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In this study, four basic arithmetic operators (+, −, ×, /) and four basic mathematical functions (√, exp, sin, cos) were utilized as the GEP function set. Further, each GEP model was evolved till the fitness function remained unchanged for 10,000 runs for each pre-defined number of genes (varying from 3 to 4), then the program was stopped. The model parameters and the size of the developed GEP models were then tuned (optimized) throughout refining (optimizing) the trained and fixed model as a starter. Table 2 lists the combination of all genetic operators used in this study. Further details about GEP applications in hydraulic structures studies might be found in e.g. Roushangar et al. (2014a, 2014b).

Table 2

Parameters of GEP models used in this study

Description of parameterSetting of parameter
Function set +, −, *, /, √, Exp, sin, cos 
Chromosomes 30 
Head size 
Number of genes 3, 4 
Linking function Addition 
Fitness function error type RMSE 
Mutation rate 0.044 
Inversion rate 0.1 
One-point recombination rate 0.3 
Two-point recombination rate 0.3 
Gene recombination rate 0.1 
Gene transposition rate 0.1 
Description of parameterSetting of parameter
Function set +, −, *, /, √, Exp, sin, cos 
Chromosomes 30 
Head size 
Number of genes 3, 4 
Linking function Addition 
Fitness function error type RMSE 
Mutation rate 0.044 
Inversion rate 0.1 
One-point recombination rate 0.3 
Two-point recombination rate 0.3 
Gene recombination rate 0.1 
Gene transposition rate 0.1 

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