region to search for the optimal solution. Too wide a boundary will increase the computational time while too narrow a boundary may lead to the solution missing the global optimum (Purojit et al., 2013; Roeva et al., 2013).
The aim of this work is to present a new development of the GA, known as the dynamic GA (DGA), that is more efficient and rapid than the simple GA (SGA) in arriving at an optimal solution. The objectives are to:
i. Review the literature dealing with the deployment of GA in reservoir optimisation;
ii. Present the development of the new DGA optimisation;
iii. Apply both the SGA and DGA to a real water resources optimisation problem and make comparisons;
Methods
GA is an efficient, adaptive and robust population-based optimisation method that uses the principles of natural selection and evolution. The SGA starts with an initial population which is generated randomly and the genetic operations are repeated over several generations until the stopping criterion is met, at which point the optimum solution is said to have been reached. Because the GA is initialised with random numbers which are unlikely to be the same over repeated trials, the algorithm is normally repeated several times, typically 100, and either an average solution or the best among the 100 taken. SGA, however, often fails to search adequately for the global optimum and is time consuming, especially when the search space is not in an optimum space. The new DGA developed in this work overcomes this limitation by using the reducing-search-space techniques to increasingly focus on the confined area of the true optimum point. It does this by progressively reducing individual constraint boundary of the feasible region.
The DGA also starts with an initial random population like the SGA and runs over "g" generations from which the best string is selected. This process is repeated "r" times, thus leading to "r" best strings. "g" and "r" are parameters of the DGA and their best values are determined by trial-and-error but, as will be seen later, are much lower than those normally required for the SGA. The best of the "r" strings are then observed for the purpose of updating the boundaries for the search space for the next iteration. The best value for any two consecutive iterations are compared and if the difference is above a specified value "
Application, Results and Discussion
Both the SGA and DGA were applied to develop optimised rules curves for Ubonratana reservoir in Thailand that provides water for public (domestic & industrial), environmental flows, irrigation and hydro-power generation. Water allocation is prioritised during scarcity with public demand having the greatest priority and other sectors are satisfied with any left over water in the sequence listed. The active storage capacity of the reservoir is 2413 Mm
The GA operations used roulette-wheel selection, scattered crossover, uniform mutation, crossover fraction of 0.8 and mutation rate of 0.01. An investigation of the effect of population size on the fitness values for the SGA revealed that a population size of 200 is adequate. A similar investigation revealed that 1500 generations will produce the best fitness for the population of 200 (Table 1). Thus, the SGA implementation used a combination of 200 population and 1500 generations.
The DGA algorithm was tested for generations "g" (= 2, 5, 10, 15 and 20) and repetitions "r" (= 3, 5, 7 and 10) and the results showed that "r"=2 and "g" = 7 represented the best combination. The best fitness value for the "2" & "7" combination was 6021, which is about 43% of that achieved with the SGA. Additionally, the computational time for the best DGA was 352 seconds, i.e. less than 50% of time taken by the SGA.
The ordinates of the optimised rule curves are listed in Table 2; the FCRC is the flood control rule curve which has not been optimised in this study. Table 3 summarises the reservoir performance (in terms of failure duration in months (f
Conclusion
The simple genetic algorithm (SGA) has been improved by search space modification using DGA. The boundaries are updated by the reducing-search-space based technique, and then the consequent algorithm is performed within new intervals. The search space is then focused around the area of the optimal solution, hence speeding up the convergence process and improving the precision of solutions. The DGA approach performed better than SGA. Test results have shown that the proposed technique could significantly speed up the convergence and improve the best fitness.
Table 1. Influence of number of generations on the fitness value for SGA
Table 2. Ordinates of rule curves tested by SGA and DGA
Table 3. Summary of evaluated reservoir performance indices for the optimised policies
Purohit GN, Sherry AM and Saraswat M (2013) Optimization of function by using a new MATLAB based genetic algorithm procedure. International Journal of Computer Applications, 6(15).
Roeva O, Fidanova S and Paprzycki M (2013) Influence of the population size on the genetic algorithm performance in case of the cultivation process modelling. Proceeding of the 2013 federated conference on computer science and information systems, 371-376.
Senthill kumar A, Goyal M, Ojha C, Singh R, Swamee P and Nema R (2012) Application of ANN, Fuzzy Logic and Decision Tree Algorithms for the Development of Reservoir Operating Rules. Water Resour Manage (2013), 27, 911–925.