Parameters Optimization using Fuzzy Rule Based Multi-Objective Genetic Algorithm for an Event Based Rainfall-Runoff Model

The calibration of an event based rainfall-runoff model for steam flow forecasting is challenging because, it is difficult to measure the parameters physically on the field for each rainfall event. In the present study, Fuzzy rule based Multi-objective Genetic Algorithm (MGA) is developed to optimize the infiltration and roughness parameters of an event based rainfall-runoff model. Nash Sutcliffe Efficiency (NSE), Coefficient of Determination (R²) and transformed volume difference (f(V)) are used as the objective functions of the MGA and all Pareto optimal solutions are identified using Nondominated Sorting method. As three objective functions are included in the calibration, the number of Pareto optimal solutions are also increases and hence, the optimization problem now becomes a decision making problem. Therefore, to select the best solution from all Pareto optimal solutions, a Fuzzy Rule-Based Model (FRBM) is developed to get alternative values of each Pareto optimal solution. First, the Fuzzy rule based MGA is developed by integrating the FRBM with the MGA. Then the Fuzzy rule based MGA is integrated with an event based runoff model. The developed Fuzzy-MGA based runoff model is tested on three different watersheds and the simulation results of Fuzzy-MGA based runoff model are compared with observed data and previous study results. From the simulated events of three watersheds using Fuzzy-MGA based runoff model, it is observed that the mean percentage error in any criteria (i.e. volume of runoff, peak runoff, and time to peak) of the developed model for a watershed is less than 16.33%. It is also noted that the developed Fuzzy-MGA based runoff model is able to produce hydrographs that are much closer to the measured hydrographs.