1
Puma Optimizer (PO): A Novel Metaheuristic Optimization
Algorithm and its Application in Machine Learning
𝑓1
𝐸𝑥𝑝𝑙𝑜𝑟
=
𝑃𝐹
1
∙
𝑆𝑒𝑞
1
𝐶𝑜𝑠𝑡 𝐸𝑥𝑝𝑙𝑜𝑟𝑒
𝑆𝑒𝑞
𝑇𝑖𝑚𝑒
(1)
𝑓1
𝐸𝑥𝑝𝑙𝑜𝑖𝑡
=
𝑃𝐹
1
∙
𝑆𝑒𝑞
1
𝐶𝑜𝑠𝑡 𝐸𝑥𝑝𝑙𝑜𝑖𝑡
𝑆𝑒𝑞
𝑇𝑖𝑚𝑒
(2)
𝑓2
𝐸𝑥𝑝𝑙𝑜𝑟
=
𝑃𝐹
2
∙
𝑆𝑒𝑞
1
𝐶𝑜𝑠𝑡 𝐸𝑥𝑝𝑙𝑜𝑟𝑒
+
𝑆𝑒𝑞
2
𝐶𝑜𝑠𝑡 𝐸𝑥𝑝𝑙𝑜𝑟𝑒
+
𝑆𝑒𝑞
3
𝐶𝑜𝑠𝑡 𝐸𝑥𝑝𝑙𝑜𝑟𝑒
𝑆𝑒𝑞
1
𝑇𝑖𝑚𝑒
+
𝑆𝑒𝑞
2
𝑇𝑖𝑚𝑒
+
𝑆𝑒𝑞
3
𝑇𝑖𝑚𝑒
(3)
𝑓2
𝐸𝑥𝑝𝑙𝑜𝑖𝑡
=
𝑃𝐹
2
∙
𝑆𝑒𝑞
1
𝐶𝑜𝑠𝑡 𝐸𝑥𝑝𝑙𝑜𝑖𝑡
+
𝑆𝑒𝑞
2
𝐶𝑜𝑠𝑡 𝐸𝑥𝑝𝑙𝑜𝑖𝑡
+
𝑆𝑒𝑞
3
𝐶𝑜𝑠𝑡 𝐸𝑥𝑝𝑙𝑜𝑖𝑡
𝑆𝑒𝑞
1
𝑇𝑖𝑚𝑒
+
𝑆𝑒𝑞
2
𝑇𝑖𝑚𝑒
+
𝑆𝑒𝑞
3
𝑇𝑖𝑚𝑒
(4)
Seq
1
Cost Explore
=
|
Cost
𝐼𝑛𝑖𝑡𝑖𝑎𝑙
Best
―
Cost
1
Explore
|
(5)
Seq
2
Cost Explore
=
|
Cost
2
Explore
―
Cost
1
Explore
|
(6)
Seq
3
Cost Explore
=
|
Cost
3
Explore
―
Cost
2
Explore
|
(7)
Seq
1
Cost Exploit
=
|
Cost
𝐼𝑛𝑖𝑡𝑖𝑎𝑙
Best
―
Cost
1
Exploit
|
(8)
Seq
2
Cost Exploit
=
|
Cost
2
Exploit
―
Cost
1
Exploit
|
(9)
Seq
3
Cost Exploit
=
|
Cost
3
Exploit
―
Cost
2
Exploit
|
(10)
𝑆𝑐𝑜𝑟𝑒
𝐸𝑥𝑝𝑙𝑜𝑟𝑒
=
(
𝑃𝐹
1
∙
𝑓1
𝐸𝑥𝑝𝑙𝑜𝑟
)
+
(
𝑃𝐹
2
∙
𝑓2
𝐸𝑥𝑝𝑙𝑜𝑟
)
(11)
𝑆𝑐𝑜𝑟𝑒
𝐸𝑥𝑝𝑙𝑜𝑖𝑡
=
(
𝑃𝐹
1
∙
𝑓1
𝐸𝑥𝑝𝑙𝑜𝑖𝑡
)
+
(
𝑃𝐹
2
∙
𝑓2
𝐸𝑥𝑝𝑙𝑜𝑖𝑡
)
(12)
𝑓
1
𝑒𝑥𝑝𝑙𝑜𝑖𝑡
𝑡
=
𝑃𝐹
1
∙
|
𝐶𝑜𝑠𝑡
𝑒𝑥𝑝𝑙𝑜𝑖𝑡
𝑜𝑙𝑑
―
𝐶𝑜𝑠𝑡
𝑒𝑥𝑝𝑙𝑜𝑖𝑡
𝑛𝑒𝑤
𝑇
𝑒𝑥𝑝𝑙𝑜𝑖𝑡
𝑡
|
(13)
𝑓
1
𝑒𝑥𝑝𝑙𝑜𝑟𝑒
𝑡
=
𝑃𝐹
1
∙
|
𝐶𝑜𝑠𝑡
𝑒𝑥𝑝𝑙𝑜𝑟𝑒
𝑜𝑙𝑑
―
𝐶𝑜𝑠𝑡
𝑒𝑥𝑝𝑙𝑜𝑟𝑒
𝑛𝑒𝑤
𝑇
𝑒𝑥𝑝𝑙𝑜𝑟𝑒
𝑡
|
(14)
𝑓
2
𝑒𝑥𝑝𝑙𝑜𝑖𝑡
𝑡
=
𝑃𝐹
2
∙
|
𝐶𝑜𝑠𝑡
𝑒𝑥𝑝𝑙𝑜𝑖𝑡
𝑂𝑙𝑑,1
―
𝐶𝑜𝑠𝑡
𝑒𝑥𝑝𝑙𝑜𝑖𝑡
𝑁𝑒𝑤,1
+
𝐶𝑜𝑠𝑡
𝑒𝑥𝑝𝑙𝑜𝑖𝑡
𝑂𝑙𝑑,2
―
𝐶𝑜𝑠𝑡
𝑒𝑥𝑝𝑙𝑜𝑖𝑡
𝑁𝑒𝑤,2
+
𝐶𝑜𝑠𝑡
𝑒𝑥𝑝𝑙𝑜𝑖𝑡
𝑂𝑙𝑑,3
―
𝐶𝑜𝑠𝑡
𝑒𝑥𝑝𝑙𝑜𝑖𝑡
𝑁𝑒𝑤,3
𝑇
𝑒𝑥𝑝𝑙𝑜𝑖𝑡
𝑡,1
+
𝑇
𝑒𝑥𝑝𝑙𝑜𝑖𝑡
𝑡,2
+
𝑇
𝑒𝑥𝑝𝑙𝑜𝑖𝑡
𝑡,3
|
(15)
𝑓
2
𝑒𝑥𝑝𝑙𝑜𝑟𝑒
𝑡
=
𝑃𝐹
2
∙
|
𝐶𝑜𝑠𝑡
𝑒𝑥𝑝𝑙𝑜𝑟𝑒
𝑂𝑙𝑑,1
―
𝐶𝑜𝑠𝑡
𝑒𝑥𝑝𝑙𝑜𝑟𝑒
𝑁𝑒𝑤,1
+
𝐶𝑜𝑠𝑡
𝑒𝑥𝑝𝑙𝑜𝑟𝑒
𝑂𝑙𝑑,2
―
𝐶𝑜𝑠𝑡
𝑒𝑥𝑝𝑙𝑜𝑟𝑒
𝑁𝑒𝑤,2
+
𝐶𝑜𝑠𝑡
𝑒𝑥𝑝𝑙𝑜𝑟𝑒
𝑂𝑙𝑑,3
―
𝐶𝑜𝑠𝑡
𝑒𝑥𝑝𝑙𝑜𝑟𝑒
𝑁𝑒𝑤,3
𝑇
𝑒𝑥𝑝𝑙𝑜𝑟𝑒
𝑡,1
+
𝑇
𝑒𝑥𝑝𝑙𝑜𝑟𝑒
𝑡,2
+
𝑇
𝑒𝑥𝑝𝑙𝑜𝑟𝑒
𝑡,3
|
(16)
