Differential evolution algorithm (DEA) is one featured kind of population based evolutionary algorithms. Although it is stated in previous studies that the algorithm is more sensitive to the crossover rate, it is tried out in this study whether DEA depends on mutation operation in which scaled differences of randomly chosen individuals existed in the population are used. Within this context, the presented study aims to carry out an empirical assessment regarding the comparison of DEA with the different mutation strategies for the calibration phase of a lumped water balance model. Both stable solution availabilities and convergence capabilities of DEA variants operated through five mutation approaches were performed on four parameter-Thorthwaite water balance model prepared for Gordes watershed. The findings derived from the model calibrations have recommended the usage of the fifth mutation strategy, which is not only convergent but also predominant in guaranteeing the achievement of stable solutions.

Keywords - Model Calibration, Differential Evolution Algorithm, Mutation Strategies, Gordes watershed

[1] Goswami, M., and O’Connor, K. M. 2007. Comparative assessment of six automatic optimization techniques for calibration of a conceptual rainfall-runoff model. Hydrological Sciences Journal, 52(3), 432-449. doi:10.1623/hysj.52.3.432
[2] Arsenault, R., Poulin, A., Côté, P., and Brissette, F. 2014. Comparison of stochastic optimization algorithms in hydrological model calibration. Journal of Hydrologic Engineering, 19(7), 1374–1384. doi: 10.1061/(asce)he.1943-5584.0000938
[3] Zhang, X., Srinivasan, R., Zhao, K., and Liew, M. V. 2009. Evaluation of global optimization algorithms for parameter calibration of a computationally intensive hydrologic model. Hydrological Processes,23(3), 430-441. doi:10.1002/hyp.7152
[4] Leon M., and Xiong N. 2014 Investigation of Mutation Strategies in Differential Evolution for Solving Global Optimization Problems. In: Rutkowski L., Korytkowski M., Scherer R., Tadeusiewicz R., Zadeh L.A., Zurada J.M. (eds) Artificial Intelligence and Soft Computing pp 372-383. ICAISC 2014. Lecture Notes in Computer Science, vol 8467. Springer, Cham
[5] Storn, R., and Price, K. 1997. Differential evolution - a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization, 11, 341–359.
[6] Kirdemir, U., Okkan, U. (2019). “Determining Dynamic Sensitivity of Differential Evolution Algorithm Parameters Employed for Hydrological Model Calibration”, IV. International Conference on Civil, Environmental, Geology, and Mining Engineering (ICOCEM’19), 20 – 22 April 2019, The Convention Center of DoubleTree Hilton Hotel in Trabzon-Turkey, pp.984-990.
[7] Xu, H., and Wen, J. (2012). Differential evolution algorithm for the optimization of the vehicle routing problem in logistics. In: Proc. 2012 Eighth International Conference on Computational Intelligence and Security (CIS), Guangzhou, China, pp. 48–51.
[8] Gong, W., and Cai, Z. (2013) Differential evolution with ranking-based mutation operators. IEEE Transactions on Cybernetics, 43(6), 2066 – 2081.
[9] Thornthwaite CW, Mather JR (1955) The water balance. Publications in climatology, vol 8. Laboratory of Climatology, Drexel Institute of Technology, Centerton, pp 1–104
[10] Okkan, U., and Kirdemir, U. (2016). Investigation of a dam reservoir behavior under climate change scenarios of IPCC-AR5, pp. 769-779. In Proceeding of 3rd International Scientific Meeting: State and Trends of Civil and Enviromental Engineering – EGTZ 2016, Editors: Adnan Ibrahimović and Damir Zenunović, 2– 4 June 2016, Bosnia, Tuzla.
[11] Okkan, U., ve Kırdemir, U. (2016) Bayes Model Ortalaması Yöntemiyle Farklı Hidrolojik Model Çıktılarının Değerlendirilmesi. DSİ Teknik Bülteni, 121, 41-57
[12] Refsgaard, J. C., and Knudsen, J. 1996. Operational validation and intercomparison of different types of hydrological models. Water Resources Research, 32(7), 2189–2202. doi: 10.1029/96wr00896.
[13] He, J., and Lin, G. 2016.Average convergence rate of evolutionary algorithms. IEEE Transactions on Evolutionary Computation, 20(2), 316-321. doi:10.1109/tevc.2015.2444793.