Sustainable Reservoir Operation Using Multi-Objective Optimization Methods

Abstract
Background and Objectives: Reservoirs operation problems have various and diverse objectives that rarely lead to a global optimized answer, and usually there are a set of optimal answers (Pareto Front). Solving these problems in the past has been possible only with the use of simpler methods, including the use of weight coefficients for various purposes and the conversion of them into a just one objective function. But in recent years, with the development of multi-objective methods, there is a good way to solve them. In this regard, the purpose of the present study was to investigate the efficiency of multi-objective optimization algorithms MOPSO, SPEA-II and NSGA-II in the reservoir operation problem using LDR, N-LDR operation models to generate the optimal Pareto front in order to sustainable development.
Materials and Methods: In order to obtain the mentioned purpose, First, the NSGA-II, MOPSO, and SPEA-II optimization methods were evaluated using some benchmark problems such as standard ZDT family functions with identical conditions (equal population number and number of runs). After evaluating multi-objective optimization methods using standard ZDT family functions, NLDR, LDR and SOP operation models were coded in MATLAB programming environment and linked with multi-objective optimization methods. For each of the two optimization-simulation models (LDR and NLDR), the two objective functions were defined as follows: the first objective function was to minimize the sum of the MSI and the second objective function was the reliability maximization that the maximum of which is usually obtained under the SOP operation conditions. It turns out the two aforementioned objective functions are have a reverse relationship with each other and by increasing one of them, the other one will decrease. Reservoir operation models for a 37-year period from 1356 to 1392 were executed to find the coefficients in both linear and nonlinear models in the same conditions for each multi-objective optimization algorithm with 5000 itrations. The optimal Pareto front was obtained.
Results: By addressing obtained results, It was observed the SPEA-II optimization method in NLDR operation model, has reached to the best optimal Pareto front among others. So from its three answers were selected (by using various criteria) as sample and then sustainability indices such as reliability, resilience, vulnerability and MSI were computed for those three answers. By comparing the values of objective functions and other sustainable development criteria in SOP conditions and the NLDR-C response, it can be seen that using the multi-objective optimization model, we can by less shortages (less MSI 21, 79 compared to 32, 29), reach to approximately maximum reliability (reliability in SOP conditions). However in NLDR-A solution, the least shortage (MSI equal to 13.02) can be seen compare to other sample solutions and SOP policy.
Conclusion: Due to research findings, it was observed the SPEA-II optimization method in all of the standard ZDT family functions has reached to a more optimal Pareto front than other optimization methods. Also this method compared to other optimization methods, has a more complete front of Pareto's solutions, which indicates the efficiency of this optimization method in multi-objective optimization problems. In the case of LDR and NLDR models with the same number of iterations, also It was observed that the NLDR model has shown better results, which can be due to the higher degree of freedom of nonlinear relationship in determining the operation policy of the reservoir releasing. In this research, a series of optimal (Pareto optimal) solutions was presented to meet the stated objectives.