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

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4.6 Application in Engineering Optimization Problems 49<br />

Table 4.9: Statistical results <strong>for</strong> pressure vessel design problem case D . The<br />

mean number of evaluations of the successful runs is given in parentheses.<br />

The infeasible solutions are highlighted in italics<br />

Methods fBest fMean fworst Sd F Es<br />

GA1 [17] 6288.7445 6293.8432 6308.1497 7.413E+00 N/A<br />

GA2 [19] 6059.9463 6177.2533 6469.3220 1.309E+02 80000<br />

(µ + λ)ES [66] 6059.7143 6379.938037 NA 2.10E+02 30000<br />

CPSO [45] 6061.0777 6147.1332 6363.8041 8.645E+01 200000<br />

HPSO [44] 6059.7143 6099.9323 6288.6770 8.620E+01 81000<br />

RSPSO [95] 6059.7143 6066.2032 6100.3196 1.33E+01 30000<br />

NM-PSO [98] 5930.3137 5946.7901 5960.0557 9.161E+00 80000<br />

PSOLVER [50] 6059.7143 6059.7143 6059.7143 4.625E-12 310<br />

ABC [5] 6059.7143 6245.3081 NA 2.05E+02 30000<br />

ACOMV 6059.7143 6059.7143 6059.7143 3.45E-12 30717<br />

(9448.08)<br />

Table 4.10: Results <strong>for</strong> the coil spring design problem. The mean number<br />

of evaluations of the successful runs is given in parentheses.<br />

[80] [16] [96] [54] [40] [20] ACOMV<br />

N 10 9 9 9 9 9 9<br />

D [inch] 1.180701 1.2287 1.227411 1.223041 1.223 1.223044 1.223041<br />

d [inch] 0.283 0.283 0.283 0.283 0.283 0.283 0.283<br />

fbest 2.7995 2.6709 2.6681 2.65856 2.659 2.658565 2.65856<br />

success rate 100% 95.4% 95.3% 95.0% -

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