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Table 1:
The experimental results obtained by the IMMA with varying population size M for the test functions with n=30, while NFEs are shown for the functions that can be solved successfully in the 25 trials, and the best error values are shown for the hard functions.
FunctionM = 30M = 60M=150M=300
AVGNSDN     
f1 2.86e+03 2.08e+02 6.55e+03 6.27e+02 1.52e+04 5.83e+03 3.03e+04 1.17e+03 
f2 8.68e+03 9.55e+02 1.01e+04 1.03e+03 1.33e+04 1.75e+03 1.90e+04 3.70e+03 
f3 2.95e+04 2.05e+03 3.13e+04 2.57e+03 3.32e+04 2.24e+03 3.80e+04 2.83e+03 
f6 2.10e+04 1.84e+04 3.11e+04 3.03e+04 4.13e+04 3.02e+04 6.01e+04 2.97e+04 
f7 6.55e+03 4.09e+03 1.02e+04 6.28e+03 5.11e+04 1.06e+04 9.61e+04 5.16e+04 
f9 3.79e+04 1.12e+04 3.94e+04 1.46e+04 3.90e+04 9.43e+03 4.41e+04 7.93e+03 
f10 5.47e+04 1.45e+04 4.20e+04 1.61e+04 3.97e+04 1.63e+04 5.19e+04 1.64e+04 
f28 2.87e+03 1.36e+02 6.30e+03 3.56e+02 1.85e+04 1.36e+03 4.05e+04 3.70e+03 
f29 2.83e+04 8.77e+03 2.67e+04 6.21e+03 3.93e+04 9.28e+03 5.09e+04 1.72e+04 
f31 4.35e+04 1.19e+04 4.69e+04 1.46e+04 5.60e+04 1.66e+04 6.81e+04 1.23e+04 
f33 2.73e+04 1.23e+04 2.02e+04 9.15e+03 2.67e+04 8.68e+03 4.28e+04 3.43e+03 
f37 1.19e+04 7.70e+03 1.93e+04 1.65e+04 4.56e+04 5.93e+03 6.85e+04 4.63e+04 
AVGESDE     
f4 1.31e+05 2.35e+04 2.94e+04 6.16e+03 5.39e+04 3.59e+04 6.23e+04 5.35e+03 
f5 1.67e+03 3.78e+02 1.68e+03 3.27e+02 2.05e+03 2.20e+02 2.20e+03 1.97e+02 
f8 2.00e+01 1.28e–10 2.00e+01 1.12e–10 2.00e+01 1.77e–10 2.00e+01 1.37e–10 
f26 2.92e–01 4.00e–02 2.84e–01 4.73e–02 3.80e–01 7.07e–02 3.84e–01 6.88e–02 
f27 4.13e+01 5.32e+01 4.13e+01 4.97e+01 1.31e+02 7.13e+01 1.93e+02 1.08e+02 
f30 9.72e–14 7.77e–14 1.63e–13 3.26e–13 2.86e–03 4.37e–03 4.24e–03 5.88e–03 
f32 3.82e–04 1.01e–12 3.82e–04 7.00e–13 3.82e–04 7.59e–13 3.82e–04 1.34e–12 
f34 6.61e–13 4.42e–13 5.56e–13 4.21e–13 9.98e–08 2.76e–08 8.79e–04 3.04e–04 
FunctionM = 30M = 60M=150M=300
AVGNSDN     
f1 2.86e+03 2.08e+02 6.55e+03 6.27e+02 1.52e+04 5.83e+03 3.03e+04 1.17e+03 
f2 8.68e+03 9.55e+02 1.01e+04 1.03e+03 1.33e+04 1.75e+03 1.90e+04 3.70e+03 
f3 2.95e+04 2.05e+03 3.13e+04 2.57e+03 3.32e+04 2.24e+03 3.80e+04 2.83e+03 
f6 2.10e+04 1.84e+04 3.11e+04 3.03e+04 4.13e+04 3.02e+04 6.01e+04 2.97e+04 
f7 6.55e+03 4.09e+03 1.02e+04 6.28e+03 5.11e+04 1.06e+04 9.61e+04 5.16e+04 
f9 3.79e+04 1.12e+04 3.94e+04 1.46e+04 3.90e+04 9.43e+03 4.41e+04 7.93e+03 
f10 5.47e+04 1.45e+04 4.20e+04 1.61e+04 3.97e+04 1.63e+04 5.19e+04 1.64e+04 
f28 2.87e+03 1.36e+02 6.30e+03 3.56e+02 1.85e+04 1.36e+03 4.05e+04 3.70e+03 
f29 2.83e+04 8.77e+03 2.67e+04 6.21e+03 3.93e+04 9.28e+03 5.09e+04 1.72e+04 
f31 4.35e+04 1.19e+04 4.69e+04 1.46e+04 5.60e+04 1.66e+04 6.81e+04 1.23e+04 
f33 2.73e+04 1.23e+04 2.02e+04 9.15e+03 2.67e+04 8.68e+03 4.28e+04 3.43e+03 
f37 1.19e+04 7.70e+03 1.93e+04 1.65e+04 4.56e+04 5.93e+03 6.85e+04 4.63e+04 
AVGESDE     
f4 1.31e+05 2.35e+04 2.94e+04 6.16e+03 5.39e+04 3.59e+04 6.23e+04 5.35e+03 
f5 1.67e+03 3.78e+02 1.68e+03 3.27e+02 2.05e+03 2.20e+02 2.20e+03 1.97e+02 
f8 2.00e+01 1.28e–10 2.00e+01 1.12e–10 2.00e+01 1.77e–10 2.00e+01 1.37e–10 
f26 2.92e–01 4.00e–02 2.84e–01 4.73e–02 3.80e–01 7.07e–02 3.84e–01 6.88e–02 
f27 4.13e+01 5.32e+01 4.13e+01 4.97e+01 1.31e+02 7.13e+01 1.93e+02 1.08e+02 
f30 9.72e–14 7.77e–14 1.63e–13 3.26e–13 2.86e–03 4.37e–03 4.24e–03 5.88e–03 
f32 3.82e–04 1.01e–12 3.82e–04 7.00e–13 3.82e–04 7.59e–13 3.82e–04 1.34e–12 
f34 6.61e–13 4.42e–13 5.56e–13 4.21e–13 9.98e–08 2.76e–08 8.79e–04 3.04e–04 
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