As an environment-friendly and renewable energy source, biomethane plays a significant role in the supply of sustainable energy. To determine location of reactor and allocate feedstocks, to the reactor in a biomethane production system by minimizing the supply chain cost, a mathematical model is studied in this article. Constraints, such as the limited workforce, the reactors’ demand on the residues, and the deterioration of the residues in the hubs are considered. Two evolutionary Algorithm, Genetic and differential evolutionary algorithms for solving mixed integer nonlinear programming model is proposed. The speed of obtaining the solution is the same but differential evolutionary algorithm finds better solutions than Genetic Algorithm when applied to the given problems.

The nonlinear Muskingum model has a significant advantage as compared to the linear model due to the nonlinear relationship between the storage and the flow dishcrage. In this model, the correct estimation of the parameters is necessary to achieve the proper precision. Previous studies indicated that there are five nonlinear corrected models which, with different optimization algorithms, tried to increase the prediction accuracy of output hydrographs. Due to the error in the output hydrograph of the previous models, in this study, a new structure of nonlinear Muskingum model was developed based on hybrid PSO and DSO algorithms. In this eight-parameter model (NL6 model), the improvement coefficient γ was used which held values less or more than one according to the number of peak discharges in the output hydrograph. By applying the proposed approach to the three types of input hydrographs and determining the optimal values of the parameters for the NL6 model, this research showed that the proposed model has a high accuracy in estimating the discharge values of the output hydrograph. The error reduction rate of the NL6 model based on SSQ and SAD indicators for multi-peak hydrographs were 53 and 35.6 percent compared to the last proposed model, respectively. So, this model have a high performance in estimating flood routing hydrograph.