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.
| | MLBBO | DE | BBO | DE/BBO | aBBOmDE | 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 | () | ()+ | ()+ | | |
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Note: “+”, “−”, and “~” indicate that MLBBO is significantly better, worse, and indifferent, respectively, compared with other algorithms.
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