SCA: A Sine Cosine Algorithm for solving optimization problems
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...π§ β π£πππ’π π β π£πππ’π πΌ/π , πΌ = 0.05 πΌ/π, πΌ = 0.10 T rad itio n al alg o rith m s PBIL 9.9878 8.6010E-24 0.0042 0.0083 DA 8.2494 7.9860E-17 0.0045 0.0091 SCA 6.9851 1.4240E-12 0.005 0.01 MFO 6.7639 6.7120E-12 0.0056 0.0111 PSO 4.9307 4.0900E-07 0.0063 0.0125 WOA 4.2669 9.9060E-06 0.0071 0.0143 GOA 3.8877 5.0540E-05 0.0083 0.0167 ALO 3.7296 9.5740E-05 0.01 0.02 GWO 2.9394 1.6460E-03 0.0125 0.025 SSA 2.3389 9.6680E-03 0.0167 0.0333 MVO 1.7384 0.04111 0.025 0.05 DE 1.6436 0.05009 0.05 0.1 A d v an ced alg o rith m s BLPSO 12.0748 7.1760E-34 0.00556 0.01111 CLPSO 10.7331 3.5580E-27 0.00625 0.0125 CSSA 9.3915 2.9580E-21 0.00714 0.01429 CDLOBA 8.0498 4.1460E-16 0.00833 0.01667 CBA 6.7082 9.8520E-12 0.01 0.02 RCBA 5.3666 4.0120E-08 0.0125 0.025 IWOA 4.0249 2.8500E-05 0.01667 0.03333 m_SCA 2.6833 0.00365 0.025 0.05 LWOA 1.3416 0.08986 0.05 0.1 E v alu atio n PSO 5.648039 8.1160E-09 0.005 0.01 MFO 4.896673 4.8730E-07 0.0056 0.0111 SCA 4.801299 7.8820E-07 0.00625 0.0125 GOA 3.532738 2.0570E-04 0.0071 0.0143 MVO 2.644126 0.0041 0.0083 0.0167 SSA 2.422361 0.0077 0.01 0.02 GWO 2.130033 0.0166 0.0125 0.025 WOA 1.901289 0.0286 0.0167 0.0333 AGA 1.156902 0.1237 0.025 0.05 DE 1.077811 0.1406 0.05 0.1...
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...The first kind mainly simulate physical phenomena, apply mathematical rules or methodologies including: Multi-Verse Optimizer (MVO) [3], Gravitational Local Search Algorithm (GLSA) [4], Charged System Search (CSS) [5], Gravitational Search Algorithm (GSA) [6], Sine Cosine Algorithm (SCA) [7], Simulated Annealing (SA) [8], Teaching-Learning-Based Optimization (TLBO) [9], Central Force Optimization (CFO) [10] and Tabu Search (TS) [11]....
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...The MAs used for comparison include well-regarded and recent ones: WOA [50], GWO [21], MFO [23], BA [20], SCA [7], FA[51], PSO[18], SSA [52], MVO [3], ALO...
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...Table 15 True p-value obtained from comparison on thirty-three benchmarks F1 F2 F3 F4 F5 F6 F7 F8 F9 F10 F11 T rad itio n al M A s #TSS 2.08E-05 2.08E-05 2.08E-05 2.08E-05 2.08E-05 4.13E-03 2.68E-05 1.34E-04 1.00E+00 2.31E-05 1.00E+00 F12 F13 F14 F15 F16 F17 F18 F19 F20 F21 F22 #TSS 3.71E-05 5.23E-02 5.53E-02 6.34E-03 7.95E-01 1.32E-01 3.26E-01 2.24E-01 1.98E-01 6.88E-02 7.01E-01 F23 F24 F25 F26 F27 F28 F29 F30 F31 F32 F33 #TSS 4.53E-01 7.59E-01 9.96E-01 5.34E-01 4.96E-01 2.29E-05 2.08E-05 2.63E-04 4.36E-01 2.08E-05 2.16E-05 A d v a n ced F1 F2 F3 F4 F5 F6 F7 F8 F9 F10 F11 #TSS 1.56E-05 1.56E-05 1.56E-05 1.56E-05 1.85E-02 1.40E-03 2.60E-03 1.60E-05 1.00E+00 2.74E-05 1.00E+00 F12 F13 F14 F15 F16 F17 F18 F19 F20 F21 F22 #TSS 1.83E-01 4.91E-01 1.25E-01 1.91E-01 9.93E-01 1.86E-05 7.57E-01 5.59E-04 1.56E-05 3.22E-05 2.04E-03 F23 F24 F25 F26 F27 F28 F29 F30 F31 F32 F33 #TSS 3.37E-01 5.58E-02 3.91E-02 3.62E-01 8.15E-01 1.56E-05 1.56E-05 7.49E-05 7.75E-01 1.56E-05 1.64E-05 Table 166 Results of Friedman test of iterative version and function evaluation version Iterative version on F1-33 SMA SCA SSA GWO MFO WOA GOA DA ALO MVO PBIL PSO DE Avg 3.057 9.396 5.180 5.280 8.037 6.735 6.690 10.580 6.124 5.013 12.228 7.865 4.815 Rank 1 11 4 5 10 8 7 12 6 3 13 9 2 Iterative version on F1-33 SMA BLPS CLPS CBA RCBA CDLO m_SC IWOA LWOA CSSA Avg 2.297 7.578 6.996 5.507 5.408 6.100 5.000 4.710 4.907 6.497 Rank 1 10 9 6 5 7 4 2 3 8 Evaluation version on F1-21 SMA SCA SSA GWO MFO WOA GOA MVO PSO DE AGA Avg 3.189 8.103 5.668 5.369 8.201 5.135 6.805 5.895 8.970 4.292 4.373 Rank 1 9 6 5 10 4 8 7 11 2 3 Table 177 Holmsβ test (take SMA as the control algorithm) πππ΄ ππ....
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...The MAs used for comparison include well-regarded and recent ones: WOA [50], GWO [21], MFO [23], BA [20], SCA [7], FA[51], PSO[18], SSA [52], MVO [3], ALO [53], PBIL [54], DE [55] and advanced MAs: AGA[56], BLPSO [57], CLPSO [58], CBA [59], RCBA [60], CDLOBA [61], m_SCA [62], IWOA [63], LWOA [64], and CSSA [65]....
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