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

1,347,812,101

0.984

1,348,043,655

1.099

1,348,824,104

1.437

P2

1,353,943,093

0.875

1,354,165,275

1.037

1,354,916,518

1.5

P3

1,353,589,922

0.797

1,353,818,814

0.918

1,354,572,437

1.406

P4

1,348,651,591

0.875

1,348,874,253

0.988

1,349,651,010

1.438

P5

1,353,236,978

0.859

1,353,454,443

0.970

1,354,223,675

1.422

P6

1,345,291,759

0.859

1,345,512,522

0.954

1,346,286,225

1.5

P7

1,354,089,798

0.875

1,354,306,453

0.976

1,355,101,717

1.578

P8

1,350,526,131

0.89

1,350,746,131

1.032

1,351,547,781

1.562

P9

1,347,779,924

0.844

1,348,003,925

0.939

1,348,783,579

1.563

P10

1,352,052,432

0.968

1,352,282,416

1.141

1,353,075,218

1.547

P11

1,348,474,977

0.875

1,348,704,892

0.998

1,349,452,863

1.531

P12

1,358,050,071

0.859

1,358,285,014

1.010

1,358,999,314

1.61

P13

1,360,492,873

0.875

1,360,727,422

0.989

1,361,471,188

1.563

P14

1,347,055,192

0.86

1,347,287,155

0.949

1,348,053,275

1.578

P15

1,346,813,104

0.86

1,347,032,769

0.957

1,347,825,533

1.409

P16

1,351,598,681

0.859

1,351,818,451

0.990

1,352,597,768

1.556

P17

1,352,634,141

0.844

1,352,873,693

0.938

1,353,614,996

1.438

P18

1,347,143,013

0.828

1,347,368,659

0.928

1,348,101,467

1.422

P19

1,347,578,203

0.844

1,347,811,739

0.996

1,348,549,057

1.375

P20

1,354,172,979

0.86

1,354,405,219

1.024

1,355,188,299

1.407

P21

1,353,131,970

0.844

1,353,350,636

0.974

1,354,106,286

1.407

P22

1,352,195,677

0.875

1,352,423,658

1.000

1,353,198,611

1.437

P23

1,354,067,995

0.875

1,354,309,967

1.036

1,355,054,115

1.532

P24

1,348,354,628

0.828

1,348,587,758

0.950

1,349,338,895

1.478

P25

1,348,863,378

0.86

1,349,093,359

1.030

1,349,868,041

1.578

P26

1,350,507,863

0.984

1,350,725,025

1.156

1,351,509,090

1.516

P27

1,351,696,314

1

1,351,938,538

1.191

1,352,686,083

1.453

P28

1,348,216,115

1

1,348,458,524

1.139

1,349,190,279

1.469

P29

1,349,155,465

0.969

1,349,378,346

1.123

1,350,167,144

1.406

P30

1,355,404,108

0.968

1,355,636,560

1.078

1,356,383,297

1.422