IEEE Computational Intelligence Magazine - May 2023 - 37

Algorithm 3. Proposed evolutionary multi-objective algorithm
Input :
List of all kinds of amino acids;
Feasible range of peptide sequence length;
Population size N;
Parameter Nls for triggering local search;
Output :
FIGURE 4. Maintaining solutions such as x7, x8, and x9 can help
population-based metaheuristics exploit and explore solutions such as
x2 and x4 in Figure 3.
local search strategies to solve the AMP design problem. Algorithm
3 gives a general framework ofthe algorithm.
The proposed algorithm is described according to Algorithm
3 in the following section. An elite archive E is
employed to keep solutions with f1 ( is a small positive
value) andf2 ¼ 0 during the evolution process. E is empty in
the initialization phase (Line 1). N peptide sequences
fx1; ... ; xNg are randomly generated as the initial population
P (Line 2), where N is the population size. Subsequently, N
weight vectors W ¼fw1,...,wN} are uniformly generated in
the objective space (Line 3). For each weight vector wi; i ¼
1; ... ;N, BðiÞ contains the indices of some weight vectors in
W that are closest to it. BðiÞ defines the neighborhood of wi
for local cooperation in the crossover operator. While the stop
criterion has not been met (Line 5), the algorithm has three
main operations in each iteration (Lines 6-17). First, for i ¼
1; ... ;N (Line 6), two parents are randomly selected from
BðiÞ and produce an offspring xo that updates xi and E by environmental
selection (Lines 7-9). Next, while nonelite solutions
exist in E (Line 11), they are removed one by one. An elite
solution in E may become nonelite since there may be some
new solutions in the population close to it. The solution with
the largest value off2 is denoted as ~x in Line 12, and the weight
vector closest to ~x by cosine similarity (whose index is j)is
identified in Line 13. The environmental selection operator is
applied to check whether ~x can replace xj (Line 14) and then
x~ is removed from E (Line 15). In the later stage ofevolution,
i.e., when the number of evaluated solutions is larger than a
given parameter Nls, a local search operator is used to improve
promising solutions in P (Lines 17-19).
Population P;
Elite archive E;
" E keeps solutions with f1 and
f2 ¼ 0 during the evolution process
1: Initialize elite archive E to be an empty set;
2: Initialize population P ¼fx1; ... ;xNg as N random peptide
segments;
3: Generate N weight vectors W ¼fw1,...,wN} uniformly
distributed in the objective space;
4: Set BðiÞ; i ¼ 1; .. . ; N to be the indices of neighbor weight
vectors in W closest to wi; i ¼ 1; .. . ; N;
5: while the stop criterion has not been met do
6: for i ¼ 1; .. . ; N do
7:
8:
9:
10: end
11: while nonelite solutions exist in E do
12:
x~ ¼ arg maxx2Ef2ðxÞ;
13:
14:
15:
j ¼ arg maxj¼1;...;N
k~xkkwjk ; " Identify theweight vector
closest to ~x by cosine
x~wj
similarity.
ðxj; EÞ¼ Environmental_Selectionð~x;j; wj; P; EÞ;
E ¼ Ef~xg;
16: end
17: if the number of evaluations is larger than Nls then
18:
P ¼ Local_SearchðPÞ;
19: end
20: end
Randomly choose two different values, a and b,fromBðiÞ;
xo ¼ Crossover&Mutationðxa;xbÞ;
ðxi; EÞ¼ Environmental_Selectionðxo; i; wi; P; EÞ;
" Identify the solution with
the worst f2 in E.
The crossover, mutation, environmental selection, and
local search operators are explained in the next section.
1)Crossover and Mutation
Offspring are generated by crossover and mutation operators in
Line 8 ofAlgorithm 3. In the crossover operator, each parent is
split into two parts by a random splitting point. Then, parts
from both parents are combined to obtain a new peptide
sequence. In the mutation operator, one amino acid in the
new peptide sequence is randomly chosen and replaced with
another amino acid ofa different kind.
Figure 5 gives an example ofcrossover and mutation for easy
FIGURE 5. Example of crossover and mutation for generating new
peptides.
understanding. There are two parent peptide sequences in this
figure: 'CTYCSYGV' and 'QTCCDLY.''CTYCSYGV' is
divided into 'CTYCSY' and 'GV,' while 'QTCCDLY' is divided
into 'QTCCD' and 'LY'. Then, 'CTYCSY' and 'LY' are combined
into a new peptide sequence, 'CTYCSYLY' ('GV' and
MAY 2023 | IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE 37
IEEE Computational Intelligence Magazine - May 2023

Table of Contents for the Digital Edition of IEEE Computational Intelligence Magazine - May 2023
