IEEE Computational Intelligence Magazine - February 2023 - 30
FIGURE 6 Convergence plots and boxplots representing the distribution of the best solutions found over 30 runs by GP4DFs (blue) and GA-FSTPSO
(orange) on the benchmark functions defined in 30 dimensions. *** p-value 0:001.
space ofoptimization problems. Different from the previous related
works, GP4DFs encodes solutions composed ofa number ofDFs
equal to the number ofdimensions ofthe problem under investigation.
This feature permits the identification of suitable solutions
even when the global optimum has different coordinates in different
dimensions, which is a typical situation for many real-world
optimization problems, e.g., the parameter estimation ofbiochemicalsystems.GP4DFsusesaneffective
initialization strategy and
improves the speed ofconvergence towards global optima.
The performance ofGP4DFs has been assessed by comparing
it against GA-FSTPSO [27], which is a methodology that
achieved promising results in many benchmark functions. A set of
experiments has been performed on standard, shrinked, and shifted
benchmark functions, as well as on the CEC'17 benchmark suite,
defined with 2, 30, 50, and 100 dimensions. The collected results
highlight that GP4DFs outperforms GA-FSTPSOon the majority
ofthe tested benchmark functions. GP4DFs achieved better results
on the optimization problems where GA-FSTPSO was inadequate
(e.g., Michalewicz and Deceptive functions). Moreover,
30 IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE | FEBRUARY 2023
GP4DFs identified suitable DFs for all the problems where the
global optimum has the same coordinate in all the dimensions.
From the computational point ofview, the obtained results
indicate that GP4DFs requires a smaller budget for fitness evaluations
than GA-FSTPSO to achieve similar or even better
results. The convergence plots indeed point out that GP4DFs
starts the evolution with a promising initial population and
improves its quality throughout the entire process, on most of
the benchmark functions.
Even though GA-FSTPSO outperformed GP4DFs in a
limited number of cases, e.g., Shubert and shrinked Rosenbrock,
the obtained results suggest that the proposed approach
is overall the most suitable solution for the evolution ofDFs.
As a future extension ofthis work, the performance ofGP4DFs
with different initialization strategies and different crossover and
mutation operators will be investigated. The introduction of
genetic operators specifically defined for this context, which will
help improve the quality ofthe evolvedDFs, will also be taken into
account. Moreover, strategies for the identification of DFs
IEEE Computational Intelligence Magazine - February 2023
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