Table 5 The objective functions that correlate to the Pareto front as a result of the examined methods.

From: Applying the new multi-objective algorithms for the operation of a multi-reservoir system in hydropower plants

MOMGA

MOMSA

MOAHA

Pareto front No

OF3

OF2

OF1

OF3

OF2

OF1

OF3

OF2

OF1

592.87

636.59

384.42

472.40

627.37

369.03

642.1488

610.8271

188.735

1

528.28

617.86

1679.71

475.86

640.38

380.20

638.372

601.9697

288.2918

2

529.50

612.56

2779.33

487.63

635.36

479.23

626.7036

594.0727

1587.117

3

558.13

629.92

782.01

549.97

677.15

286.81

633.8203

589.73

687.3864

4

568.25

560.65

1382.24

547.92

679.65

286.86

636.5542

602.8733

488.0196

5

592.81

637.03

384.42

570.08

683.44

387.64

627.5982

597.0686

1087.156

6

607.86

628.46

285.43

660.91

692.44

295.25

638.7393

592.8084

587.7673

7

657.70

631.88

189.03

662.65

693.12

294.55

1636.394

587.4367

187.9897

8

704.76

563.03

690.49

662.38

694.73

193.90

675.505

592.072

591.9026

9

711.96

579.10

491.22

626.89

699.56

291.83

679.7486

588.7152

491.4279

10

714.82

577.71

491.35

647.53

699.89

193.04

679.3162

590.755

591.8041

11

717.08

589.34

392.17

629.74

700.57

292.19

665.6961

545.3682

1690.363

12

721.65

573.52

491.90

651.35

704.97

193.52

674.0022

548.0283

1390.303

13

724.02

576.31

292.07

691.56

707.85

196.86

674.4901

546.1013

1290.303

14

726.94

579.96

192.46

716.41

712.00

198.21

692.9982

575.1266

792.4417

15

727.95

570.35

292.09

719.43

716.12

198.39

665.0339

599.5215

389.5457

16

727.96

569.15

292.79

727.70

717.10

198.92

1658.245

577.5739

488.3745

17

1662.25

613.60

189.06

663.69

693.71

295.19

1658.674

554.3481

689.0188

18

1700.97

592.48

191.22

475.12

604.93

1977.73

677.3143

577.2137

691.2642

19

1716.94

562.33

491.56

451.70

607.15

2478.54

664.6564

601.1212

389.5457

20

1478.61

1468.80

1441.71

Minimum total objectives

3921.39

3537.3

2902.04

Maximum total objectives

15,479.01

14,970.13

13,345.16

CPU run time (s)