Research Article
Solutions to No-Wait Flow Shop Scheduling Problem Using the Flower Pollination Algorithm Based on the Hormone Modulation Mechanism
Table 5
The comparative statistical results between HMM-PFA and DPSO, IIGA, HPSO, HDE, TMIIG, and GA.
| | Problem | | Best | DPSO | IIGA | HPSO | HDE | TMIIG | GA | HMM-PFA | | BRD | ARD | | BRD | ARD | | BRD | ARD | | BRD | ARD | | BRD | ARD | | BRD | ARD | | BRD | ARD | |
| | Rec1 | 20 × 5 | 1526 | 0.00 | 0.00 | 0.01 | 0.00 | 0.00 | 0.02 | 0.26 | 0.66 | 3.90 | 0.00 | 0.00 | 3.10 | — | 0.00 | 0.20 | 0.39 | — | — | 0.00 | 0.00 | 0.018 | | Rec3 | 20 × 5 | 1361 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.02 | 0.00 | 0.44 | 4.80 | 0.00 | 0.00 | 3.10 | — | 0.00 | 0.20 | 0.22 | — | — | 0.00 | 0.00 | 0.018 | | Rec5 | 20 × 5 | 1511 | 0.00 | 0.00 | 0.02 | 0.00 | 0.00 | 0.02 | 0.33 | 0.60 | 4.10 | 0.00 | 0.07 | 3.10 | — | 0.00 | 0.20 | 0.60 | — | — | 0.00 | 0.04 | 0.019 | | Rec7 | 20 × 10 | 2042 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.02 | 0.00 | 0.54 | 6.60 | 0.00 | 0.00 | 3.90 | — | 0.00 | 0.20 | 2.25 | — | — | 0.00 | 0.00 | 0.020 | | Rec9 | 20 × 10 | 2042 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.02 | 0.05 | 0.39 | 6.70 | 0.00 | 0.00 | 3.80 | — | 0.00 | 0.20 | 0.78 | — | — | 0.00 | 0.00 | 0.021 | | Rec11 | 20 × 10 | 1881 | 0.00 | 0.00 | 0.01 | 0.00 | 0.00 | 0.02 | 0.00 | 1.06 | 7.00 | 0.00 | 0.16 | 3.90 | — | 0.00 | 0.20 | 1.33 | — | — | 0.00 | 0.00 | 0.020 | | Rec13 | 20 × 15 | 2545 | 0.00 | 0.00 | 0.01 | 0.00 | 0.00 | 0.02 | 0.00 | 0.63 | 11.00 | 0.00 | 0.00 | 5.10 | — | 0.00 | 0.20 | 0.79 | — | — | 0.00 | 0.00 | 0.015 | | Rec15 | 20 × 15 | 2529 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.02 | 0.00 | 0.36 | 8.60 | 0.00 | 0.00 | 5.20 | — | 0.00 | 0.20 | 1.42 | — | — | 0.00 | 0.00 | 0.016 | | Rec17 | 20 × 15 | 2587 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.02 | 0.00 | 0.15 | 8.60 | 0.00 | 0.00 | 5.20 | — | 0.00 | 0.20 | 0.46 | — | — | 0.00 | 0.00 | 0.015 | | Rec19 | 30 × 10 | 2850 | 0.00 | 0.11 | 0.02 | 0.00 | 0.00 | 0.04 | 0.63 | 1.37 | 23.00 | 0.00 | 0.07 | 10.40 | — | 0.00 | 0.45 | 3.58 | — | — | 0.00 | 0.00 | 0.030 | | Rec21 | 30 × 10 | 2821 | 0.00 | 0.11 | 0.04 | 0.00 | 0.18 | 0.04 | 0.78 | 1.17 | 24.00 | 0.00 | 0.18 | 10.20 | — | 0.07 | 0.45 | 2.48 | — | — | 0.00 | 0.15 | 0.036 | | Rec23 | 30 × 10 | 2700 | 0.00 | 0.07 | 0.05 | 0.00 | 0.00 | 0.04 | 0.11 | 1.30 | 24.00 | 0.00 | 0.11 | 10.40 | — | 0.00 | 0.45 | 3.07 | — | — | 0.00 | 0.01 | 0.032 | | Rec25 | 30 × 15 | 3593 | 0.00 | 0.17 | 0.03 | 0.00 | 0.00 | 0.04 | 0.64 | 1.22 | 32.00 | 0.00 | 0.03 | 15.00 | — | 0.00 | 0.45 | 1.92 | — | — | 0.00 | 0.09 | 0.401 | | Rec27 | 30 × 15 | 3431 | 0.00 | 0.26 | 0.06 | 0.00 | 0.00 | 0.05 | 0.00 | 1.17 | 39.00 | 0.00 | 0.17 | 14.80 | — | 0.01 | 0.45 | 3.91 | — | — | 0.00 | 0.07 | 0.451 | | Rec29 | 30 × 15 | 3291 | 0.00 | 0.06 | 0.02 | 0.00 | 0.00 | 0.06 | 0.36 | 1.34 | 31.00 | 0.00 | 0.18 | 14.90 | — | 0.03 | 0.45 | 2.80 | — | — | 0.00 | 0.13 | 0.480 | | Rec31 | 50 × 10 | 4311 | 0.12 | 0.39 | 0.33 | 0.00 | 0.28 | 0.11 | 1.07 | 1.83 | 122.00 | 0.32 | 0.56 | 3.80 | — | 0.13 | 1.25 | 5.03 | — | — | 0.13 | 0.20 | 0.713 | | Rec33 | 50 × 10 | 4428 | 0.25 | 0.72 | 0.34 | 0.41 | 0.68 | 0.10 | 1.78 | 3.32 | 116.00 | 0.20 | 0.88 | 3.70 | — | 0.30 | 1.25 | 6.39 | — | — | 0.00 | 0.54 | 0.715 | | Rec35 | 50 × 10 | 4397 | 0.00 | 0.39 | 0.34 | 0.00 | 0.16 | 0.10 | 0.84 | 1.80 | 105.00 | 0.25 | 0.75 | 3.70 | — | 0.19 | 1.25 | 5.39 | — | — | 0.00 | 0.83 | 0.690 | | Rec37 | 75 × 20 | 8014 | 0.27 | 0.69 | 1.16 | 0.32 | 0.69 | 0.18 | 2.08 | 2.86 | 635.00 | 0.44 | 0.81 | 14.70 | — | 0.33 | 2.81 | 18.73 | — | — | 0.25 | 0.67 | 1.982 | | Rec39 | 75 × 20 | 8428 | 0.19 | 0.70 | 0.99 | 0.26 | 0.62 | 0.18 | 1.28 | 2.50 | 897.00 | 0.25 | 0.71 | 14.60 | — | 0.46 | 2.81 | 17.29 | — | — | 0.20 | 0.65 | 2.014 | | Rec41 | 75 × 20 | 8442 | 0.36 | 0.71 | 0.88 | 0.37 | 0.75 | 0.18 | 1.90 | 3.19 | 883.00 | 0.00 | 0.73 | 14.70 | — | 0.44 | 2.81 | 17.13 | — | — | 0.00 | 0.69 | 2.135 | | Average | 0.06 | 0.21 | 0.21 | 0.06 | 0.16 | 0.06 | 0.58 | 1.33 | 142.49 | 0.07 | 0.26 | 7.97 | — | 0.09 | 0.79 | 4.57 | — | — | 0.03 | 0.20 | 0.47 | | APRT | 0.0067 | 0.0078 | 4.3732 | 1.5113 | 0.0808 | | 0.0202 |
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