Journal of Applied Mathematics

Research Article

Modified Biogeography-Based Optimization with Local Search Mechanism

Table 5

Scalability study at Dim = 10, 50, 100, and 200 a ter Dim * 10,000 NFFEs for standard functions f1–f13.
 MLBBODEBBODE/BBOaBBOmDE
Mean (std)Mean (std)Mean (std)Mean (std)Mean (std)
dim  = 10     
 f1 ( ) ( )+ ( )+
 f2 ( ) ( )+ ( )+ —
 f3 ( ) ( )− ( )+ —
 f4 ( ) ( )+ ( )− —
 f5 ( ) ( )− ( )+
 f6 ( ) ( )− ( )~ —
 f7 ( ) ( )− ( )~ —
 f8 ( ) ( )+ ( )+
 f9 ( ) ( )+ ( )+
 f10 ( ) ( )− ( )+
 f11 ( ) ( )+ ( )+
 f12 ( ) ( )− ( )+
 f13 ( ) ( )− ( )+
dim = 50     
 f1 ( ) ( )+ ( )+
 f2 ( ) ( )+ ( )+ —
 f3 ( ) ( )+ ( )+ —
 f4 ( ) ( )+ ( )+ —
 f5 ( ) ( )+ ( )+
 f6 ( ) ( )+ ( )~ —
 f7 ( ) ( )+ ( )− —
 f8 ( ) ( )+ ( )+
 f9 ( ) ( )+ ( )+
 f10 ( ) ( )− ( )+
 f11 ( ) ( )+ ( )+
 f12 ( ) ( )+ ( )+
 f13 ( ) ( )− ( )+
dim  = 100     
 f1 ( ) ( )+ ( )+
 f2 ( ) ( )+ ( )+ —
 f3 ( ) ( )+ ( )+ —
 f4 ( ) ( )+ ( )+ —
 f5 ( ) ( )+ ( )+
 f6 ( ) ( )+ ( )~ —
 f7 ( ) ( )+ ( )- —
 f8 ( ) ( )+ ( )+
 f9 ( ) ( )+ ( )+
 f10 ( ) ( )+ ( )+
 f11 ( ) ( )~ ( )+
 f12 ( ) ( )+ ( )+
 f13 ( ) ( )+ ( )+
dim  = 200     
 f1 ( ) ( )− ( )+
 f2 ( ) ( )− ( )+ —
 f3 ( ) ( )+ ( )+ —
 f4 ( ) ( )+ ( )+ —
 f5 ( ) ( )~ ( )+
 f6 ( ) ( )+ ( )~ —
 f7 ( ) ( )+ ( )− —
 f8 ( ) ( )+ ( )+
 f9 ( ) ( )+ ( )+
 f10 ( ) ( )+ ( )+
 f11 ( ) ( )~ ( )+
 f12 ( ) ( )+ ( )+
 f13 ( ) ( )+ ( )+
Note: “+”, “−”, and “~” indicate that MLBBO is significantly better, worse, and indifferent, respectively, compared with other algorithms.