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Note that the example SMD6 has been left out in the experiments as it is characterized by infinitely many optimums at the lower level for any given upper level design vector, of which only one corresponds to the best upper level value [29].
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In Table 2, we compare the upper level objective value obtained in this paper with that in the corresponding references.
Then we obtain the following result: the optimal solution is ((x^,y^)= 0,6)), the corresponding upper level objective value is (F_{0.6}^{I}=[24,54]).
It is noted that in [6], a Pareto optimal solution to Example 1 is ((x,y)= 0,0.5)^{T}), and the upper level objective value is (F x,y)=(1,-2)^{T}).
After solving the above problem by estimation of distribution algorithm at (gamma=0.7), we obtain its optimal solution ((x^,y^)=(12.4317,9.2434)) and the corresponding upper level objective value (F_{0.7}^{I}=[-9.2434,-4.6217]).
Step 3 Evaluate the fitness value defined by the upper level objective function value for each individual.
However, in this paper the Pareto optimal solution of Example 1 is ((x,y)= 0,0)^{T}) obtained by the weights algorithm, and the corresponding upper level objective function value is (F x,y)= 0,0)^{T}).
Further, Table 1 presents the accuracy achieved by the two algorithms for upper level objective function values, the theoretical optimum being equal to zero in all cases.
Notably, CHS-828 seems to show an upper level in LD50 values around 5-10 μM which is significantly lower than what is seen for APO866.
They also suggest that the upper level of the reference value for lactate in critically ill patients may require readjustment.
This indicates that the obtained interval value of the upper level objective function is superior to the interval goal.
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