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Open image in new window Figure 4 Convergent curves of numerical example obtained by our previous algorithm.
Open image in new window Figure 8 Convergent curves of the upper beam's mechanical performance indices obtained by our previous algorithm.
The constrained interval robust optimization model in Eq. (13) is also solved by our previous algorithm [27] with the GA parameters and convergent threshold settled the same as those in the proposed algorithm.
That is, the optimal solution x* obtained by our previous algorithm is not a robust one as far as the constraints are concerned while the optimal solution xo obtained by the proposed algorithm is.
The robust optimization model in Eq. (12) is also solved by our previous algorithm [27] with the GA parameters and convergent threshold prescribed the same as those in the proposed one.
But the 1st constraint function (g_{1} left( {{varvec{x}},{varvec{U}}} right) ge [8.0,10.0]) may be violated at the optimal solution ({varvec{x}}^ = left( {3.11,0.20,2.08} right)) obtained by our previous algorithm while it is always satisfied at the optimal solution ({varvec{x}}^{text{o}} = left( {3.17,0.02,2.00} right)) obtained by the proposed algorithm.
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Table 5 compares the optimization results obtained by the proposed and our previous algorithm [27], which shows that the 2nd constraint function (delta (varvec{x},varvec{U}) le [45,46]{text{ MPa}}) is fully satisfied at both optimal solutions.
Our current approach was to extend our previous algorithm.
We use HORN-4 as an attached processor to enhance the performance of a general-purpose computer when it is used to generate holograms using a "recurrence formulas" algorithm developed by our previous paper.
Here we argue that the earlier calculations were misleading due to uncontrolled autocorrelation times encountered by the previous algorithm.
Since the Markov chain has a stationary distribution Π, a migration rate λ SU j, i exist and can be estimated by the previous Algorithm.
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