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Table 5 lists the results for three selected points (solutions) of the obtained OPs illustrated in Figure 7 for a better comparison of the performances of the MOGA, MOFA, and MODFA. The selected points are the first point (from left to right), a middle point (specified with a thick bordered rectangle in Figure 7), and the last point (from left to right) of each OP. According to Table 5, the number of OPs' points increases for all methods as the value of Rate decreases. Moreover, the MODFA solutions are better that those of MOGA and MOFA for each value of Rate. Also, it can be concluded that the values of and associated with the three selected points become more favorable for MODFA when . In fact, in this case, the distinct number of OPs' points of MODFA is seven (more that in the OPs of MOGA and MOFA), and, also, the range between the first and the last point of the MODFA's OP is larger than those of the OPs of MOGA and MOFA when .

Table 5

OPs' points obtained with MOGA, MOFA, and MODFA for different values of in the two-objective three-reservoir system operation problem

CharacteristicsNumber of OP pointsThe first point
The middle point
The last point
Number of distinct solution
Model  
MOGA 0.5012 Do not exists 0.0083 0.5828 
MOFA 0.5012 Do not exists 0.0083 0.5828 
MODFA 0.5012 Do not exists 0.0083 0.5828 
MOGA 0.75 0.0250 0.4177 0.0500 04345 0.0750 0.6047 
MOFA 0.0417 0.3602 0.0667 0.3775 0.0833 0.3924 
MODFA 0.0833 0.2887 0.1000 0.4140 0.1167 0.4532 
MOGA 0.5 0.4417 0.1761 0.4750 0.1842 0.5000 0.2049 
MOFA 0.5167 0.1086 0.5586 0.1219 0.5833 0.1631 
MODFA 0.5333 0.0501 0.5917 0.0559 0.6417 0.0733 
CharacteristicsNumber of OP pointsThe first point
The middle point
The last point
Number of distinct solution
Model  
MOGA 0.5012 Do not exists 0.0083 0.5828 
MOFA 0.5012 Do not exists 0.0083 0.5828 
MODFA 0.5012 Do not exists 0.0083 0.5828 
MOGA 0.75 0.0250 0.4177 0.0500 04345 0.0750 0.6047 
MOFA 0.0417 0.3602 0.0667 0.3775 0.0833 0.3924 
MODFA 0.0833 0.2887 0.1000 0.4140 0.1167 0.4532 
MOGA 0.5 0.4417 0.1761 0.4750 0.1842 0.5000 0.2049 
MOFA 0.5167 0.1086 0.5586 0.1219 0.5833 0.1631 
MODFA 0.5333 0.0501 0.5917 0.0559 0.6417 0.0733 

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