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

1,349,044,304

0.953

1,349,310,336

1.076

1,350,052,277

1.328

P2

1,341,330,308

0.891

1,341,585,965

1.079

1,342,364,193

1.344

P3

1,357,367,491

0.875

1,357,634,078

1.040

1,358,357,501

1.313

P4

1,344,761,701

0.907

1,345,022,451

1.072

1,345,749,092

1.312

P5

1,353,950,432

0.906

1,354,231,377

1.065

1,354,948,263

1.343

P6

1,345,725,674

0.86

1,345,986,206

1.060

1,346,727,389

1.328

P7

1,350,064,031

0.875

1,350,340,929

0.991

1,351,070,255

1.344

P8

1,349,599,349

0.859

1,349,856,043

1.048

1,350,587,142

1.312

P9

1,347,042,608

0.875

1,347,306,898

1.071

1,348,010,275

1.328

P10

1,359,202,269

0.891

1,359,485,934

1.034

1,360,184,283

1.313

P11

1,347,843,751

0.875

1,348,111,163

1.080

1,348,840,103

1.328

P12

1,347,079,789

0.859

1,347,339,910

0.996

1,348,069,301

1.344

P13

1,345,959,280

0.875

1,346,232,645

1.005

1,346,948,448

1.36

P14

1,352,533,674

0.844

1,352,817,571

0.995

1,353,537,564

1.359

P15

1,344,792,939

0.891

1,345,071,043

1.021

1,345,811,206

1.312

P16

1,346,897,235

0.828

1,347,173,079

1.006

1,347,857,811

1.344

P17

1,335,591,579

0.765

1,335,869,115

0.905

1,336,633,363

1.344

P18

1,352,021,379

0.813

1,352,281,103

0.976

1,353,033,815

1.344

P19

1,340,538,436

0.828

1,340,813,112

0.994

1,341,534,569

1.375

P20

1,358,293,736

0.796

1,358,553,985

0.893

1,359,285,053

1.329

P21

1,349,182,387

0.828

1,349,458,565

0.983

1,350,197,272

1.343

P22

1,350,465,764

0.844

1,350,736,127

0.978

1,351,464,235

1.328

P23

1,342,712,142

0.828

1,342,975,448

0.978

1,343,717,026

1.344

P24

1,349,696,083

0.812

1,349,955,090

0.925

1,350,685,192

1.312

P25

1,344,666,743

0.813

1,344,942,265

0.967

1,345,654,739

1.281

P26

1,349,872,300

0.812

1,350,155,773

0.941

1,350,889,585

1.328

P27

1,346,328,212

0.797

1,346,606,633

0.951

1,347,349,390

1.344

P28

1,349,420,910

0.812

1,349,697,811

0.919

1,350,411,598

1.359

P29

1,350,343,978

0.828

1,350,602,029

1.010

1,351,345,376

1.313

P30

1,358,015,527

0.828

1,358,295,142

0.945

1,359,024,827

1.313