IEEE Computational Intelligence Magazine - May 2023 - 39

operator is only applied at the later stage ofevolution (Line 17,
Algorithm 3) since peptides at the early stage of evolution are
usually not worth exploitation. In Algorithm 5, the operator
selects K promising peptides,x1; .. . ;xK, from P for local
search (Line 1). Here, a promising peptide is a peptide with
good antimicrobial activity (f1 <) but poor diversity
(f2 > 0). For k ¼ 1; ... ; K (Line 2), L peptides,xk1; .. . ;xkL,
are generated by randomly adding an amino acid toxk or deleting
an amino acid fromxk (Lines 3-10). Then, the peptide ^xk
with the smallest value off2 is identified amongxk1; ... ;xkL
(Line 11). Iff2ð^xkÞ¼ 0,xk is replaced by ^xk in P (Lines 12-14).
K is set to 10 and L is set to 5 according to preliminary
investigations. Note that the population may contain less than
K promising peptides. In such a case, all promising peptides
are used for local search.
Algorithm 5. Local Search
Input:
Population P;
Number of peptides to be selected for local search K;
Number of perturbations for each selected peptide L;
Output:
Population P;
1: Randomly select K peptides with f1 < and f2 > 0,
x1; .. . ;xK, from P;
2: for k ¼ 1; .. . ; K do
3: for l ¼ 1; .. . ; L do
4:
5:
6:
7:
8:
9:
if rand < 0:5(rand is a random number in the range of
[0,1]) then
Generatexkl by adding a random amino acid at a
random position inxk;
end
else
Generatexkl bydeleting a randomamino acid fromxk;
end
10: end
11:
14: end
15: end
C.Another Perspective ofAMPEMO
AMPEMO formulates AMP design as a multi-objective optimization
problem and solves it with an evolutionary multi-objective
algorithm. AMPEMO can also be termed an evolutionary optimization
approach with constraint handling techniques. From
this perspective, AMPdesign is considered a single-objective optimization
problem with a constraint, where the objective isf1ðxÞ
and the constraint is gðxÞ¼f2ðxÞ¼ 0. In constrained optimization,
a penalty function [58] is often employed to simultaneously
optimize the objective value and constraint violation value, such
asf1ðxÞþgðxÞ,where is a weight. When the decompositionbased
evolutionary multi-objective algorithm is used to solve the
x^k ¼ arg minl¼1;...;Lf2ðxklÞ;
12: if f2ð^xkÞ¼ 0 then
13:
Replacexk by ^xk in P;
problem, the PBI function can be termed a penalty function that
aggregates the objective value and the constraint violation value
by a weight vector. However, there are a series ofpenalty functions
in AMPEMO, and the weight vectors in these penalty functions
are different. Some penalty functions focus mainly on
objective values (with weight vectors near thef1 axis in Figure 7),
while other penalty functions emphasize constraint violation values
(with weight vectors near thef2 axis in Figure 7). The evolutionary
algorithm cooperatively optimizes these penalty functions
to efficiently obtain feasible solutions with good objective values.
In addition, the local search operator helps improve promising
infeasible solutions to feasible solutions. This perspective of
AMPEMO also explains why it is preeminent in searching for
various AMPs.
IV. Experiments
This section investigates the effectiveness of the proposed
AMPEMO. AMPEMO is compared with four state-of-theart
computational intelligence-based de novo AMP design
approaches: LSTM RNN [19], AMP-LM [20], AMPGAN
v2 [26], and LSTMAMP [21]. A standard evolutionary algorithm
(denoted as sEA) [28] and a traditional niching method
based on clearing (denoted as nEA) [37] are also included for
comparison. For both sEA and nEA, the only objective to
optimize isf1 in Section III-A1. Both algorithms use the same
crossover and mutation operators as those in AMPEMO. nEA
employs a clearing method to improve the diversity of the
population in the decision space. The niching radius r of the
clearing method in nEA is equal to that in AMPEMO.
For a fair comparison, the dataset for training learning
models is the same for all the compared approaches, with the
exception ofAMPGAN v2. The dataset is provided by Daniel
et al. [46], which contains 1,778 experimentally validated
AMPs from APD3 [59] and 1,778 experimentally validated
non-AMPs chosen from UniProt [45]. AMPGAN v2 has to
use a much larger dataset for training. Hence, the algorithm
uses the dataset suggested in its original study, which contains
6,238 AMPs from DBAASP [60], 312 AMPs from
AVPdb [61], and 490,341 non-AMPs from UniProt.
In AMPEMO, the size of BðiÞ is set to 6, parameter u for
the PBI method is set to 2, and parameter Nls for triggering
local search is set to 10,000 according to our preliminary investigations.
The population size N is 200, and the stop criterion
is that the number of evaluated solutions reaches 40,000 in
AMPEMO, sEA, and nEA. The parameters in LSTM RNN,
AMP-LM, AMPGAN v2, and LSTMAMP are the same as
those in their original studies. The numbers ofpeptides generated
by LSTM RNN, AMP-LM, AMPGAN v2, and
LSTMAMP are equal to the number of peptides in the final
population and elite archive ofAMPEMO.
In the experiments, the performance of the compared
approaches in discovering AMPs with a length in the range of
½7; 48 (i.e., n 2½7; 48)is first examined. The lengths of the
most known AMPs fall within this range. Second, AMPEMO
is compared with LSTM RNN, where n is 7, 8,..., 47, and 48.
MAY 2023 | IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE 39
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