Problem instance

number

Weak bound

(relaxed formulation I)

Hybrid formulation bound (relaxed weak formulation with most promising strong linking constraints added)

Strong bound

(relaxed formulation II)

Value

CPU time

Value

CPU time

Value

CPU time

P1

1,356,765,481

1

1,356,988,805

1.028

1,357,747,787

1.375

P2

1,348,578,687

0.906

1,348,784,480

0.934

1,349,566,313

1.375

P3

1,350,776,977

0.89

1,351,005,393

0.910

1,351,787,791

1.391

P4

1,356,692,279

0.89

1,356,918,304

0.913

1,357,678,393

1.337

P5

1,359,305,911

0.953

1,359,517,283

0.975

1,360,284,488

1.39

P6

1,349,187,512

0.922

1,349,390,565

0.951

1,350,173,750

1.359

P7

1,347,497,209

0.953

1,347,721,702

0.979

1,348,495,827

1.406

P8

1,351,561,595

0.922

1,351,780,684

0.943

1,352,539,359

1.39

P9

1,352,908,377

0.906

1,353,135,936

0.935

1,353,917,629

1.375

P10

1,355,180,785

0.906

1,355,411,030

0.928

1,356,176,036

1.359

P11

1,349,471,170

0.968

1,349,679,258

0.990

1,350,467,442

1.422

P12

1,347,863,661

0.922

1,348,079,993

0.948

1,348,867,681

1.422

P13

1,354,473,571

0.922

1,354,688,119

0.947

1,355,463,506

1.359

P14

1,350,205,726

0.922

1,350,433,235

0.948

1,351,193,519

1.344

P15

1,349,060,862

0.922

1,349,290,067

0.945

1,350,041,009

1.375

P16

1,347,587,320

0.859

1,347,789,863

0.886

1,348,577,355

1.453

P17

1,351,522,612

0.813

1,351,733,179

0.839

1,352,521,657

1.359

P18

1,348,302,161

0.828

1,348,510,204

0.847

1,349,326,170

1.422

P19

1,357,334,766

0.828

1,357,545,560

0.852

1,358,323,179

1.406

P20

1,346,200,443

0.844

1,346,428,489

0.867

1,347,193,192

1.485

P21

1,356,509,204

0.828

1,356,734,656

0.852

1,357,494,571

1.391

P22

1,350,745,322

0.829

1,350,970,356

0.852

1,351,735,380

1.438

P23

1,356,703,210

0.812

1,356,919,469

0.832

1,357,678,909

1.422

P24

1,357,978,256

0.844

1,358,191,187

0.864

1,358,962,351

1.5

P25

1,349,813,482

0.828

1,350,026,212

0.848

1,350,818,186

1.422

P26

1,354,216,441

0.937

1,354,434,470

0.963

1,355,225,303

1.516

P27

1,354,135,174

0.844

1,354,343,981

0.871

1,355,144,688

1.344

P28

1,345,665,627

0.844

1,345,879,453

0.869

1,346,652,596

1.407

P29

1,353,034,625

0.859

1,353,261,123

0.883

1,354,003,682

1.375

P30

1,352,589,054

0.844

1,352,793,971

0.869

1,353,593,395

1.343