IEEE Computational Intelligence Magazine - May 2023 - 40

AMP-LM, AMPGAN v2 and LSTMAMP cannot generate
AMPs with fixed lengths.
A peptide generated by a compared approach is termed an
AMP if the probability of an AMP given by the BERT-based
prediction model [43] is larger than 0.9. Hence, in
AMPEMO is set to 0.1.
Because all the compared approaches are stochastic processes,
each approach runs 20 independent times. Then, based on the
results of20 runs, Wilcoxon's rank-sum test at a level of0.05 is
used to determine whether an approach performs statistically significantly
better than another according to a performance metric.
A. Performance Metrics
The AMP set obtained by a compared approach is denoted as
X. The following four methods are used to evaluate the performance
ofX.
1) Scalable Niching Method (SC) [62]
AMP design is essentially a multimodal optimization problem.
The maximum peak ratio (MPR) [63] is a popular metric in
multimodal optimization to measure how many global optimal
solutions and good local optimal solutions are obtained. However,
the MPR requires the knowledge of all the true optimal
solutions to a problem a priori, which is usually impossible for
real-world problems such as AMP design. On the other hand,
SC is an alternative metric that does not make this assumption
and is calculated as follows:
SCðXÞ¼
X
BjBinkðclustðXÞÞ
Equation (8) requires a clustering and binning step on X, sorting
the AMPs into k bins B1; ... ; Bk. Here, a clearing
method [37] is employed with a niche radius equal to 0.45 to
remove redundancy. Only one optimal solution is retained
within the niche radius, while other solutions are deleted;
then, k is automatically determined based on the results of the
clearing method by the niche radius, that is, k is set as the number
ofniches. Each bin Bj is assigned a weighting factor wj used
to weigh the quality of the identified optima against each
other. wj is set to kjþ1
k
for 1j k. A larger value of SC
indicates that X contains more AMPs dissimilar to each other.
2) Pure Diversity (PD) [64]
PD measures the diversity of a solution set. The PD value of a
solution set X is calculated as follows:
PDðXÞ¼ max
xi2X
where
dðx; XÞ¼ minðdissimilarityðx; xiÞÞ:
xi2X
(10)
Here, dðx; XÞ is the dissimilarity from x to X. A larger value of
PD implies a higher diversity.
40 IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE | MAY 2023
DD ¼
X
xi2X
min
xj2D
fdðxi; xjÞg;
(14)
ðPDðX xiÞþ dðxi; X xiÞÞ;
(9)
wijBjj:
(8)
FIGURE 8. Relationship between PD and the set size.
Note that the value ofa diversity metric such as PD usually
changes according to the size of the solution set. In Figure 8,
each point represents a randomly generated peptide set with a
size ranging from 10 to 500. The peptide set in each size is
generated twice. According to the distribution of these points,
the relationship between their PD values and their sizes is
assumed as a power function as follows:
PD ¼ aNb;
(11)
where PD is the PD value,N is the size ofthe peptide set, and
a and b are parameters to be determined. Here, the nonlinear
least-squares method [65] is applied to determine a and b. An
objective function eða; bÞ about the square error between the
real value PD and the predicted value
PD
mized as follows:
min eða; bÞ¼ min
X
X2PS
where PS are all the peptide sets in Figure 8. The Gauss-Newton
method [66] is employed to quickly find the optimal solution,
a ¼ 0:2452 and b ¼0:055.
To compare the PD values ofpeptide sets in different sizes, the
PD value in (9) is divided by the PD value in (11) (i.e., PD when
N ¼jXj). Theresultisregarded asthe final PDvalue, that is,
PDfinal ¼
PD
PD :
(13)
3)Dissimilarity to Dataset (DD)
A metric named DD is proposed to evaluate the dissimilarity of
a peptide set to the known AMPs in the dataset. In this study,
these known AMPs are utilized for training learning models,
i.e., 1,778 AMPs from APD3 [59], 6,238 AMPs from
DBAASP [60], and 312 AMPs from AVPdb [61]. DD is calculated
as follows:
needs to be minijjPDðXÞ
PDðXÞjj ;
2
(12)
IEEE Computational Intelligence Magazine - May 2023

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