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

1,365,932,733

0.969

1,366,215,071

1.085

1,366,941,579

1.562

P2

1,356,964,622

1.062

1,357,249,992

1.144

1,357,960,054

1.572

P3

1,366,670,095

1.093

1,366,946,572

1.248

1,367,675,025

1.65

P4

1,364,344,024

1.047

1,364,630,536

1.145

1,365,354,097

1.578

P5

1,359,252,277

1.109

1,359,550,905

1.265

1,360,243,625

1.578

P6

1,362,703,027

1.031

1,362,989,604

1.137

1,363,687,229

1.547

P7

1,357,648,342

1.094

1,357,931,004

1.248

1,358,646,263

1.532

P8

1,361,734,440

1.078

1,362,015,230

1.234

1,362,771,012

1.578

P9

1,363,335,394

1.094

1,363,626,057

1.226

1,364,326,431

1.578

P10

1,354,662,978

1.062

1,354,940,548

1.126

1,355,672,184

1.625

P11

1,359,010,784

1.031

1,359,297,671

1.111

1,360,015,221

1.578

P12

1,360,290,820

1.031

1,360,566,551

1.118

1,361,275,760

1.484

P13

1,359,813,107

1.015

1,360,106,147

1.136

1,360,804,455

1.516

P14

1,360,229,705

1.094

1,360,524,059

1.190

1,361,194,499

1.563

P15

1,357,065,375

1

1,357,352,530

1.080

1,358,068,651

1.485

P16

1,366,116,379

1.063

1,366,414,875

1.185

1,367,101,877

1.797

P17

1,354,295,387

1.016

1,354,575,049

1.166

1,355,307,736

1.547

P18

1,362,453,698

1.093

1,362,753,165

1.196

1,363,466,065

1.656

P19

1,351,212,750

1.047

1,351,506,098

1.133

1,352,228,221

1.594

P20

1,354,546,726

1.062

1,354,825,085

1.156

1,355,567,185

1.593

P21

1,361,671,542

1.078

1,361,968,932

1.167

1,362,652,718

1.515

P22

1,365,090,355

1.031

1,365,366,240

1.125

1,366,081,015

1.531

P23

1,353,711,255

1.015

1,353,984,975

1.125

1,354,692,174

1.594

P24

1,359,167,606

1.078

1,359,454,798

1.239

1,360,142,833

1.547

P25

1,354,759,090

1.078

1,355,052,259

1.185

1,355,756,040

1.546

P26

1,360,824,145

0.984

1,361,122,302

1.101

1,361,829,294

1.594

P27

1,357,519,457

1.047

1,357,817,161

1.210

1,358,490,606

1.516

P28

1,355,437,009

1.047

1,355,724,226

1.148

1,356,416,967

1.562

P29

1,360,832,833

0.985

1,361,119,561

1.126

1,361,815,955

1.578

P30

1,349,511,932

1.062

1,349,797,353

1.191

1,350,507,838

1.578