Comparison of the efficiency of gray wolf optimizer and imperialist competitive algorithms in an optimal allocation of water in irrigation and drainage networks (case study: Sofi-Chay network)

Document Type : Original Article


1 Water Engineering Department, Agriculture Faculty, University of Zanjan, Zanjan, Iran

2 Department of Hydraulic Structures, Agriculture Faculty, Shahid Chamran University, Ahvaz, Iran


Water scarcity is one of the most important issues in the 21st century that human societies encounter. Population growth, industrial and agricultural production, rapid urbanization, and severe climate change have had a major impact on limited water resources and the environment in river basins. The optimal allocation of water resources among consumers requires effective measurements of water resources and its integrated management for human and environmental justice. Optimization of water resource allocation is a very complex decision to make in several levels, stages, subjects, objectives, and non-linear communications. With the complexity of water allocation issues, its algorithms have been gradually improved, and the use of intelligent meta-analysis algorithms in optimizing the allocation of water resources from traditional math planning has surpassed. However, the effectiveness of conventional optimization algorithms is not ideal from a variety of perspectives, and issues such as convergence, computational speed, initial sensitivity, etc., due to the complexity and multi-purpose of optimizing water allocation, require further studies to improve the efficiency of the algorithm and obtaining a desirable overall solution.
Material and methods:
The gray wolf algorithm mimics the hierarchy of leadership and the mechanism of hunting gray wolves in nature. In this algorithm, four types of gray wolves, including alpha, beta, delta, and omega have been used to simulate a hierarchy of leadership. Also, the colonial competition algorithm begins with some primary random populations, each of which is called a "country". Some of the best population elements (equivalent to the elites in the genetic algorithm) are chosen as imperialists. The remaining population is considered as a colony. Colonialists, depending on their power, are pulling these colonies into a particular process. In this research, the gray wolf and colonial competition algorithms were used to optimize water resources values during 2000-2012 regarding the Sofi-Chay irrigation and drainage network and Alavian dam to achieve the optimal policy. The Alavian dam in the province of East Azerbaijan, 3km north of Maragheh city, near the village of Alavian, has been constructed on the Sofi-Chai River, and supplies drinking water to the Maragheh, Miandoab, Bonab, Ajbashir, and Malekan counties.
Results and discussion:
The results of the implementation of the gray wolf algorithm, compared to the colonial competition algorithm, were very close to the measured value of the amount of allocated water and this suggests the coherence and efficiency of the gray wolf algorithm in water resources system. According to the RMSE values in all four areas, the gray wolf algorithm was 44% less than the colonial competition algorithm and 64% higher in the Nash-Sutcliff coefficient.
The results of this study showed that the gray wolf algorithm has a suitable speed for finding the optimal response. In other words, it has a high convergence rate and can find an optimal global optimization problem. The results showed that the gray wolf algorithm yielded better and more acceptable results in water utilization in combination with utilizing surface water and underground water resources.


  1. Abdulbaki, D., Al-Hindi, M., Yassine, A. and Najm, M.A., 2017. An optimization model for the allocation of water resources. Journal of Cleaner Production. 164, 994-1006.
  2. Abed-Elmdoust, A. and Kerachian, R., 2012. Water Resources allocation using a cooperative game with Fuzzy Payoffs and Fuzzy Coalitions. Water Resources Management. 26(13), 3961-3976.
  3. Anvari, S., Mousavi, S.J. and Morid, S., 2014. Sampling/stochastic dynamic programming for optimal operation of multi-purpose reservoirs using artificial neural network-based ensemble stream flow predictions. Journal of Hydro informatics. 16(4), 907-921.
  4. Atashpaz-Gargari, E. and Lucas, C., 2007a. Imperialist Competitive Algorithm: An algorithm for optimization inspired by imperialistic competition, IEEE Congress on Evolutionary Computation, 25-28 Sept. 2007, Singapore, 4661–4667.
  5. Atashpaz Gargari, E., Hashemzadeh, F., Rajabioun, R. and Lucas, C., 2008. Colonial competitive algorithm: a novel approach for PID controller design in MIMOdistillation column process. International Journal of Intelligent Computing and Cybernetics (IJICC). 1(3), 337–355.
  6. Bozorg-Haddad, O., Karimirad, I., Seifollahi-Aghmiuni, S. and Loaiciga, H.A., 2014. Development and application of the Bat Algorithm for optimizing the operation of reservoir systems. Journal of Water Resources Planning and Management. 141(8), 1947-1957.
  7. Connor, W. and Paulin, C., 2017. Hydrometric network design using dual entropy multi-objective optimization in the Ottawa River Basin. Hydrology Research. 48(6), 1639-1651.
  8. Dalin, C., Qiu, H., Hanasaki, N., Mauzerall, D.L. and Rodriguez-Iturbe, I., 2015. Balancing water resource conservation and food security in China. PNAS. 112(15), 4588.
  9. Davijani, M.H., Banihabib, M.E., Anvar, A.N. and Hashemi, S.R., 2016a. Optimization model for the allocation of water resources based on the maximization of employment in the agriculture and industry sectors. Journal of Hydrology. 533(1), 430-438.
  10. Davijani, M.H., Banihabib, M.E., Anvar, A.N. and Hashemi, S.R., 2016b. Multi-Objective optimization model for the allocation of water resources in arid regions based on the maximization of socioeconomic efficiency. Water Resources Management. 30(3), 1-20.
  11. Eliasson, J., 2015.The rising pressure of global water shortages. Nature. 517, 6 (01 January 2015).
  12. Gaur, S., Ch, S., Graillot, D., Chahar, B.R. and Kumar, D.N., 2013. Application of artificial neural networks and particle Swarm Optimization for the management of groundwater resources. Water Resources Management. 27(3), 927-941.
  13. Georgakakos, K.P., 2012. Water supply and demand sensitivities of linear programming solutions to a water allocation problem. Applied Mathematics. 3(10), 1285-1297.
  14. Girard, C., Rinaudo, J. and Pulido-Velazquez, M., 2016. Sharing the cost of a river basin adaptation portfolios to climate change: Insights from social justice and cooperative game theory. Water Resources Research. 52(10), 7945–7962.
  15. Grizzetti, B., Pistocchi, A., Liquete, C., Udias, A., Bouraoui, F. and van de Bund, W., 2017. Human pressures and ecological status of European rivers. Scientific Reports. 7(1), 205.
  16. Haddeland, I., Heinke, J., Biemans, H., Eisner, S., Flörke, M., Hanasaki, N., Konzmann, M., Ludwig, F., Masaki, Y., Schewe, J., Stacke, T., Tessler, Z.D., Wada, Y. and Wisser, D., 2014. Global water resources affected by human interventions and climate change. PNAS, 111(9), 3251-3256.
  17. Hassan-Esfahani, L., Torres-Rua, A. and Mckee, M., 2015. Assessment of optimal irrigation water allocation for pressurized irrigation system using water balance approach, learning machines, and remotely sensed data. Agricultural Water Management. 153, 42-50.
  18. He, L.X. and He, S.H., 2015. Solving water resource scheduling problem through an improved artificial Fish Swarm Algorithm. International Journal of Simulation Modelling. 14(1), 170-181.
  19. He, L., Shen, J. and Zhang, Y., 2017. Ecological vulnerability assessment for ecological conservation and environmental management. Journal of Environmental Management. 206, 1115-1125.
  20. Jafarzadegan, K., Abed-Elmdoust, A. and Kerachian, R., 2013. A fuzzy variable least core game for Inter-basin water resources allocation under uncertainty. Water Resources Management. 27(9), 3247-3260.
  21. Karamouz, M., Nazif, S., Sherafat, M.A. and Zahmatkesh, Z., 2014. Development of an optimal reservoir operation scheme using extended evolutionary computing algorithms based on conflict resolution approach: a case study. Water Resources Management. 28(11), 3539-3554.
  22. Larsen, T.A., Hoffmann, S., Lüthi, C., Truffer, B. and Maurer, M., 2016. Emerging solutions to the water challenges of an urbanizing world. Science. 352(6288), 928.
  23. Li, M., Fu, Q., Singh, V.P., Ma, M. and Liu, X., 2017. An intuitionistic fuzzy multi-objective non-linear programming model for sustainable irrigation water allocation under the combination of dry and wet conditions. Journal of Hydrology. 555, 80-94.
  24. Lu, H.W., Ren, L.X., Chen, Y.Z., Tian, P.P. and Liu, J., 2017. A cloud model based multi-attribute decision making approach for selection and evaluation of groundwater management schemes. Journal of Hydrology. 555, 881-893.
  25. Mansouri, R., Torabi, H. and Morshedzadeh, H., 2015. Optimization of the water distribution networks with Differential Evolution (DE) and Mixed Integer Linear Programming (MILP). Journal of Water Resource & Protection. 7(9), 715-729.
  26. Marques, G.F., Lund, J.R. and Howitt, R.E., 2010. Modeling conjunctive use operations and farm decisions with two-stage stochastic quadratic programming. Journal of Water Resources Planning & Management. 136(3), 386-394.
  27. Mianabadi, H., Mostert, E., Zarghami, M. and Giesen, N.V.D., 2014. A new bankruptcy method for conflict resolution in water resources allocation. Journal of Environmental Management. 144(144), 152-159.
  28. Miguel, L.F.F., Miguel, L.F.F. and Lopez, R.H., 2014. A firefly algorithm for the design of force and placement of friction dampers for control of man-induced vibrations in footbridges. Optimization & Engineering. 16(3), 633-661.
  29. Mirjalili, S., Mirjalili, S.M. and Lewis, A., 2014. Grey Wolf Optimizer. Advances in Engineering Software. 69, 46-61.
  30. Mosleh, Z., Salehi, M.H., Fasakhodi, A.A., Jafari, A., Mehnatkesh, A. and Borujeni, I.E., 2017. Sustainable allocation of agricultural lands and water resources using suitability analysis and mathematical multi-objective programming. Geoderma. 303, 52-59.
  31. Nicklow, J., Reed, P., Savic, D., Dessalegne, T., Harrell, L., Chan-Hilton, A., Karamouz, M., Minsker, B., Ostfeld, A., Singh, A. and Zechman, E., 2010. State of the art for Genetic Algorithms and beyond in water resources planning and management. Journal of Water Resources Planning & Management. 136(4), 412-432.
  32. Niknam, T., Narimani, M.R., Jabbari, M. and Malekpour, A.R., 2011. A modified shuffle frog leaping algorithm for multi-objective optimal power flow. Energy. 36(11), 6420-6432.
  33. Nikoo, M.R., Kerachian, R., Karimi, A. and Azadmia, A.A., 2013. Optimal water and waste-load allocations in rivers using a fuzzy transformation technique: a case study. Environmental Monitoring and Assessment. 185(3), 2483-2502.
  34. Perez, C.J., Vega-Rodriguez, M.A., Reder, K. and Flörke, M., 2017. A multi-objective artificial bee colony-based optimization approach to design water quality monitoring networks in river basins. Journal of Cleaner Production. 166, 579-589.
  35. Ryu, J.H., Contor, B., Johnson, G., Allen, R. and Tracy, J., 2012. System dynamics to sustainable water resources management in the eastern snake plain aquifer under water supply uncertainty. Journal of the American Water Resources Association. 48(6), 1204-1220.
  36. Singh, A., 2014. Simulation–optimization modeling for conjunctive water use management. Agricultural Water Management. 141, 23-29.
  37. Sivakumar, B., 2000. Chaos theory in hydrology: important issues and interpretations. Journal of Hydrology. 227(1), 1-20.
  38. Szemis, J.M., Dandy, G.C. and Maier, H.R., 2013. A multi-objective ant colony optimization approach for scheduling environmental flow management alternatives with application to the River Murray, Australia. Water Resources Research. 49(10), 6393–6411.
  39. Vaghefi, S.A., Mousavi, S.J., Abbaspour, K.C., Srinivasan, R. and Arnold, J.R., 2015. Integration of hydrologic and water allocation models in basin-scale water resources management considering crop pattern and climate change: Karkheh River Basin in Iran. Regional Environmental Change. 15(3), 475-484.
  40. Yu, S. and Wang, M.Y., 2014. Comprehensive evaluation of scenario schemes for Multi-objective decision-making in river ecological restoration by artificially recharging river. Water Resources Management. 28(15), 5555-5571.