عنوان مقاله [English]
Introduction: Flood is a natural phenomenon that can cause numerous financial and life casualties in civil, industrial, and agricultural areas. Therefore, knowing its characteristics such as its peak during a period and in different places of the river is of the utmost importance. In general, forecasting these characteristics and changes in depth and flow in the river could be done using the flood routing methods. Flood routing is one of the most important issues in water engineering projects. Hydrologic routing is common particularly in braided rivers and rivers with the lack of mid-basin data. To do that, there is a need to perform cross-sections and determine the river slope in every region. The Muskingum method is frequently used to route floods in the hydrology literature. The implementation of metaheuristic algorithm methods has shown satisfactory results in this regard. Therefore, in this study, we evaluated the efficiency of the Symbiotic Organisms Search (SOS) in estimating the optimal parameter estimation of the Non-linear Muskingum model.
Materials and Methods: This study evaluated the performance of Symbiotic Organisms Search (SOS) algorithm in estimating the optimum parameters of the Muskingum Non-linear model. To investigate the research’s findings desirability, the results of the Symbiotic Organisms Search (SOS) were compared to the results of otherMeta-Heuristic methods including the Genetic Algorithm (GA), the Particle Swarm Optimization (PSO), and the Imperialist Competitive Algorithm (ICA). Meta-heuristics sample is a set of solutions which are too large to be completely sampled. Meta-heuristics may make few assumptions about the optimization problem being solved, and they may, therefore, be usable for a variety of problems. SOS algorithm simulates the interactions between two species in a way that one species seeks to find the most suitable. SOS algorithm starts with an initial population called ecosystem. In the early stages of ecosystem, a group of organisms (decision variable) are randomly generated in the search space. Each organism is a candidate for a solution that corresponds to a certain degree of fit, representing the degree of conformity with the intended purpose (amount of objective function). This algorithm uses a new solution by mimicking the biological interaction between the two species in the ecosystem. Three distinct phases (cross-use), commensalism, and parasitic, similar to the biological interaction model in the real world, are introduced. Each interaction is defined based on the type of interaction. In this way, the two-way profit represents the cooperation phase, the one-way profit represents the commensalism phase, and the one-way profit and the other side losses represent the parasitic phase. In all phases, each is being interacted randomly with the other. This process continues until the process is completed (reaching the maximum number of iterations). In this research, the Kardeh River in Khorasan Razavi province was chosen as a real instance and Wilson River as a previous instance (1974), to investigate the performance of algorithms used in the non-linear Muskingum equation in the flood routing model. In this study, minimizing the sum of squares (SSQ) between the volume of real and routed outputs was considered as an objective function to evaluate the optimum parameters of K, X, and m in the non-linear Muskingum equation. The obtained optimum parameters from algorithms for both rivers showed that the SOS, PSO, and ICA algorithms could approximate the SSQ to optimal value and all meta-heuristic algorithms could route the output flood as well.
Results and Discussion: The SSQ algorithm results for the rivers showed the minimization of the sum of squares (SSQ) which MSE was equal to 5.85 and SSQ was equal to 128.78 for the Wilson River, and MSE was equal to 0.505 and SSQ was equal to 4.55 and had better functionality than the GA algorithms same as the PSO and ICA algorithms. The meta-Heuristic methods were from solutions which succeeded to estimate these parameters. In this study, the novel Symbiotic Organisms Search (SOS) was used to estimate the non-linear Muskingum model parameters. The observational data of two river studies of Kardeh and Wilson Rivers were employed. The results of SOS implementation were compared to other meta-heuristic algorithms such as GA, PSO, and ICA to investigate the SOS functionality. In this research, firstly, the experimental example used by the researchers was investigated to survey the optimum Non-linear Muskingum flood routing model parameters. The results showed the SOS precise estimation was comparable to the previous methods. According to the results, the SSQ was improved by using the objective functions as compared to the other reported algorithms at a rate of 7% in GA, and 0.004% in ICA. In the second experimental river, which is a real flood routing, estimated statistical parameters for the Kardeh River were 0.5059 for MSE and 4.5528 for SSQ in the SOS algorithm. This shows that the appropriate functionality of the Symbiotic Organisms Search algorithm in estimating the optimum Non-linear Muskingum flood routing model parameters. Finally, this research work highlights the SOS ability to optimize the Muskingum model parameters.
Conclusion: In the SSQ flood stream, SOS showed good performance, such as the PSO and ICA algorithms. In this regard, SOS was 13% better than the GA in the objective function SSQ and MSE, and improved the objective function SSQ and MSE by 0.002 and 4%, respectively, in respect to the PSO and ICA. This denotes the appropriate functionality of the Symbiotic Organisms Search algorithm in estimating the optimum non-linear Muskingum flood routing model parameters. The findings indicate the SOS ability to optimize the Muskingum model parameters. Therefore, using the SOS in flood routing with the Muskingum model is recommendable.