کاربست مقایسه‌ای الگوریتم جستجوی موجودات همزیست با الگوریتم‌های فراکاوشی در مدل روندیابی سیلاب

نوع مقاله : مقالات پژوهشی

نویسندگان

دانشگاه فردوسی مشهد

چکیده

روندیابی سیلاب یکی از الزامات مهم در مطالعات مهندسی رودخانه محسوب می­شود. روندیابی هیدرولوژیکی در رودخانه­های شریانی و رودخانه‌های فاقد آمار حوضه میانی متداول است. به این منظور نیاز به تهیه مقاطع عرضی و تعیین شیب­ها در کلیه بازه­های رودخانه می­باشد. روش ماسکینگام می تواند با استفاده از آن ضمن صرفه­جویی در زمان و هزینه، اطلاعات مربوط به عمق و دبی جریان سیلابی را در هر زمان مشخص نماید. کاربست روش­های فراکاوشی نتایج رضایت بخشی را در این زمینه تاکنون نشان داده است. از این رو در این پژوهش، به ارزیابی کارایی الگوریتم جستجوی موجودات همزیست (SOS) در تخمین پارامترهای بهینه مدل غیرخطی ماسکینگام پرداخته شد. به­منظور بررسی میزان مطلوبیت یافته­های پژوهش، نتایج حاصل از الگوریتم موجودات همزیست (SOS)، با نتایج سایر روش های فراکاوشی شامل الگوریتم وراثتی (GA)، الگوریتم ازدحام ذرات (PSO)، الگوریتم رقابت استعماری (ICA) مقایسه گردید. در الگوریتم پیشنهادی، روش تابع جریمه غیرمستقیم در مدل برای جلوگیری از منفی شدن خروجی و ذخیره اعمال شده است. الگوریتم مذکور بهینه سراسری یا نزدیک سراسری را بدون در نظر گرفتن مقادیر اولیه پارامترها با همگرایی سریع پیدا می‌کند. نتایج الگوریتم SOS برای دو رودخانه ویلسون و کارده نشان دهنده کمینه‌سازی مجموع مربعات باقیمانده‌ها (SSQ) می­باشد که برای رودخانه ویلسون با MSE (85/5) و SSQ (78/128) و رودخانه کارده با MSE (505/0) و SSQ (552/4) می باشد و مانند الگوریتم‌های PSO و ICA عملکرد بهتری نسبت به الگوریتم‌ GA داشته است در نتیجه الگوریتم پیشنهادی می‌تواند با اطمینان خوبی به­منظور برآورد مقادیر بهینه پارامترهای مدل ماسکینگام غیر خطی مورد استفاده قرار گیرد.

کلیدواژه‌ها


عنوان مقاله [English]

Comparison of the Symbiotic Organisms Search Algorithm with Meta-Heuristic Algorithms in Flood Routing Model

نویسندگان [English]

  • S. Khalife
  • S.A. Esmaili
  • K. Esmaili
  • S.R. Khodashenas
Ferdowsi University of Mashhad
چکیده [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.

کلیدواژه‌ها [English]

  • Braided rivers
  • Hydrologic routing
  • Metaheuristic
  • Meta-Heuristic
  • Muskingum model
  • Optimization
1- Akbari G., and Barati R., and Fadafan M. 2010. Present of a New Algorithm for Parameter Estimation of Nonlinear Muskingum Model. 9th Iranian Hydraulic Conference, Iranian Hydraulic Society, 9-11 Nov. 2010- Iranian Hydraulic Society. Tarbiat Modarres University, Tehran, Iran. (In persian with English abstract)
2- Akbarifard S., Madadi M.R., and Aliannejad M. 2017. Parameters Estimation of the Nonlinear Muskingum Flood-Routing Model Using Wolf Search Algorithm (WSA) (Case Study: Kardeh River). Irrigation and Drainage Structures Engineering Research 17(67): 95-112. (In Persian with English abstract)
3- Bazargan J., and Norouzi H. 2018. Investigation the effect of using variable values for the parameters of the linear Muskingum method using the particle swarm algorithm (PSO). Water Resources Management 32(14): 4763-4777. (In persian with English abstract)
4- Chen J., and Yang X. 2007. Optimal parameter estimation for Muskingum model based on Gray-encoded accelerating genetic algorithm. Communications in Nonlinear Science and Numerical Simulation 12(5): 849-858.
5- Cheng M.Y., and Prayogo D. 2014. Symbiotic Organisms Search: A new metaheuristic optimization algorithm.Computers & Structures 139: 98-112.
6- Choudhury P., Shrivastava R.K., and Narulkar S.M. 2002. Flood Routing in River Networks Using Equivalent Muskingum Inflow. Journal of Hydrologic Engineering 7(6): 413-419.
7- Chow V.T. 2009. Open Channel Hydraulic.The Blackburn Press.
8- Chu H.J., and Chang L.C. 2009. Applying Particle Swarm Optimization to Parameter Estimation of the Nonlinear Muskingum Model. Journal of Hydrologic Engineering 14(9): 1024-1027.
9- Das A. 2004. Parameter Estimation for Muskingum Models. Journal of Irrigation and Drainage Engineering 130(2): 140-147.
10- Ehteram M., Binti Othman F., Mundher Yaseen Z., Abdulmohsin Afan H., Falah Allawi M., Najah Ahmed Al., Shahid Sh., P.Singh V., and El-Shafie A. 2018. Improving the Muskingum flood routing method using a hybrid of particle swarm optimization and bat algorithm.Water 10(6): 807.
11- Farzin S., Singh V., Karami H., Farahani N., Ehteram M., Kisi O., Allawi M-F., Mohd N-S., and El-Shafie A. 2018. Flood routing in river reaches using a three-parameter Muskingum model coupled with an improved bat algorithm.Water 10(9): 1130.
12- Ghaleni M., Bozorg Hadad O., and Ebrahimi K. 2010. Parameter Estimation of the Nonlinear Muskingum Model Using Simulated Annealing. Journal of Water and Soil 24(5): 908-919. (In Persian)
13- Gill M.A. 1978. Flood routing by the Muskingum method.Journal of hydrology 36(3-4):353-363.
14- Hamedi F., Bozorg Hadad O., and Vatan khah A. 2014. Improve nonlinear Muskingum model by a new combinatorial storage equation. 5th National Conference on Water Resources Management 29-1 Feb 2014,.Shahid Beheshti University-Iranian Association of Water Resources Science and Engineering.Tehran - Iran. (In persian with English abstract)
15- Karahan H., Gurarslan G., and Geem Z.W. 2013. Parameter Estimation of the Nonlinear Muskingum Flood Routing Model Using a Hybrid Harmony Search Algorithm. Journal of Hydrologic Engineering 18(3): 352-360.
16- Khalifeh S., Esmaili K., Khodashenas S., and Akbarifard S. 2020. Data on Optimization of the Non-linear Muskingum Flood Routing in Kardeh River Using GOA Algorithm. Journal of Data in Brief. Volume 30, https://doi.org/10.1016/j.dib.2020.105398.
17- Kim J.H., Geem Z.W., and Kim E.S. 2001. Parameter estimation of the nonlinear muskingum model using harmony search 1. JAWRA Journal of the American Water Resources Association 37(5): 1131-1138.
18- Mohan S. 1997. Parameter Estimation of Nonlinear Muskingum Models Using Genetic Algorithm. Journal of Hydraulic Engineering 123(2): 137-142.
19- Perumal M.E., and Raju K.G.R. 2001. Field Applications of a Variable-Parameter Muskingum Method. Journal of Hydrologic Engineering 6(3): 196-207.
20- Perumal M., and Raju K.G.R. 1998. Variable-Parameter Stage-Hydrograph Routing Method. II: Evaluation. Journal of Hydrologic Engineering 3(2): 115-121.
21- Saghi H., Delbari A. 2013. Investigation performance linear and nonlinear models for routing focus Muskingum flood. 15th Fluid Dynamic, Iranian Physics Society.17-19 Dec. 2013. Bandar Abbas. Iran. (In Persian with English abstract)
22- Samani H.M., and Shamsipour G. 2004. Hydrologic flood routing in branched river systems via nonlinear optimization. Journal of Hydraulic Research 42(1): 55-59.
23- Singh V.P., and Scarlatos P.D. 1987. Analysis of nonlinear Muskingum flood routing. Journal of Hydraulic Engineering 113(1): 61-79.
24- Tung Y.K. 1985. River flood routing by nonlinear Muskingum method. Journal of Hydraulic Engineering 111(12): 1447-1460.
25- Wilson E.M. 1974. Engineering hydrology, MacMillan Education, Hampshire, United Kingdom.
26- Khalife S., Barani Gh., Khalifeh V., and Zonnemat Kermani M. 2019. Optimization of water distribution Systems using genetic algorithms in WaterGems model (Case study: part of Rooydar). Journal of Ferdowsi Civil Engineering 32(3): 111-124. (In Persian with English abstract)