Advertisement

Water Resources Management

, Volume 33, Issue 3, pp 905–921 | Cite as

Pareto Optimal Multigene Genetic Programming for Prediction of Longitudinal Dispersion Coefficient

  • Hossien Riahi-Madvar
  • Majid DehghaniEmail author
  • Akram Seifi
  • Vijay P. Singh
Article
  • 30 Downloads

Abstract

The longitudinal dispersion coefficient (Kx) is fundamental to modeling of pollutant and sediment transport in natural rivers, but a general expression for Kx, with applicability in low or high flow conditions, remains a challenge. The objective of this paper is to develop a Pareto-Optimal-Multigene Genetic Programming (POMGGP) equation for Kx by analyzing 503 data sets of channel geometry and flow conditions in natural streams worldwide. In order to acquire reliable data subsets for training and testing, Subset Selection of Maximum Dissimilarity Method (SSMD), rather than the classical trial and error method, was used by a random manipulation of these data sets. A new hybrid framework was developed that integrates SSMD with Multigene Genetic Programming (MGP) and Pareto-front optimization to produce a set of selected dimensionless equations of Kx and find the best equation with wide applicability. The POMGGP-based final equation was evaluated and compared with 8 published equations, using statistical indices, graphical visualization of 95% confidence ellipse, Taylor diagram, discrepancy ratio (DR) distribution, and scatter plots. Besides being simple and applicable to a broad range of conditions, the proposed equation predicted Kx more accurately than did the other equations and can therefore be used for the prediction of longitudinal dispersion coefficient in natural river flows.

Keywords

Multigene genetic programming Pareto-optimal model Maximum dissimilarity method Longitudinal dispersion coefficient Natural streams 

Notes

Compliance with ethical standards

Conflict of Interest

The authors declare that they have no conflict of interest.

References

  1. Alizadeh MJ, Shabani A, Kavianpour MR (2017) Predicting longitudinal dispersion coefficient using ANN with metaheuristic training algorithms. Int J Environ Sci Technol 14:2399CrossRefGoogle Scholar
  2. Ahmad Z (2013) Prediction of longitudinal dispersion coefficient using laborary and field data: relationship comparisons. Hydrol Res 44(2)Google Scholar
  3. Carr ML, Rehmann CR (2007) Measuring the dispersion coefficent with acoustic doppler current profilers. J HydraulEng-Asce 133(8):977–982CrossRefGoogle Scholar
  4. DanandehMehr AD, Kahya E (2017) A Pareto-optimal moving average multigene genetic programming model for daily streamflow prediction. J Hydrol 549:603–615CrossRefGoogle Scholar
  5. DanandehMehr AD, Nourani V (2017) A Pareto-optimal moving average-multigene genetic programming model for rainfall-runoff modelling. Environ Model Softw 92:239–251CrossRefGoogle Scholar
  6. Deng Z-Q, Singh VP, Bengtsson L (2001) Longitudinal dispersion coefficient in straight rivers. J Hydraul Eng 127:919–927CrossRefGoogle Scholar
  7. Elder JW (1959) The dispersion of a marked fluid in turbulent shear flow. J Fluid Mech 5(04):544–560CrossRefGoogle Scholar
  8. Fan FM, Fleischmann AS, Collischonn W, Ames DP, Rigo D (2015) Large-scale analytical water quality model coupled with GIS for simulation of point sourced pollutant discharges. Environ Model Softw 64:58–71CrossRefGoogle Scholar
  9. Fischer BH, (1975) Discussion of ‘‘simple method for predicting dispersion in streams,’’ by R.S. McQuivey and T.N. Keefer. J Environ Eng Div 101:453Google Scholar
  10. Fischer HB, List EJ, Koh RCY, Imberger J, Brooks NH (1979) Mixing in Inland and Coastal Waters. Academic, New YorkGoogle Scholar
  11. Gandomi AH, Alavi AH (2012a) A new multi-gene genetic programming approach to nonlinear system modeling. Part I: materials and structural engineering problems. Neural Comput & Applic 21(1):171–187CrossRefGoogle Scholar
  12. Gandomi AH, Alavi AH (2012b) A new multi-gene genetic programming approach to non-linear system modeling. Part II: geotechnical and earthquake engineering problems. Neural Comput & Applic 21(1):189–201CrossRefGoogle Scholar
  13. Hadgu LT, Nyadawa MO, Mwangi1 JK, Kibetu PM, Mehari BB (2014) Application of Water Quality Model QUAL2K to Model the Dispersion of Pollutants in River Ndarugu, Kenya. Computational Water, Energy, and Environmental Engineering 3:162–169Google Scholar
  14. Johnson RA, Wichern DW (2007) Multivariate analysis. Encyclopedia of Statistical Sciences, 8. [Chapter 4 (result 4.7 on page 163)Google Scholar
  15. Kashefipour MS, Falconer RA (2002) Longitudinal dispersion coefficients in natural channels. Water Res 36(6):1596–1608CrossRefGoogle Scholar
  16. Kennard RW, Stone LA (1969) Computer aided design of experiments. Technometrics 11(1):137–148CrossRefGoogle Scholar
  17. Koza JR (1992) Genetic programming: on the programming of computers by means of natural selection (Vol. 1). MIT pressGoogle Scholar
  18. Li X, Liu H, Yin M (2013) Differential evolution for prediction of longitudinal dispersion coefficients in natural streams. Water ResourManag 27:5245–5260Google Scholar
  19. Liu H (1977) Predicting dispersion coefficient of streams. J Environ Eng Div 103:59–69Google Scholar
  20. May RJ, Maier HR, Dandy GC, Fernando TG (2008) Non-linear variable selection for artificial neural networks using partial mutual information. Environ Model Softw 23(10):1312–1326CrossRefGoogle Scholar
  21. Moses SA, Janaki L, Joseph S, Joseph J (2016) Water quality prediction capabilities of WASP model for a tropical lake system. Lake and Reservoirs 20(4):285–299CrossRefGoogle Scholar
  22. Najafzadeh M, Tafarojnoruz A (2016) Evaluation of neuro-fuzzy GMDH-based particle swarm optimization to predict longitudinal dispersion coefficient in rivers. Environ Earth Sci 75(2):1–12CrossRefGoogle Scholar
  23. Noori R, Deng Z, Kiaghadi A, Kachoosangi FT (2016) How reliable are ANN, ANFIS, and SVM techniques forpredicting longitudinal dispersion coefficient in natural rivers? J Hydraul Eng 142:04015039CrossRefGoogle Scholar
  24. Noori R, Karbassi A, Farokhnia A, Dehghani M (2009) Predicting the longitudinal dispersion coefficient using support vector machine and adaptive neuro-fuzzy inference system techniques. Environ Eng Sci 26(10):1503–1510CrossRefGoogle Scholar
  25. Parveen N, Singh SK (2016) Application of Qual2e Model for River Water Quality Modelling. International Journal of Advance Research and Innovation 4(2):429–432Google Scholar
  26. Rajeev RS, Dutta S (2009) Prediction of longitudinal dispersion coefficients in natural rivers using genetic algorithm. Hydrol Res 40(6):544–552CrossRefGoogle Scholar
  27. Riahi-Madvar H, Ayyoubzadeh SA, Khadangi E, Ebadzadeh MM (2009) An expert system for predicting longitudinal dispersion coefficient in natural streams by using ANFIS. Expert Syst Appl 36(4):8589–8596CrossRefGoogle Scholar
  28. Sattar AM, Gharabaghi B (2015) Gene expression models for prediction of longitudinal dispersion coefficient in streams. J Hydrol 524:587–596CrossRefGoogle Scholar
  29. Searson DP (2015) GPTIPS 2: an open-source software platform for symbolic data mining. In: Handbook of genetic programming applications (pp. 551–573). Springer International PublishingGoogle Scholar
  30. Seo IW, Cheong TS (1998) Predicting longitudinal dispersion coefficient in natural streams. J Hydraul Eng 124:25CrossRefGoogle Scholar
  31. Tayfour G, Singh VP (2005) Predicting longitudinal dispersion coefficient in natural streams by artificial neural network. J Hydraul Eng 131(11):991–1000CrossRefGoogle Scholar
  32. Taylor KE (2001) Summarizing multiple aspects of model performance in a single diagram. J Geophys Res-Atmos 106(D7):7183–7192CrossRefGoogle Scholar
  33. Wang YF, Huai WX, Wang WJ (2017) Physically sound formula for longitudinal dispersion coefficients of natural rivers. J Hydrol 544:511–523CrossRefGoogle Scholar
  34. Wang Y, Huai W (2016) Estimating the longitudinal dispersion coefficient in straight natural rivers. J Hydraul Eng 142(11):04016048CrossRefGoogle Scholar
  35. Yapo PO, Gupta HV, Sorooshian S (1998) Multi-objective global optimization for hydrologic models. J Hydrol 204(1–4):83–97CrossRefGoogle Scholar
  36. Zhang T, Georgiopoulos M, Anagnostopoulos GC (2017) Pareto-optimal model selection via SPRINT-race. IEEE Transactions on CyberneticsGoogle Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of Water Engineering, Faculty of AgricultureVali-e-Asr University of RafsanjanRafsanjanIran
  2. 2.Technical and Engineering Department, Faculty of Civil EngineeringVali-e-Asr University of RafsanjanRafsanjanIran
  3. 3.Department of Biological and Agricultural Engineering and Zachry Department of Civil EngineeringTexas A&M UniversityCollege StationUSA

Personalised recommendations