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The parameters and required initial inputs of this section are the same as those of the previous section. Table 3 lists the values of and the corresponding calculated after 1,500,000 functional evaluations using the obtained decision variables in the formulation of for different values of . It follows from Table 3 that as the value of decreases the values of and decrease and increase, respectively, which means the reduction of improves the desirability of the two objective functions. According to Table 3, the reservoir system has unsatisfactory values for both objective functions when . The value of produces and that are approximately 5% and 30%, respectively. From Table 3, considering , the point (0.2917, 0.0494) is used as the left boundary of the OP which is calculated from the two-objective run. This point is the second point (as stated at the end of the previous sub-section) that is used for calculating the point entitled as in Figure 4.

Table 3

Values of and the corresponding for different values of in the single-objective three-reservoir system considering as the objective function

Objective functionRate
10.750.5
 0.5008 0.2880 0.0494 
 0.0083 0.2917 
Objective functionRate
10.750.5
 0.5008 0.2880 0.0494 
 0.0083 0.2917 

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