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The results of the MOGA, MOFA, and MODFA are presented in Table 4, from which it follows that as the value of Rate decreases, the value of HV improves for each method. This means that the performance of the OP improves. The value of increases and worsens when Rate decreases. A key realization is that it is not proper to compare the performance of the algorithms only based on the values of Pareto performance criteria. The OP shown in Figure 7(c) dominates the other OPs, and the value of HV measures closeness and diversity, whereas only measures the spread of solutions. Therefore, it can be asserted that the performance of the MODFA in solving the multi-objective multi-reservoir problem is superior when Rate is equal to 0.5.

Table 4

The computed Pareto performance values for OPs obtained with MOGA, MOFA, and MODFA for different values of in the two-objective three-reservoir system operation problem

RatePareto performance criteriaAlgorithm
MOGAMOFAMODFA
 
 0.0007 0.0007 0.0007 
0.75  0.0332 0.0065 0.0381 
 0.0129 0.0023 0.0138 
0.5  0.0066 0.0127 0.0132 
 0.0140 0.0311 0.0145 
RatePareto performance criteriaAlgorithm
MOGAMOFAMODFA
 
 0.0007 0.0007 0.0007 
0.75  0.0332 0.0065 0.0381 
 0.0129 0.0023 0.0138 
0.5  0.0066 0.0127 0.0132 
 0.0140 0.0311 0.0145 

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