Table 7 Mean and standard deviation of the (a) EMS, (b) EMWT and (c) EMFT objective value of the considered algorithms in the testing phase.

From: Learning dispatching rules via novel genetic programming with feature selection in energy-aware dynamic job-shop scheduling

Scenarios

RBR

SGP

SGP-FS

NGP

NGP-FS

(a) Mean and standard deviation of the EMS objective value of the considered algorithms in the testing phase

 (20, 2, 80%)

857.25 ± 12.79 (PT + WINQ)

854.14 ± 8.21

858.75 ± 5.66

846.37 ± 8.42

842.81 ± 6.17 (+ , + , + , +)

 (20, 2, 90%)

956.12 ± 20.25 (2PT + NPT + WINQ)

929.57 ± 10.27

939.65 ± 7.38

925.31 ± 18.25

924.54 ± 19.77 (+ , + , + , +)

 (20, 2, 99%)

813.15 ± 20.13 (PT + WINQ)

825.34 ± 10.56

837.57 ± 16.47

828.34 ± 13.34

734.88 ± 4.58 (+ , + , + , +)

 (20, 4, 80%)

892.34 ± 16.57 (PT + WINQ)

893.12 ± 11.58

897.34 ± 14.16

891.27 ± 13.78

887.24 ± 12.24 (+ , + , + , +)

 (20, 4, 90%)

920.57 ± 25.37 (PT + WINQ)

921.63 ± 17.41

925.58 ± 18.34

915.67 ± 27.81

916.52 ± 28.61(+ , + , + , =)

 (20, 4, 99%)

1129.34 ± 15.22 (COVERT)

1122.34 ± 3.3

1138.85 ± 25.15

1113.78 ± 18.67

1114.45 ± 15.28 (+ , + , + , =)

 (20, 6, 80%)

935.37 ± 21.09 (COVERT)

927.27 ± 11.57

933.58 ± 8.18

925.38 ± 17.35

921.21 ± 15.29 (+ , + , + , +)

 (20, 6, 90%)

898.25 ± 14.37 (PT + WINQ)

897.37 ± 11.24

899.62 ± 10.48

894.87 ± 15.16

892.54 ± 12.38 (+ , + , + , =)

 (20, 6, 99%)

917.25 ± 25.02 (SL/RO)

918.66 ± 15.27

919.27 ± 18.34

913.28 ± 12.28

915.37 ± 10.48 (+ , + , + , +)

 (50, 2, 80%)

884.28 ± 18.62 (PT + WINQ)

883.24 ± 4.69

885.19 ± 5.16

878.32 ± 5.15

875.27 ± 4.29 (+ , + , + , +)

 (50, 2, 90%)

975.51 ± 15.92 (PT + WINQ)

969.17 ± 8.56

972.29 ± 9.71

969.19 ± 4.31

965.18 ± 5.57 (+ , + , + , +)

 (50, 2, 99%)

1236.24 ± 56.21 (2PT + NPT + WINQ)

1223.78 ± 13.34

1245.56 ± 45.75

1175.73 ± 11.34

1115.48 ± 12.15 (+ , + , + , +)

 (50, 4, 80%)

847.25 ± 13.15 (2PT + NPT + WINQ)

847.37 ± 5.85

851.34 ± 10.62

837.14 ± 6.75

834.28 ± 5.23 (+ , + , + , +)

 (50, 4, 90%)

803.5 ± 38.27 (COVERT)

799.45 ± 20.26

810.26 ± 25.15

787.12 ± 20.10

785.14 ± 15.34 (+ , + , + , =)

 (50, 4, 99%)

877.97 ± 20.25 (RR)

875.15 ± 10.63

885.84 ± 12.16

880.63 ± 7.27

867.23 ± 10.34 (+ , + , + , +)

 (50, 6, 80%)

848.89 ± 30.45 (PT + WINQ)

845.52 ± 14.06

856.29 ± 13.81

842.87 ± 11.93

837.65 ± 14.34 (+ , + , + , +)

 (50, 6, 90%)

867.34 ± 19.78 (SL/RO)

869.29 ± 14.43

872.37 ± 11.67

860.25 ± 12.29

854.34 ± 13.26 (+ , + , + , +)

 (50, 6, 99%)

875.35 ± 13.38 (COVERT)

878.67 ± 7.88

882.34 ± 8.13

869.65 ± 6.08

864.21 ± 5.12 (+ , + , + , +)

 (100, 2, 80%)

961.67 ± 7.14 (2PT + NPT + WINQ)

958.97 ± 5.76

963.79 ± 5.28

941.18 ± 4.47

865.28 ± 3.68 (+ , + , + , +)

 (100, 2, 90%)

941.25 ± 25.94 (PT + WINQ)

938.15 ± 18.13

945.17 ± 17.99

926.48 ± 17.79

917.26 ± 16.52 (+ , + , + , +)

 (100, 2, 99%)

947.57 ± 22.46 (2PT + NPT + WINQ)

942.68 ± 13.57

952.49 ± 26.14

905.37 ± 12.21

853.23 ± 14.13 (+ , + , + , +)

 (100, 4, 80%)

935.54 ± 25.65 (PT + WINQ)

934.32 ± 3.48

940.14 ± 8.27

927.37 ± 6.28

871.57 ± 4.67 (+ , + , + , +)

 (100, 4, 90%)

842.83 ± 32.71 (COVERT)

840.18 ± 25.06

851.29 ± 21.28

829.16 ± 20.42

825.84 ± 20.28 (+ , + , + , +)

 (100, 4, 99%)

1301.55 ± 10.68 (PT + WINQ)

1283.67 ± 15.47

1302.47 ± 22.09

1162.28 ± 15.13

1056.42 ± 14.67 (+ , + , + , +)

 (100, 6, 80%)

827.26 ± 43.24 (COVERT)

822.71 ± 25.16

832.71 ± 36.30

811.06 ± 30.95

898.08 ± 32.16 (+ , + , + , +)

 (100, 6, 90%)

898.05 ± 75.36 (COVERT)

895.78 ± 14.26

815.48 ± 24.21

887.26 ± 18.81

881.27 ± 18.28 (+ , + , + , +)

 (100, 6, 99%)

842.34 ± 25.38 (SL/RO)

837.85 ± 4.87

849.92 ± 13.51

834.91 ± 8.29

832.35 ± 6.45 (+ , + , + , +)

(b) Mean and standard deviation of the EMWT objective value of the considered algorithms in the testing phase

 (20, 2, 80%)

1783.27 ± 85.48 (WATC)

1726.94 ± 87.61

1794.65 ± 121.26

1789 ± 99.34

1368.67 ± 71.27 (+ , + , + , +)

 (20, 2, 90%)

2389.42 ± 68.15 (PT + WINQ)

2374.36 ± 68.27

2383.19 ± 68.67

2364.22 ± 67.27

2329.45 ± 48.38 (+ , + , + , +)

 (20, 2, 99%)

2924.32 ± 78.31 (WATC)

2914.53 ± 85.25

2945.96 ± 98.67

2847.29 ± 105.28

2515.84 ± 23.56 (+ , + , + , +)

 (20, 4, 80%)

2687.66 ± 34.98 (WATC)

2699.39 ± 32.43

2713.47 ± 44.21

2616.48 ± 48.16

2459.24 ± 29.13 (+ , + , + , +)

 (20, 4, 90%)

3796.54 ± 19.58 (2PT + NPT + WINQ)

3834.67 ± 22.15

3867.49 ± 24.14

3791.94 ± 20.36

3579.29 ± 25.41 (+ , + , + , +)

 (20, 4, 99%)

3948.76 ± 25.48 (PT + WINQ)

3951.48 ± 20.95

3995.37 ± 28.31

3927.64 ± 33.78

3475.24 ± 20.28 (+ , + , + , +)

 (20, 6, 80%)

3589.76 ± 21.79 (COVERT)

3607.38 ± 24.13

3635.07 ± 32.95

3665.67 ± 28.37

3637.85 ± 27.12 (+ , + , + , +)

 (20, 6, 90%)

3837.95 ± 40.15 (COVERT)

3825.11 ± 50.48

3837.59 ± 64.37

3812.48 ± 75.05

3858.24 ± 64.27 (+ , + , + , +)

 (20, 6, 99%)

2795.61 ± 16.47(RR)

2784.29 ± 11.23

2894.82 ± 17.89

2737.33 ± 9.34

2331.11 ± 8.97 (+ , + , + , +)

 (50, 2, 80%)

2484.58 ± 16.87 (PT + WINQ)

2413.41 ± 15.26

2485.29 ± 2321

2378.52 ± 14.35

1957.39 ± 15.21 (+ , + , + , +)

 (50, 2, 90%)

1768.52 ± 24.19 (PT + WINQ)

1769.37 ± 25.48

1872.94 ± 47.58

1699.31 ± 23.57

1575.28 ± 12.96 (+ , + , + , +)

 (50, 2, 99%)

2395.77 ± 18.59 (COVERT)

2395.56 ± 39.71

2428.27 ± 41.82

2385.52 ± 27.65

1835.56 ± 19.24 (+ , + , + , +)

 (50, 4, 80%)

4558.98 ± 21.44 (2PT + NPT + WINQ)

4607.54 ± 21.64

4692.23 ± 28.26

4548.12 ± 24.19

4435.61 ± 24.24 (+ , + , + , +)

 (50, 4, 90%)

2514.67 ± 32.78 (COVERT)

2519.53 ± 37.79

2520.28 ± 35.27

2487.55 ± 31.72

2399.47 ± 25.67 (+ , + , + , +)

 (50, 4, 99%)

3256.67 ± 19.74 (SL/RO)

3255.25 ± 19.63

3267.64 ± 21.26

3150.47 ± 18.25

3138.33 ± 19.31 (+ , + , + , +)

 (50, 6, 80%)

2683.89 ± 12.21 (PT + WINQ)

2645.12 ± 15.17

2658.29 ± 18.35

2799.28 ± 13.72

2037.45 ± 12.13 (+ , + , + , +)

 (50, 6, 90%)

3667.31 ± 30.38 (SL/RO)

3660.37 ± 31.83

3665.37 ± 28.67

3560.25 ± 42.69

3454.15 ± 28.35 (+ , + , + , +)

 (50, 6, 99%)

1972.59 ± 14.72 (COVERT)

1989.37 ± 15.18

982.16 ± 11.23

869.45 ± 6.27

689.25 ± 8.74 (+ , + , + , +)

 (100, 2, 80%)

3651.37 ± 15.18 (2PT + NPT + WINQ)

3648.26 ± 15.24

3686.81 ± 15.27

3531.48 ± 34.61

3225.76 ± 15.28 (+ , + , + , +)

 (100, 2, 90%)

3526.65 ± 26.18 (PT + WINQ)

3518.15 ± 27.13

3545.45 ± 24.99

3326.21 ± 28.81

3117.46 ± 26.42 (+ , + , + , +)

 (100, 2, 99%)

2466.67 ± 15.86 (2PT + NPT + WINQ)

2452.68 ± 15.29

2487.59 ± 17.21

2385.71 ± 16.21

1983.65 ± 10.13 (+ , + , + , +)

 (100, 4, 80%)

2530.64 ± 24.61 (PT + WINQ)

2529.32 ± 20.35

2635.74 ± 22.59

2482.77 ± 27.14

2415.57 ± 18.27 (+ , + , + , +)

 (100, 4, 90%)

2442.83 ± 53.92 (COVERT)

2483.58 ± 57.06

2541.29 ± 58.47

2429.56 ± 42.47

2285.95 ± 41.18 (+ , + , + , +)

 (100, 4, 99%)

2539.55 ± 33.37 (PT + WINQ)

2533.17 ± 35.28

2618.37 ± 34.29

2429.78 ± 37.53

2176.42 ± 35.87 (+ , + , + , +)

 (100, 6, 80%)

1927.16 ± 16.05 (COVERT)

1928.81 ± 18.26

1999.87 ± 18.27

1911.26 ± 12.96

1618.48 ± 14.36 (+ , + , + , +)

 (100, 6, 90%)

2798.25 ± 18.17 (COVERT)

2795.78 ± 15.19

2815.48 ± 20.38

2687.26 ± 16.71

2481.47 ± 10.54 (+ , + , + , +)

 (100, 6, 99%)

2922.54 ± 37.56 (COVERT)

2917.85 ± 34.73

3149.92 ± 33.74

2834.91 ± 28.29

2232.55 ± 17.34 (+ , + , + , +)

(c) Mean and standard deviation of the EMFT objective value of the considered algorithms in the testing phase

 (20, 2, 80%)

461.21 ± 9.45 (PT + WINQ)

455.74 ± 3.07

459.27 ± 3.14

451.35 ± 2.37

435.57 ± 2.76 (+ , + , + , +)

 (20, 2, 90%)

442.89 ± 11.25 (2PT + NPT + WINQ)

438.68 ± 4.57

441.56 ± 5.34

433.63 ± 4.21

422.28 ± 3.58 (+ , + , + , +)

 (20, 2, 99%)

455.33 ± 12.42 (PT + WINQ)

355.68 ± 5.64

351.61 ± 5.39

315.27 ± 4.59

318.25 ± 3.31 (+ , + , + , +)

 (20, 4, 80%)

394.23 ± 7.19 (PT + WINQ

388.57 ± 5.14

392.25 ± 5.29

386.63 ± 3.13

381.23 ± 3.17 (+ , + , + , +)

 (20, 4, 90%)

438.62 ± 10.86 (PT + WINQ)

431.18 ± 5.42

434.69 ± 8.92

428.37 ± 7.65

422.42 ± 7.64 (+ , + , + , +)

 (20, 4, 99%)

498.67 ± 15.38 (PT + WINQ)

489.28 ± 7.13

494.23 ± 6.13

487.48 ± 5.17

465.15 ± 3.27 (+ , + , + , +)

 (20, 6, 80%)

328.52 ± 13.97 (PT + WINQ)

329.15 ± 4.49

339.60 ± 5.27

333.75 ± 3.15

328.75 ± 4.08 (+ , + , + , +)

 (20, 6, 90%)

405.79 ± 15.28 (PT + WINQ)

396.33 ± 16.01

401.75 ± 6.27

494.67 ± 6.15

485.84 ± 3.47 (+ , + , + , +)

 (20, 6, 99%)

634.84 ± 28.76 (PT + WINQ)

630.52 ± 6.35

633.34 ± 8.48

716.57 ± 4.17

556.21 ± 3.12 (+ , + , + , +)

 (50, 2, 80%)

451.85 ± 11.34 (PT + WINQ)

441.25 ± 6.93

447.69 ± 6.09

435.12 ± 6.25

425.26 ± 6.26 (+ , + , + , +)

 (50, 2, 90%)

589.62 ± 15.05 (PT + WINQ)

588.23 ± 5.57

585.49 ± 5.25

586.19 ± 2.74

575.38 ± 2.11 (+ , + , + , +)

 (50, 2, 99%)

695.27 ± 34.23 (2PT + NPT + WINQ)

687.36 ± 6.24

691.21 ± 5.32

685.12 ± 3.71

635.18 ± 3.27 (+ , + , + , +)

 (50, 4, 80%)

517.98 ± 45.24 (2PT + NPT + WINQ)

498.26 ± 4.95

515.23 ± 4.17

485.15 ± 3.94

480.69 ± 2.76 (+ , + , + , +)

 (50, 4, 90%)

531.16 ± 48.28 (PT + WINQ)

525.15 ± 5.79

528.15 ± 6.08

521.67 ± 4.88

512.66 ± 2.89 (+ , + , + , +)

 (50, 4, 99%)

727.57 ± 59.25 (PT + WINQ)

724.27 ± 9.73

725.24 ± 10.16

691.23 ± 7.13

628.58 ± 4.15 (+ , + , + , +)

 (50, 6, 80%)

458.19 ± 12.79 (PT + WINQ)

448.12 ± 8.15

456.29 ± 8.91

445.81 ± 8.12

437.25 ± 6.21 (+ , + , + , +)

 (50, 6, 90%)

597.11 ± 31.67 (PT + WINQ)

592.29 ± 14.43

596.17 ± 9.23

585.36 ± 7.19

574.37 ± 6.28 (+ , + , + , +)

 (50, 6, 99%)

795.25 ± 67.36 (2PT + NPT + WINQ)

789.37 ± 6.98

793.26 ± 7.27

786.35 ± 5.98

708.48 ± 5.12 (+ , + , + , +)

 (100, 2, 80%)

581.27 ± 45.48 (2PT + NPT + WINQ)

574.21 ± 6.27

583.29 ± 6.18

586.18 ± 5.62

575.86 ± 3.24 (+ , + , + , +)

 (100, 2, 90%)

741.55 ± 56.34 (PT + WINQ)

732.25 ± 7.27

738.47 ± 7.25

726.58 ± 6.71

718.46 ± 4.23 (+ , + , + , +)

 (100, 2, 99%)

932.17 ± 84.52 (2PT + NPT + WINQ)

912.38 ± 3.59

926.19 ± 4.23

898.27 ± 4.62

813.25 ± 2.73 (+ , + , + , +)

 (100, 4, 80%)

665.27 ± 43.35 (PT + WINQ)

651.12 ± 6.34

665.24 ± 6.15

640.27 ± 4.21

645.28 ± 4.20 (+ , + , + , +)

 (100, 4, 90%)

653.83 ± 62.71 (2PT + NPT + WINQ)

646.18 ± 7.08

651.29 ± 8.23

639.26 ± 7.12

627.34 ± 6.18 (+ , + , + , +)

 (100, 4, 99%)

915.34 ± 82.56 (PT + WINQ)

908.27 ± 8.26

912.47 ± 8.09

904.28 ± 7.58

856.12 ± 7.12 (+ , + , + , +)

 (100, 6, 80%)

637.45 ± 76.19 (PT + WINQ)

628.31 ± 8.09

632.78 ± 8.31

621.76 ± 7.25

598.48 ± 5.52 (+ , + , + , +)

 (100, 6, 90%)

768.34 ± 76.16 (PT + WINQ)

761.78 ± 14.27

765.25 ± 24.11

757.26 ± 8.23

725.17 ± 8.56 (+ , + , + , +)

 (100, 6, 99%)

956.54 ± 98.38 (PT + WINQ)

938.75 ± 7.48

952.92 ± 8.35

928.11 ± 7.34

858.16 ± 5.02 (+ , + , + , +)

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