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


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.


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


Compliance with ethical standards

Conflict of Interest

The authors declare that they have no conflict of interest.


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© 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

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