Peak Identification in Evolutionary Multimodal Optimization: Model, Algorithms, and Metrics

. 2024 Oct 19;9(10):643. doi: 10.3390/biomimetics9100643

Algorithm 5 HVPIC

Input:

P O P

–the final generation of an EA;

ε

–accuracy level;
Output:

1:
Initialize a cluster list $L_{C}$ to contain the cluster consisting of all the points, initialize the solution list;
2:
$p h = g b e s t . fitness$ // $p h$ is the estimated peak height
3:
repeat
4:
Remove the cluster $C_{h}$ at the head of the clusters list;
5:
if $| C_{h} | > 1$ then
6:
${C_{1}, C_{2}} \leftarrow$ K-means( $C_{h}$ ,2);
7:
for $i = 2$ to number of trials do
8:
${C_{1}^{'}, C_{2}^{'}} \leftarrow$ K-means( $C_{h}$ ,2);
9:
if $SSE ({C_{1}^{'}, C_{2}^{'}}) < SSE ({C_{1}, C_{2}})$ then
10:
${C_{1}, C_{2}} \leftarrow {C_{1}^{'}, C_{2}^{'}}$
11:
end if
12:
end for
13:
else
14:
$c b e s t_{h} \leftarrow$ the best individual in $C_{h}$ ;
15:
$S \leftarrow S \cup {c b e s t_{h}}$ ;
16:
continue;
17:
end if
18:
$c b e s t_{1} \leftarrow$ the best individual in $C_{1}$ ;
19:
$c b e s t_{2} \leftarrow$ the best individual in $C_{2}$ ;
20:
if hill-valley( $c b e s t_{1}$ , $c b e s t_{2}$ )==TRUE then
21:
if $p h - c b e s t_{1} . fitness \leq ε$ then
22:
$L_{C} \leftarrow L_{C} \cup {C_{1}}$ ;
23:
end if
24:
if $p h - c b e s t_{2} . fitness \leq ε$ then
25:
$L_{C} \leftarrow L_{C} \cup {C_{2}}$ ;
26:
end if
27:
else
28:
$S \leftarrow S \cup {c b e s t_{h}}$ ;
29:
end if
30:
until $L_{C} = \emptyset$