Multi-Objective Optimal Operation Policy of Boostan Dam Reservoir Using Whale and NSGA-II Algorithms Based on Game Theory and Shannon Entropy Method

It is inevitable to use optimization methods for multi-objective reservoirs' operation. In this research, after introducing the whale multi-objective optimization algorithm, its performance as optimal operation of the Boostan dam reservoir was evaluated based on the Conflict Resolution Method of Kalai-Smorodinsky. In the present optimization problem, while applying the constraints of reservoir continuity equations, the objective functions were defined as minimization of downstream water demand deficiencies and minimizing reservoir volume for flood control during the operation period. The performance of the proposed algorithm was compared with NSGA-II as one of the common algorithms in this field. Model performance was compared and evaluated based on reliability, reversibility, vulnerability and sustainability indices. To solve the conflict between the goals, the game theory-based method (Kalai-Smorodinsky method) was used to find the optimal solution. The optimization results showed better performance of the whale multi-objective algorithm than NSGA-II, in both objective functions. In terms of optimization time, the multi-objective whale algorithm converges faster than NSGA-II because of the fewer regulatory parameters. The model performance evaluation indices show that whale algorithm reliability is higher (86%) than NSGA-II. Moreover, the results of Shannon entropy method for weighting the indices showed that the model evaluation parameters are more weighted than the objective functions. The results of the Kalai-Smorodinsky method showed that the operation policies of Boostan Dam Reservoir have got a very good agreement with the whale multi-objective algorithm. On the other hand, since the most and the least desirable objective function values estimated by the whale multi-objective optimization algorithm are less than the other one, the performance of the whale multi-objective algorithm can be more appropriately identified.