IEEE Robotics & Automation Magazine - December 2023 - 36

TABLE 2. Results on CEC 2017 standard benchmark problems. (Continued )
FITNESS
F
Best
f20
Mean
Best
f21
Mean
Best
f22
Mean
Best
f23
Mean
Best
f24
Mean
Best
f25
Mean
Best
f26
Mean
Best
f27
Mean
Best
f28
Mean
Best
f29
Mean
WOA [4]
2.66E + 02
2.66E + 02
3.77E + 02
3.77E + 02
6.48E + 02
6.48E + 02
8.86E + 02
8.87E + 02
9.65E + 02
9.66E + 02
3.42E-03
4.58E-03
1.33E + 03
1.33E + 03
2.66E + 02
2.67E + 02
2.54E-08
2.66E-08
1.73E + 03
1.68E + 03
APSO [5]
1.40E-05
1.73E-05
2.29E + 03
4.01E + 04
2.88E + 03
3.16E + 04
2.11E-04
5.30E-04
2.02E-05
2.56E-05
1.48E-06
1.60E-06
7.34E-06
8.05E-06
9.80E-08
4.01E-07
2.11E-06
1.31E-07
2.88E + 10
2.91E + 10
GWO [6]
1.71E-05
2.10E-05
1.82E + 03
2.42E + 03
2.21E + 03
2.67E + 03
2.00E-05
4.04E-04
3.19E-06
5.94E-06
7.45E-06
6.71E-05
2.35E-05
8.19E-06
2.49E-08
2.98E-08
1.57E + 08
6.21E-08
4.55E + 08
3.40E + 10
SMA [20]
1.07E-05
USMA
3.19E-01
7.89E + 02
7.90E + 02
1.28E + 03
1.28E + 03
1.26E-06
4.80E-06
1.70E-07
1.79E-07
1.34E-07
2.26E-07
1.63E-08
1.71E-08
5.10E-11
1.80E-11
3.06E-08
3.06E-08
4.24E + 10
5.10E + 06
6.43E-06
8.29E-06
2.26E + 02
2.26E + 02
3.89E + 02
3.89E + 02
7.56E-07
2.88E-06
1.02E-07
1.07E-07
8.05E-08
1.36E-07
9.79E-09
1.02E-08
3.06E-11
1.08E-11
1.52E-08
1.60E-08
1.04E + 03
1.01E + 03
histogram using DDCCT to show the frequency count of each
visual word in the image after the best visual words have been
determined using USMA. Additionally, the classifier is
trained through an encoded histogram and image annotation.
RESULTS AND DISCUSSION
In this study, two sets of experiments are conducted. In the first
set of experiments, the performance of the proposed USMA is
compared with those of the state-of-the-art metaheuristic algorithms
WOA [4], APSO [5], GWO [6], and SMA [20] on IEEE
CEC 2017 benchmark functions [28]. In the second set of experiments,
the performance of USMA-BOF is tested on a dataset
consisting of 800 leaf images (infected and noninfected)
acquired from the PlantaeK repository [29] for precision agriculture
on two classifiers: SVM and MLP. The experimental results
are obtained using a system configuration with 16GB RAM, a
Windows 10 operating system, Intel core i7 with 2.2 GHz speed,
and Nvidia Geforce GTX1080 Ti 4GB.
PERFORMANCE EVALUATION OF USMA ON CEC 2017
The parameter settings of USMA and other state-of-the-art
algorithms used for performance comparison are given in
Table 1. The considered search space for the benchmark
problems is
6 100 , 100 W
-
@ , where W depicts the dimensions.
36 IEEE ROBOTICS & AUTOMATION MAGAZINE DECEMBER 2023
The parameter tuning is performed by keeping the population
size at 30, the number of iterations at 1,000, and the dimensions
as 30. Because of the randomized nature of metaheuristic
algorithms, each algorithm is run 30 times for each
problem. The mean and best fitness values obtained on 29
benchmark problems are shown in Table 2. The observations
show that, compared to other state-of-the-art methods,
USMA provides better results on the benchmark problems.
The convergence graphs of a few representative benchmark
problems, F ,2 F ,4 F ,12 and F ,21 are illustrated in Figure
5. Here, the x-axis shows the number of iterations, and the
y-axis represents the obtained fitness value. Furthermore, Figure
5 depicts that USMA converges toward a global optimum
solution to provide an effective solution. The optimum convergence
pattern of USMA is comparatively more consistent.
The result analysis demonstrates that the proposed algorithm
USMA is resilient to local optimum search and also achieves a
balance between global and local optimum solutions. Thus, it
can be stated that USMA demonstrates a comparable or even
better optimization performance compared to other natureinspired
algorithms.
To validate the results shown in Table 2, Kruskal-Wallis,
Wilcoxon, and Friedman tests were run at 95% of the confidence
interval. The hypotheses are formulated as follows:
IEEE Robotics & Automation Magazine - December 2023

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