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Table 1 Comparison of optimization performance for benchmark functions

From: Improved fruit fly algorithm on structural optimization

FunctionDimensionAlgorithmOptimal valueAverage valueStandard deviationRunning time/s
\( f_{1} \)30IA37.154361.369833.16595.5329
PSO16.599834.672929.52673.9532
FOA15.286420.934119.55821.0299
IAFOA14.095817.95746.469311.3621
\( f_{2} \)30IA2.27633.52973.061e−033.5146
PSO2.00512.11932.796e−034.2287
FOA1.68491.96783.909e−041.9652
IAFOA01.00526.9768e−030.9537
\( f_{3} \)30IA2.18e−024.485e−023.0702e−014.7798
PSO1.96e−022.073e−012.785e−013.5669
FOA1.854e−011.6941e−011.1185e−011.2463
IAFOA0000.6805
\( f_{4} \)30IA1.952e−042.327e−046.001e−013.534
PSO1.439e−022.557e−025.026e−014.371
FOA2.005e−021.363e−013.778e−020.988
IAFOA3.958e−031.564e−052.563e−021.015