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Improved ant colony optimization algorithms for continuous ... - CoDE

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64 Appendix<br />

Table 6.6: The mathematical <strong>for</strong>mulation <strong>for</strong> the coil spring design problem.<br />

f(x, T) = n i=1 Pi = ACi<br />

Thot<br />

Ti<br />

<br />

− 1<br />

⎛<br />

Ti+1<br />

⎝ Ti ∆xi<br />

kdT<br />

No Constraint<br />

∆xi ≥ 0, i = 1, ..., n + 1<br />

g1<br />

−<br />

T i<br />

T i−1 kdT<br />

∆xi−1<br />

g2<br />

g3<br />

Tcold ≤ T1 ≤ T2 ≤ ... ≤ Tn−1 ≤ Tn ≤ Thot<br />

n+1 i=1 ∆xi<br />

where<br />

= L<br />

C = 2.5 if T ≥ 71 K<br />

C = 4 if 71 K > T > 4.2 K<br />

C = 5 if T ≤ 4.2 K<br />

⎞<br />

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