Table 11 Sensitivity analysis of the switching coefficient φ on the CEC2017 benchmark functions, evaluated in terms of the best-found objective value (lower values indicate better performance and result in a higher ranking). All algorithms are tested under identical experimental settings: tent mapping parameter α = 0.5, population size = 30, maximum iterations = 500, and 50 independent runs.
F1 | Metric | φ = 0.3 | φ = 0.4 | φ = 0.5* | φ = 0.6 | φ = 0.7 | φ = 0.8 |
|---|---|---|---|---|---|---|---|
Best | 102.754 | 114.9827 | 100.0046 | 100.8707 | 101.5534 | 100.1811 | |
Rank | 3 | 6 | 1* | 2 | 4 | 5 | |
F3 | Best | 361.9527 | 350.123 | 306.2231 | 326.7948 | 305.0728 | 314.7648 |
Rank | 6 | 5 | 2* | 4 | 1 | 3 | |
F4 | Best | 405.5689 | 404.2009 | 400.019 | 400.0705 | 400.5957 | 411.6847 |
Rank | 5 | 4 | 1* | 2 | 3 | 6 | |
F5 | Best | 553.7277 | 548.7529 | 542.7833 | 547.7579 | 546.763 | 550.7428 |
Rank | 6 | 4 | 1* | 3 | 2 | 5 | |
F6 | Best | 600.2177 | 600.1029 | 600.0726 | 600.3082 | 600.0996 | 600.4898 |
Rank | 4 | 3 | 1* | 5 | 2 | 6 | |
F7 | Best | 784.3067 | 791.8576 | 781.0016 | 787.1601 | 782.7188 | 790.2825 |
Rank | 3 | 6 | 1* | 4 | 2 | 5 | |
F8 | Best | 826.8985 | 833.8286 | 821.8959 | 845.7681 | 837.8084 | 843.7781 |
Rank | 2 | 3 | 1* | 6 | 4 | 5 | |
F9 | Best | 938.9125 | 963.9754 | 925.5966 | 924.5489 | 929.946 | 931.3232 |
Rank | 5 | 6 | 2* | 1 | 3 | 4 | |
F10 | Best | 3311.4957 | 3248.8666 | 3040.2402 | 3551.1103 | 3153.244 | 3488.401 |
Rank | 4 | 3 | 1* | 6 | 2 | 5 | |
F11 | Best | 1123.016 | 1123.0009 | 1118.1876 | 1128.4967 | 1123.0401 | 1123.599 |
Rank | 3 | 2 | 1* | 6 | 4 | 5 | |
F12 | Best | 15780.5965 | 14173.2788 | 10251.9569 | 21096.4987 | 5449.4257 | 17679.7766 |
Rank | 4 | 3 | 2* | 6 | 1 | 5 | |
F13 | Best | 1349.4964 | 1367.6006 | 1382.471 | 1367.7751 | 1376.814 | 1901.3917 |
Rank | 1 | 2 | 5* | 3 | 4 | 6 | |
F14 | Best | 1447.4206 | 1441.4458 | 1430.4513 | 1456.333 | 1463.033 | 1455.1096 |
Rank | 3 | 2 | 1* | 5 | 6 | 4 | |
F15 | Best | 1618.3151 | 1589.9665 | 1574.5973 | 1593.3631 | 1610.0228 | 1590.2761 |
Rank | 6 | 2 | 1* | 4 | 5 | 3 | |
F16 | Best | 1855.8309 | 1615.217 | 1625.4655 | 1729.1438 | 1968.3095 | 1917.6214 |
Rank | 4 | 1 | 2* | 3 | 6 | 5 | |
F17 | Best | 1735.9356 | 1707.1916 | 1721.6276 | 1732.5583 | 1721.9954 | 1726.1598 |
Rank | 6 | 1 | 2* | 5 | 3 | 4 | |
F18 | Best | 2694.3211 | 4633.3547 | 2485.6783 | 3680.7811 | 4193.3119 | 3571.292 |
Rank | 2 | 6 | 1* | 4 | 5 | 3 | |
F19 | Best | 1966.3024 | 1935.8125 | 1931.8154 | 1961.2084 | 1956.1043 | 1948.4891 |
Rank | 6 | 2 | 1* | 5 | 4 | 3 | |
F20 | Best | 2031.3098 | 2039.5117 | 2040.2452 | 2049.0427 | 2048.0845 | 2029.6122 |
Rank | 2 | 3 | 4* | 6 | 5 | 1 | |
F21 | Best | 2317.4457 | 2336.2302 | 2322.62 | 2337.1408 | 2331.6979 | 2338.803 |
Rank | 1 | 4 | 2* | 5 | 3 | 6 | |
F22 | Best | 2300.0001 | 2300 | 2300 | 2300 | 2300 | 2300 |
Rank | 6 | 1 | 1* | 1 | 1 | 1 | |
F23 | Best | 2686.0783 | 2705.8679 | 2400.0142 | 2690.7118 | 2683.8563 | 2692.4707 |
Rank | 3 | 6 | 1* | 4 | 2 | 5 | |
F24 | Best | 2866.0172 | 2856.0607 | 2850.4693 | 2859.1953 | 2868.3988 | 2874.6651 |
Rank | 4 | 2 | 1* | 3 | 5 | 6 | |
F25 | Best | 2883.5398 | 2883.5223 | 2883.5003 | 2883.451 | 2883.6519 | 2883.5782 |
Rank | 4 | 3 | 2* | 1 | 6 | 5 | |
F26 | Best | 2800.0031 | 2800.0002 | 2800 | 2800 | 2800 | 2800 |
Rank | 6 | 5 | 1* | 1 | 1 | 1 | |
F27 | Best | 3207.1547 | 3212.6521 | 3204.6351 | 3206.1916 | 3221.5106 | 3204.6461 |
Rank | 4 | 5 | 1* | 3 | 6 | 2 | |
F28 | Best | 3100.0457 | 3107.0976 | 3100.0605 | 3115.6256 | 3110.9103 | 3102.145 |
Rank | 1 | 4 | 2* | 6 | 5 | 3 | |
F29 | Best | 3302.0656 | 3303.6355 | 3367.2246 | 3299.6103 | 3377.0103 | 3384.3855 |
Rank | 2 | 3 | 4* | 1 | 5 | 6 | |
F30 | Best | 5894.5695 | 5960.129 | 5367.0285 | 6018.1299 | 6006.2421 | 6043.4467 |
Rank | 2 | 3 | 1* | 5 | 4 | 6 | |
Mean rank | 3.6 | 3.33 | 1.57* | 3.67 | 3.47 | 4.13 | |
