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Table 3 reports the best solution obtained by the SPSO-MODSIM model with a total number of function evaluations of 30,000 because of the dominance of the second stopping criterion. Due to stochastic nature of PSO algorithm, the results reported in this section (Tables 3 and 4) present the best solutions among 10 runs of the SPSO algorithm.

Table 3

Results of the SPSO-MODSIM model for the Atrak river basin problem

Optimized variablesOptimized values
Darband reservoir capacity (mcm) 
Garmab reservoir capacity (mcm) 
Ghordanlu reservoir capacity (mcm) 40 
Darband target storage level's priority number 
Garmab target storage level's priority number 
Ghordanlu target storage level's priority number 10 
Objective function 137,837 
Optimized variablesOptimized values
Darband reservoir capacity (mcm) 
Garmab reservoir capacity (mcm) 
Ghordanlu reservoir capacity (mcm) 40 
Darband target storage level's priority number 
Garmab target storage level's priority number 
Ghordanlu target storage level's priority number 10 
Objective function 137,837 
Table 4

Comparative analysis of different meta-models employed in the ASSF approach for solving the Atrak river basin water allocation problem

MethodSPSO-MODSIMSPSO-MODSIM ∼ ANNSPSO-MODSIM ∼ SVMSPSO-MODSIM ∼ KRIGINGSPSO-MODSIM ∼ POLYNOMIAL
Approximate best obj. func. value – 137,844 137,830 137,836 137,577 
Original obj. func. value 137,837 137,837 137,837 137,837 137,837 
MSE – −5.08 × 10−5 5.37 × 10−5 1.05 × 10−5 0.00188 
Number of original obj. function evaluations 30,000 482 477 1,500 1,667 
Darband reservoir capacity (mcm) 
Garmab reservoir capacity (mcm) 
Gordanlu reservoir capacity (mcm) 40 40 40 40 40 
Darband target storage level's priority number 
Garmab target storage level's priority number 
Ghordanlu target storage level's priority number 10 
MethodSPSO-MODSIMSPSO-MODSIM ∼ ANNSPSO-MODSIM ∼ SVMSPSO-MODSIM ∼ KRIGINGSPSO-MODSIM ∼ POLYNOMIAL
Approximate best obj. func. value – 137,844 137,830 137,836 137,577 
Original obj. func. value 137,837 137,837 137,837 137,837 137,837 
MSE – −5.08 × 10−5 5.37 × 10−5 1.05 × 10−5 0.00188 
Number of original obj. function evaluations 30,000 482 477 1,500 1,667 
Darband reservoir capacity (mcm) 
Garmab reservoir capacity (mcm) 
Gordanlu reservoir capacity (mcm) 40 40 40 40 40 
Darband target storage level's priority number 
Garmab target storage level's priority number 
Ghordanlu target storage level's priority number 10 

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