Mixed-Integer Nonlinear Optimization Problems: ANTIGONE 1.0 ...

Mixed-Integer Nonlinear Optimization Problems: ANTIGONE 1.0 Test Suite Ruth Misener1, 2 and Christodoulos A. Floudas1, ∗ 1 Department

of Chemical and Biological Engineering Princeton University; Princeton, NJ 08544-5263; USA 2 Department

of Chemical Engineering Imperial College London; South Kensington SW7 2AZ; UK February 22, 2014

This document outlines the test suite validating ANTIGONE 1.0. We document source files from both the academic literature and well-maintained websites, provide links to the modeling files in GAMS scalar format, and record the relative sizes of each of the problems. To validate ANTIGONE, Table 1 defines a test suite of 2571 problems from standard libraries and the open literature; Tables 2 – 11 in Appendix A give more detailed analysis as to the size and complexity of the individual problems. The examples excluded from the standard test libraries are those which either include functional forms that the current ANTIGONE implementation cannot handle (e.g., trigonometric, min/max, errorf) or have known feasible points where the objective value is minus infinity (plus infinity if MINLP is a maximization problem). Recall that the standard libraries are dynamic entities; we are using the latest versions as of 11 March 2013. The other test cases are from the open literature.

1

Test Cases from minlp.org

The models from minlp.org are documented in Table 10. As of 04 March 2013 there is a group of modeling files labeled Test Set on minlp.org; each modeling file may contain multiple MINLP problems and some modeling files require user input arguments. As it is unclear how to use the files labeled Test Set ∗ To

whom all correspondence should be addressed ([email protected]; Fax: (609)258-0211).

1

Tel: (609)258-4595;

Table 1: MINLP Test Suite of 2571 Problems Problem Class

# Cases

minlp. org

Belgian Chocolate Problem Cascading Tanks Cyclic Scheduling and Control Distillation Sep. Sequences Heat Exchanger Networks Metabolic Networks Multi-Product Batch Plants Periodic Scheduling Pooling Supply Chain Design Three-Echelon Supply Chain Unit Commitment Water Distribution Network Water Treatment Network Crude Oil Scheduling

MIQCQP

BoxQP Circles & Polygon Nesting Crude Oil Scheduling Multi-Period Blending Natural Gas Production Point Packing QAP Randomly-Generated QCQP Reform. GLOBALLib Reform. MINLPLib Standard QP Water Treatment System Water-Using Network

Test Libraries

AMPL Book Lib Bonmin Test Set GLOBALLib LINLib MacMOOPLib MPLLib MINLPLib PrincetonLib

4 8 1 1 3 2 2 13 19 2 8 2 8 18 24 90 35 7 7 3 14 67 135 32 10 15 32 35 34 134 368 39 12 22 249 1116

2

Discrete X X X X X X X X X X X X X X X

X X X

X

Source [19, 20] [26] [23] [10, 11, 12, 13] [22, 57] [28, 29] [27, 32, 59] [14, 15] [42] [58, 60] [46, 47, 61] [45, 62] [7, 21] [2, 1, 31, 48] [35, 43, 44] [8, 55, 56] [30] [36, 37] [33, 34] [38, 39, 52] [4] [3, 40] [5] [24, 41, 50] [9, 24] [51] [17, 18] [16, 53, 54]

X

[25] [6, 49] [24, 41]

X

[9, 24]

on minlp.org, we have compiled a collection of problems from the minlp.org MINLP Library; Table 1 documents their origin.

1.1

4 Belgian Chocolate Problems

The Belgian Chocolate Problems represent stabilizing controller design [19, 20]. bcp5

1.2

bcp6

bcp7

bcp8

8 Cascading Tanks

The Cascading Tank test cases are in both MINLP and MPCC formulations [26]. CascadingTanks MINLP 1Tank 20FE CascadingTanks MINLP 1Tank 40FE

1.3

CascadingTanks MINLP 3Tank 20FE

CascadingTanks MINLP 3Tank 40FE

CascadingTanks MPCC 1Tank 20FE




1 Cyclic Scheduling and Control

The Cyclic Scheduling and Control test case applies to a multi-product continuous stirred-tank reactor [23]. caso-1-sc-v2

1.4

1 Distillation Separation Sequences

The Distillation Separation Sequence test case optimally integrates thermally-coupled distillation sequences [10, 11, 12, 13]. Conventional

1.5

3 Heat Exchanger Networks

These test cases simultaneously synthesize Heat Exchanger Networks [22, 57]. Escobar HEN1

1.6

Escobar HEN2

Escobar HEN3

2 Metabolic Networks

The Metabolic Networks test cases identify metabolic pathways [28, 29]. GMA ethanol model BigM

GMA ethanol model CH

3

1.7

2 Multi-Product Batch Plants

These test cases are for the optimal design of multi-product batch plants [27, 32, 59]. batch plant nonconvex1

1.8

batch plant nonconvex2

7 Periodic Scheduling

The Periodic Scheduling test cases are for continuous multiproduct plants [14, 15]. MTG EX1 MTG EX2 MTG EX5 MTG EX6 STG EX1

1.9

STG EX5

STG EX6

19 Pooling

The pooling problems represent blending under the conditions of intermediate storage [42]. adhya1 adhya2 adhya3 adhya4 bental4

1.10

bental5

foulds2

foulds3

foulds4

foulds5

haverly1

haverly2

haverly3

lee1

lee2

meyer04

meyer10

meyer15

rt2

2 Supply Chain Design

Multi-echelon supply chain design is for inventories under uncertainty [58, 60]. you supply chain design 1

1.11

you supply chain design 2

8 Three-Echelon Supply Chain

The Three-Echelon Supply Chain examples are optimally designed under uncertainty [46, 47, 61]. ngw-r1-22020 ngw-r1-236 ngw-r1-3510 ngw-r1-53050 ngw-you-22020

1.12

ngw-you-236

ngw-you-33050

ngw-you-3510

2 Unit Commitment

The two unit commitment models minimize operating costs on a network of power generators [45, 62]. zondervan UC convex

1.13

zondervan UC nonconvex

8 Water Distribution Network

These test cases are for the optimal design of water distribution networks [7, 21].

4

1.14

wdn signvar blacksburg

wdn signvar foss iron

wdn signvar foss poly 0

wdn signvar foss poly 1

wdn signvar hanoi

wdn signvar modena

wdn signvar pescara

wdn signvar shamir

16 Water Treatment Network [1, 2, 31, 48]

ahmetovic Ex1 NoEps

ahmetovic Ex1 WithEps

ahmetovic Ex2 NoEps

ahmetovic Ex2 WithEps

concbased

Ex1b WaterNetwokProblem-WOEps pw4

Ex 2 WaterNetwokProblem-NoEps

flowbased pw4

kg example1

kg example2 pw4

kg example3 pw4

kg example4 pw4

ruiz concbased

ruiz flowbased

smith sahinidis M1

TCD MINLPorg

1.15

24 Crude Oil Scheduling

The crude oil scheduling test cases are for unloading with inventory management [35, 43, 44]. Scheduler LeeCrudeOil1 05 Scheduler LeeCrudeOil1 06

2

Scheduler LeeCrudeOil1 07






















Mixed-Integer Quadratically-Constrained Quadratic Programs

The mixed-integer quadratically-constrained quadratic programs are documented in Table 11.

5

2.1

90 Box-Constrained Quadratic Programs (BoxQP) [8, 55, 56]

spar020-100-1

spar020-100-2

spar020-100-3

spar030-060-1

spar030-060-2

spar030-060-3

spar030-070-1

spar030-070-2

spar030-070-3

spar030-080-1

spar030-080-2

spar030-080-3

spar030-090-1

spar030-090-2

spar030-090-3

spar030-100-1

spar030-100-2

spar030-100-3

spar040-030-1

spar040-030-2

spar040-030-3

spar040-040-1

spar040-040-2

spar040-040-3

spar040-050-1

spar040-050-2

spar040-050-3

spar040-060-1

spar040-060-2

spar040-060-3

spar040-070-1

spar040-070-2

spar040-070-3

spar040-080-1

spar040-080-2

spar040-080-3

spar040-090-1

spar040-090-2

spar040-090-3

spar040-100-1

spar040-100-2

spar040-100-3

spar050-030-1

spar050-030-2

spar050-030-3

spar050-040-1

spar050-040-2

spar050-040-3

spar050-050-1

spar050-050-2

spar050-050-3

spar060-020-1

spar060-020-2

spar060-020-3

spar070-025-1

spar070-025-2

spar070-025-3

spar070-050-1

spar070-050-2

spar070-050-3

spar070-075-1

spar070-075-2

spar070-075-3

spar080-025-1

spar080-025-2

spar080-025-3

spar080-050-1

spar080-050-2

spar080-050-3

spar080-075-1

spar080-075-2

spar080-075-3

spar090-025-1

spar090-025-2

spar090-025-3

spar090-050-1

spar090-050-2

spar090-050-3

spar090-075-1

spar090-075-2

spar090-075-3

spar100-025-1

spar100-025-2

spar100-025-3

spar100-050-1

spar100-050-2

spar100-050-3

spar100-075-1

spar100-075-2

spar100-075-3

6

2.2

35 Circles & Polygon Nesting [30]

kall circles c6a

kall circles c6b

kall circles c6c

kall circles c7a

kall circles c8a

kall circlespolygons c1p11



kall circlespolygons c1p5a

kall circlespolygons c1p5b

kall circlespolygons c1p6a

kall circlesrectangles c1r11






kall congruentcircles c31











kall diffcircles 10

kall diffcircles 5a

kall diffcircles 5b

kall diffcircles 6

kall diffcircles 7

kall diffcircles 8

kall diffcircles 9

2.3

7 Crude Oil Scheduling [36, 37]

ex01

2.4

ex02

ex03

ex05

ex06

ex11

ex21

7 Multi-Period Blending [33, 34]

MPBP 6T 3P 2Q 029

MPBP 8T 3P 2Q 146

MPBP 8T 3P 2Q 718

MPBP 8T 3P 2Q 721

MPBP 8T 4P 2Q 480

MPBP 8T 4P 2Q 531

MPBP 8T 4P 2Q 852

2.5

3 Natural Gas Production [38, 39, 52]

Sarawak Scenario1

Sarawak Scenario16

7

Sarawak Scenario81

2.6

14 Point Packing [4]

pnt pack 02

pnt pack 03

pnt pack 04

pnt pack 05

pnt pack 06

pnt pack 07

pnt pack 08

pnt pack 09

pnt pack 10

pnt pack 11

pnt pack 12

pnt pack 13

pnt pack 14

pnt pack 15

2.7

67 Quadratic Assignment Problems (QAP) [3, 40]

bur26a

bur26b

bur26e

bur26f

bur26g

bur26h

chr12a

chr12b

chr12c

chr15a

chr15b

chr15c

chr18a

chr18b

chr20a

chr20b

chr20c

chr22a

chr22b

chr25a

esc16b

esc16c

esc16d

esc16e

esc16g

esc16h

esc32a

esc32b

had12

had14

had16

had18

had20

kra32

nug05

nug06

nug07

nug08

nug10

nug12

nug14

nug15

nug16a

nug16b

nug17

nug18

nug20

nug21

nug22

nug24

nug25

nug27

nug28

rou12

rou15

rou20

scr12

scr15

tai10a

tai12a

tai15a

tai17a

tai20a

tai25a

tai30a

tai35a

wil50

2.8

135 Randomly-Generated QCQP [5]

unitbox c 10 10 1 100

unitbox c 10 10 1 50

unitbox c 10 10 2 100


unitbox c 10 10 3 100


unitbox c 10 15 1 100


unitbox c 10 15 2 100


unitbox c 10 15 3 100


unitbox c 10 20 1 100


unitbox c 10 20 2 100


unitbox c 10 20 3 100


unitbox c 20 20 1 100



unitbox c 20 20 2 100



unitbox c 20 20 3 100



unitbox c 20 30 1 100



unitbox c 20 30 2 100



unitbox c 20 30 3 100



unitbox c 20 40 1 100



unitbox c 20 40 2 100



unitbox c 20 40 3 100



8

2.9










unitbox c 30 30 1 100


unitbox c 30 30 2 100


unitbox c 30 30 3 100


unitbox c 30 45 1 100


unitbox c 30 45 2 100


unitbox c 30 45 3 100


unitbox c 30 60 1 100


unitbox c 30 60 2 100


unitbox c 30 60 3 100


unitbox c 40 40 1 100



unitbox c 40 40 2 100



unitbox c 40 40 3 100



unitbox c 40 60 1 100



unitbox c 40 60 2 100



unitbox c 40 60 3 100



unitbox c 40 80 1 100



unitbox c 40 80 2 100



unitbox c 40 80 3 100












unitbox c 50 100 1 100

unitbox c 50 100 1 50

unitbox c 50 100 2 100

unitbox c 50 100 2 50

unitbox c 50 100 3 100

unitbox c 50 100 3 50

unitbox c 50 50 1 100


unitbox c 50 50 2 100


unitbox c 50 50 3 100


unitbox c 50 75 1 100


unitbox c 50 75 2 100


unitbox c 50 75 3 100


unitbox c 8 12 1 25

unitbox c 8 12 2 25

unitbox c 8 12 3 25

unitbox c 8 16 1 25

unitbox c 8 16 2 25

unitbox c 8 16 3 25

unitbox c 8 8 1 25

unitbox c 8 8 2 25

unitbox c 8 8 3 25

37 Reformulated GLOBALLib [24, 41, 50]

alkylation saxena

alkyl saxena

ex14 1 1 saxena

ex14 1 2 saxena

ex4 1 1 saxena

ex4 1 3 saxena

9

ex4 1 4 saxena

ex4 1 5 saxena

ex4 1 6 saxena

ex4 1 7 saxena

ex4 1 8 saxena

ex4 1 9 saxena

ex7 3 1 saxena

ex7 3 2 saxena

ex8 1 3 saxena

ex8 1 4 saxena

ex8 1 5 saxena

ex8 1 7 saxena

ex8 1 8 saxena

ex8 4 2 saxena

harker saxena

immun saxena

mathopt1 saxena

mathopt2 saxena

prob09 saxena

process saxena

prolog saxena

rbrock saxena

st e03 saxena

st e05 saxena

st e10 saxena

st e17 saxena

st e19 saxena

st e20 saxena

st qpc-m0 saxena

st qpk1 saxena

st z saxena

2.10

11 Reformulated MINLPLib [9, 24]

elf reformulated

eniplac reformulated

fo7 2 reformulated

fo7 reformulated

fo8 reformulated

fo9 reformulated

m3 reformulated

m6 reformulated

m7 reformulated

o7 2 reformulated

o7 reformulated

2.11

14 Standard Quadratic Programs (StQP) [51]

Problem 0030 75

Problem 0050 75

Problem 0100 01

Problem 0100 50

Problem 0100 75

Problem 0200 01

Problem 0200 50

Problem 0500 01

Problem 0500 25

Problem 1000 25

Problem Q030

Problem Q050

Problem Q100

Problem Q150

2.12

32 Water Treatment System [17, 18]

castro etal 2007 wts Ex01 M1
















10

2.13

















35 Water-Using Network [16, 53, 54]

teles etal 2009 WUN Ex01



































3

Examples from Standard Test Libraries

3.1 34 AMPL Book Lib Test cases The examples from the AMPL Book Library [25] are documented in Table 2. • http://www.gamsworld.org/performance/amplbook/amplbooklib.zip 11

3.2 134 Bonmin Test Set The examples from the Bonmin Test Set [6, 49] are documented in Table 3. • http://egon.cheme.cmu.edu/ibm/page.htm

3.3 368 GLOBALLib The examples from GLOBALLib [24, 41] are documented in Table 4. • http://www.gamsworld.org/global/globallib/globallib.zip

3.4 39 LINLib The examples from LINLib are documented in Table 5. • http://www.gamsworld.org/performance/plib/linlib.zip

3.5 12 MacMOOPLib The examples from MacMOOPLib are documented in Table 6. • http://www.gamsworld.org/performance/macmoop/macmooplib.zip

3.6 22 MPLLib The examples from MPLLib are documented in Table 8. • http://www.gamsworld.org/performance/mpllib/mpllib.zip

3.7 249 MINLPLib The examples from MINLPLib [9, 24] are documented in Table 7. • http://www.gamsworld.org/minlp/minlplib/minlplib.zip

3.8 1116 PrincetonLib The examples from PrincetonLib are documented in Table 9. • http://www.gamsworld.org/performance/princetonlib/princeton.zip

12

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[28] G. Guillén-Gosálbez and C. Pozo. Optimization of metabolic networks in biotechnology, 2010. Available from CyberInfrastructure for MINLP [A collaboration of CMU and IBM Research] at: www.minlp.org/library/problem/index.php?i=81. [29] G. Guillén-Gosálbez and A. Sorribas. Identifying quantitative operation principles in metabolic pathways: a systematic method for searching feasible enzyme activity patterns leading to cellular adaptive responses. BMC Bioinformatics, 10(386), 2009. [30] J. Kallrath. Cutting circles and polygons from area-minimizing rectangles. J. Glob. Optim., 43:299 – 328, 2009. [31] R. Karuppiah and I. E. Grossmann. Global optimization for the synthesis of integrated water systems in chemical processes. Comput. Chem. Eng., 30:650 – 673, 2006. [32] G. R. Kocis and I. E. Grossmann. Global optimization of nonconvex mixed-integer nonlinear programming (MINLP) problems in process synthesis. Ind. Eng. Chem. Res., 27(8):1407–1421, 1988. [33] S. P. Kolodziej, P. M. Castro, and I. E. Grossmann. Global optimization of bilinear programs with a multiparametric disaggregation technique. J. Glob. Optim., 2013. doi: 10.1007/s10898-012-0022-1. In Press. [34] S. P. Kolodziej, I. E. Grossmann, K. C. Furman, and N. W. Sawaya. A discretization-based approach for the optimization of the multiperiod blend scheduling problem. Comput. Chem. Eng., 2013. doi: 10.1016/j.compchemeng.2013.01.016. In Press. [35] H. Lee, J. M. Pinto, I. E. Grossmann, and S. Park. Mixed-integer linear programming model for refinery short-term scheduling of crude oil unloading with inventory management. Ind. Eng. Chem. Res., 35(5):1630–1641, 1996. [36] J. Li, A. Li, I. A. Karimi, and R. Srinivasan. Improving the robustness and efficiency of crude scheduling algorithms. AIChE J., 53(10):2659–2680, 2007. [37] J. Li, R. Misener, and C. A. Floudas. Continuous-time modeling and global optimization approach for scheduling of crude oil operations. AIChE J., 58(1):205–226, 2012. [38] X. Li, E. Armagan, A. Tomasgard, and P. I. Barton. Stochastic pooling problem for natural gas production network design and operation under uncertainty. AIChE J., 57(8):2120–2135, 2011. [39] X. Li, A. Tomasgard, and P. I. Barton. Decomposition strategy for the stochastic pooling problem. J. Glob. Optim., 54(4):765–790, 2012. [40] E. M. Loiola, N. M. Maia de Abreu, P. O. Boaventura-Netto, P. Hahn, and T. Querido. A survey for the quadratic assignment problem. Eur. J. Oper. Res., 176(2):657 – 690, 2007. [41] A. Meeraus. GLOBALLib. http://www.gamsworld.org/global/globallib.htm.

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[42] R. Misener, J. P. Thompson, and C. A. Floudas. APOGEE: Global optimization of standard, generalized, and extended pooling problems via linear and logarithmic partitioning schemes. Comput. Chem. Eng., 35(5):876–892, 2011. [43] S. Mouret and I. E. Grossmann. Crude-oil operations scheduling, 2010. Available from CyberInfrastructure for MINLP [A collaboration of Carnegie Mellon University and IBM Research] at: www.minlp.org/library/problem/index.php?i=117. [44] S. Mouret, I. E. Grossmann, and P. Pestiaux. A novel priority-slot based continuous-time formulation for crude-oil scheduling problems. Ind. Eng. Chem. Res., 48(18):8515–8528, 2009. [45] T. Niknam, A. Khodaei, and F. Fallahi. A new decomposition approach for the thermal unit commitment problem. Applied Energy, 86(9):1667 – 1674, 2009. [46] A. Nyberg, I. E. Grossmann, and T. Westerlund. The optimal design of a three-echelon supply chain with inventories under uncertainty, 2012. Available from CyberInfrastructure for MINLP [www.minlp.org, a collaboration of Carnegie Mellon University and IBM Research] at: www.minlp.org/library/problem/index.php?i=157. [47] A. Nyberg, I. E. Grossmann, and T. Westerlund. An efficient reformulation of the multiechelon stochastic inventory system with uncertain demands. AIChE J., 59(1):23–28, 2013. [48] J. P. Ruiz and I. E. Grossmann. Water treatment network design, 2009. Available from CyberInfrastructure for MINLP [www.minlp.org, a collaboration of Carnegie Mellon University and IBM Research] at: www.minlp.org/library/problem/index.php?i=24. [49] N. W. Sawaya. Reformulations, relaxations and cutting planes for generalized disjunctive programming. PhD in Chemical Engineering, Carnegie Mellon University, 2006. [50] A. Saxena, P. Bonami, and J. Lee. Convex relaxations of non-convex mixed integer quadratically constrained programs: extended formulations. Math. Program., 124(1-2):383–411, 2010. [51] A. Scozzari and F. Tardella. A clique algorithm for standard quadratic programming. Discrete Applied Mathematics, 156(13):2439 – 2448, 2008. [52] A. Selot, L. K. Kuok, M. Robinson, T. L. Mason, and P. I. Barton. A short-term operational planning model for natural gas production systems. AIChE J., 54(2):495–515, 2008. [53] J. Teles, P. M. Castro, and A. Q. Novais. Lp-based solution strategies for the optimal design of industrial water networks with multiple contaminants. Chem. Eng. Sci., 63(2):376 – 394, 2008. [54] J. P. Teles, P. M. Castro, and H. A. Matos. Global optimization of water networks design using multiparametric disaggregation. Comput. Chem. Eng., 40(0):132 – 147, 2012. [55] D. Vandenbussche and G. L. Nemhauser. A branch-and-cut algorithm for nonconvex quadratic programs with box constraints. Math. Program., 102(3):559–575, 2005.

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[56] D. Vandenbussche and G. L. Nemhauser. A polyhedral study of nonconvex quadratic programs with box constraints. Math. Program., 102(3):531–557, 2005. [57] T. F. Yee and I. E. Grossmann. Simultaneous optimization models for heat integrationII. Heat exchanger network synthesis. Comput. Chem. Eng., 14(10):1165 – 1184, 1990. [58] F. You and I. E. Grossmann. Mixed-integer nonlinear programming models and algorithms for largescale supply chain design with stochastic inventory management. Ind. Eng. Chem. Res., 47(20):7802– 7817, 2008. [59] F. You and I. E. Grossmann. Mixed-integer nonlinear programming models for the optimal design of multi-product batch plant, 2009. Available from CyberInfrastructure for MINLP [A collaboration of CMU and IBM Research] at: www.minlp.org/library/problem/index.php?i=48. [60] F. You and I. E. Grossmann. Mixed-integer nonlinear programming models and algorithms for supply chain design with stochastic inventory management, 2009. Available from CyberInfrastructure for MINLP [A collaboration of CMU and IBM Research] at: www.minlp.org/library/problem/index.php?i=30. [61] F. You and I. E. Grossmann. Integrated multi-echelon supply chain design with inventories under uncertainty: Minlp models, computational strategies. AIChE Journal, 56(2):419–440, 2010. [62] E. Zondervan and I. E. Grossmann. A deterministic security constrained unit commitment model, 2009. Available from CyberInfrastructure for MINLP [A collaboration of CMU and IBM Research] at: www.minlp.org/library/problem/index.php?i=41.

A

Test Suite Definition

Table 2: 34 AMPL Book Library Case Studies; Accessed 11 March http://www.gamsworld.org/performance/amplbook/amplbooklib.zip Problem Name blend dietu1 iocol1 iocol2 iorow minmax multic

# Variables Contin

Discrete

# Constraints

4 9 8 12 8 27 19

0 0 0 0 0 0 0

9 9 6 6 6 16 31

# Nonlinear Terms 0 0 0 0 0 0 0

continued on the next page

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Table 2 (AMPL Book Library) continued # Variables # Problem Name Contin Discrete Constraints net1node net3node netasgn netfeeds netmax netmcol netmulti netshort netthru nltrans sched steel4r steelp3a steelP steelpl1 steelpl2 steelpl3 steelpl4 steelpl5 steelT transp2 transpl1 transpl2

10 10 15 27 16 15 15 11 10 22 1419858 4 41 73 29 29 29 29 29 25 22 22 22

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

9 9 11 13 6 20 20 7 9 11 18 3 13 34 13 13 13 13 13 13 11 11 11

Table 3: 134 Bonmin Case Studies; Accessed http://egon.cheme.cmu.edu/ibm/page.htm [6, 49] Problem Name BatchS101006M BatchS121208M BatchS151208M BatchS201210M CLay0203M

# Variables

# Nonlinear Terms

Contin

Discrete

# Constraints

150 204 243 308 13

129 203 203 251 18

1020 1512 1782 2328 55

0 0 0 0 0 0 0 0 0 21 0 0 0 0 4 4 12 4 12 0 0 21 19

11

March

# Nonlinear Terms 49 59 62 67 48


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Table 3 (Bonmin) continued # Variables Problem Name Contin Discrete CLay0204M CLay0205M CLay0303M CLay0304M CLay0305M FLay02H FLay02M FLay03H FLay03M FLay04H FLay04M FLay05H FLay05M FLay06H FLay06M RSyn0805H RSyn0805M RSyn0810H RSyn0810M RSyn0815H RSyn0815M RSyn0820H RSyn0820M RSyn0830H RSyn0830M RSyn0840H RSyn0840M SLay04H SLay04M SLay05H SLay05M SLay06H SLay06M SLay07H SLay07M SLay08H SLay08M

21 31 13 21 31 43 11 111 15 211 19 343 23 507 27 272 102 302 112 341 127 366 132 433 157 497 177 117 21 191 31 283 43 393 57 521 73

32 50 21 36 55 4 4 12 12 24 24 40 40 60 60 37 69 42 74 47 79 52 84 62 94 72 104 24 24 40 40 60 60 84 84 112 112

# Constraints

# Nonlinear Terms

91 136 67 107 156 52 12 145 25 283 43 466 66 694 94 430 287 484 313 553 348 605 372 717 426 838 485 175 55 291 91 436 136 610 190 813 253

64 80 72 96 120 2 2 3 3 4 4 5 5 6 6 9 3 18 6 33 11 42 14 60 20 84 28 8 8 10 10 12 12 14 14 16 16

continued on the next page 19

Table 3 (Bonmin) continued # Variables Problem Name Contin Discrete SLay09H SLay09M SLay10H SLay10M Syn05H Syn05M Syn10H Syn10M02H Syn10M02M Syn10M03H Syn10M03M Syn10M04H Syn10M04M Syn15H Syn15M Syn20H Syn20M Syn30H Syn30M Syn40H Syn40M

667 91 831 111 38 16 68 155 71 232 106 309 141 107 41 132 46 199 71 263 91

144 144 180 180 5 5 10 40 40 60 60 80 80 15 15 20 20 30 30 40 40

# Constraints

# Nonlinear Terms

1045 325 1306 406 59 29 113 295 199 487 343 709 517 182 90 234 114 346 168 467 227

18 18 20 20 9 3 18 36 12 54 18 72 24 33 11 42 14 60 20 84 28

Table 4: 368 GLOBALLib Case Studies [24, 41]; Accessed 11 http://www.gamsworld.org/global/globallib/globallib.zip Problem Name abel alkyl arki0001 arki0002 arki0003 arki0004 arki0005

# Variables Contin

Discrete

# Constraints

31 15 1031 2457 2283 2091 2371

0 0 0 0 0 0 0

15 8 514 1977 2583 2082 5153

# Nonlinear Terms 30 19 512 1064 4080 10400 12768


20

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Table 4 (GLOBALLib) continued # Variables Problem Name Contin Discrete arki0006 arki0008 arki0009 arki0010 arki0011 arki0012 arki0013 arki0014 arki0015 arki0016 arki0017 arki0018 arki0019 arki0020 arki0021 arki0022 arki0023 arki0024 bayes2 10 bayes2 20 bayes2 30 bayes2 50 bearing btest14 camcge camshape100 camshape200 camshape400 camshape800 catmix100 catmix200 catmix400 catmix800 chain100 chain200 chain400 chain50

2371 5073 7715 4145 19315 19315 19315 19306 2094 5048 4333 9805 511 1263 3188 4153 8887 8677 87 87 87 87 14 136 280 200 400 800 1600 304 604 1204 2404 203 403 803 103

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

# Constraints

# Nonlinear Terms

5153 5021 6708 3428 17738 17738 17738 17693 1497 2947 2573 10 3 3 3 3 3 26759 78 78 78 78 13 94 243 201 401 801 1601 201 401 801 1601 102 202 402 52

12768 16334 523 263 1218 1218 1218 1218 3841 6631 5982 9804 510 1262 3187 4152 8886 14053 440 440 440 440 28 224 850 299 599 1199 2399 1200 2400 4800 9600 303 603 1203 153


Table 4 (GLOBALLib) continued # Variables Problem Name Contin Discrete chakra chance chem chenery circle demo7 dispatch elec100 elec200 elec25 elec50 etamac ex14 1 1 ex14 1 2 ex14 1 3 ex14 1 5 ex14 1 6 ex14 1 7 ex14 1 8 ex14 1 9 ex14 2 1 ex14 2 2 ex14 2 3 ex14 2 4 ex14 2 5 ex14 2 6 ex14 2 7 ex14 2 8 ex14 2 9 ex2 1 1 ex2 1 2 ex2 1 3 ex2 1 4 ex2 1 5 ex2 1 6 ex2 1 7 ex2 1 8

63 5 12 44 3 71 5 301 601 76 151 98 4 7 4 7 10 11 4 3 6 5 7 6 5 6 7 5 5 6 7 14 7 11 11 21 25

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

# Constraints

# Nonlinear Terms

42 4 5 39 10 58 3 101 201 26 51 71 5 10 5 7 16 18 5 3 8 6 10 8 6 8 10 6 6 2 3 10 6 12 6 11 11

41 4 11 56 30 12 6 600 1200 150 300 35 8 26 8 10 32 100 6 2 24 12 40 24 12 24 40 12 12 5 5 4 1 7 10 20 24


Table 4 (GLOBALLib) continued # Variables Problem Name Contin Discrete ex2 ex3 ex3 ex3 ex3 ex4 ex4 ex4 ex4 ex4 ex4 ex4 ex4 ex4 ex5 ex5 ex5 ex5 ex5 ex5 ex5 ex5 ex5 ex5 ex6 ex6 ex6 ex6 ex6 ex6 ex6 ex6 ex6 ex6 ex6 ex6 ex6

1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 3 3 4 4 4 1 1 1 1 2 2 2 2 2 2 2 2 2

9 1 2 3 4 1 2 3 4 5 6 7 8 9 2 case1 2 case2 2 case3 4 5 2 3 2 3 4 1 2 3 4 10 11 12 13 14 5 6 7 8

11 9 6 7 4 2 2 2 2 3 2 2 3 3 10 10 10 8 33 23 63 9 17 28 9 5 13 7 7 4 5 7 5 10 4 10 4

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

# Constraints

# Nonlinear Terms

2 7 7 7 4 1 1 1 1 1 1 1 2 3 7 7 7 7 20 17 54 7 14 20 7 4 10 5 4 2 3 4 3 4 2 4 2

10 8 29 8 3 1 1 1 1 2 1 1 2 2 7 7 7 16 195 24 200 8 18 33 20 10 36 18 6 3 4 6 4 9 3 9 3


Table 4 (GLOBALLib) continued # Variables Problem Name Contin Discrete ex6 ex7 ex7 ex7 ex7 ex7 ex7 ex7 ex7 ex7 ex7 ex8 ex8 ex8 ex8 ex8 ex8 ex8 ex8 ex8 ex8 ex8 ex8 ex8 ex8 ex8 ex8 ex8 ex8 ex8 ex8 ex8 ex8 ex8 ex8 ex8 ex8

2 2 2 2 2 3 3 3 3 3 3 1 1 1 1 1 2 2 2 2 2 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4

9 1 2 3 4 1 2 3 4 5 6 3 4 5 6 7 1 2 3 4 5 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7

5 8 7 9 9 5 5 6 13 14 18 3 3 3 3 6 56 7511 15637 56 2511 116 111 111 111 111 111 127 127 79 23 25 53 18 16 15 63

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

# Constraints

# Nonlinear Terms

3 15 6 7 5 8 8 9 18 16 18 1 1 1 1 6 32 1948 3156 82 3775 77 77 77 77 77 77 93 94 46 11 11 26 13 12 9 41

4 35 10 10 14 3 3 5 23 25 54 2 2 2 2 13 103 15006 31256 303 30006 448 423 423 423 423 425 537 535 214 40 60 100 36 55 56 140


Table 4 (GLOBALLib) continued # Variables Problem Name Contin Discrete ex8 4 8 ex8 5 1 ex8 5 2 ex8 5 3 ex8 5 4 ex8 5 5 ex8 5 6 ex8 6 1 ex8 6 2 ex9 1 1 ex9 1 2 ex9 1 4 ex9 1 5 ex9 1 8 ex9 2 2 ex9 2 3 ex9 2 4 ex9 2 5 ex9 2 6 ex9 2 7 ex9 2 8 filter flowchan100 flowchan200 flowchan400 flowchan50 ganges gasoil100 gasoil200 gasoil400 gasoil50 glider100 glider200 glider400 glider50 gsg 0001 gtm

43 7 7 6 6 6 7 76 31 14 11 11 14 15 11 17 9 9 17 11 7 3 2401 4801 9601 1201 357 2604 5204 10404 1304 1316 2616 5216 666 78 64

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

# Constraints

# Nonlinear Terms

31 5 5 5 5 5 5 46 1 13 10 10 13 13 12 16 8 8 13 10 6 2 2399 4799 9599 1199 274 2599 5199 10399 1299 1210 2410 4810 610 112 25

130 12 12 10 10 10 12 315 30 10 8 8 10 10 10 12 6 8 16 10 6 3 1600 3200 6400 800 817 3002 5802 11402 1602 3018 6018 12018 1518 44 20


Table 4 (GLOBALLib) continued # Variables Problem Name Contin Discrete harker haverly hhfair himmel16 house hs62 hydro immun infeas1 jbearing100 jbearing25 jbearing50 jbearing75 korcge launch least like linear mathopt1 mathopt2 maxmin meanvar methanol100 methanol200 methanol400 methanol50 mhw4d minlphi minsurf100 minsurf25 minsurf50 minsurf75 nemhaus otpop pindyck pinene100 pinene200

21 13 30 19 9 4 32 22 273 5305 1405 2705 4005 96 39 4 10 25 3 3 27 9 3006 6006 12006 1506 6 65 5305 1405 2705 4005 6 104 117 5006 10006

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

# Constraints

# Nonlinear Terms

8 10 26 22 9 2 25 8 1615 1 1 1 1 78 29 1 4 21 3 5 78 3 2998 5998 11998 1498 4 80 1 1 1 1 6 77 97 4996 9996

20 7 21 84 9 6 12 6 3895 5304 1404 2704 4004 200 52 3 9 20 4 4 312 7 5895 11595 22995 3033 10 36 5304 1404 2704 4004 5 83 80 5560 10960


Table 4 (GLOBALLib) continued # Variables Problem Name Contin Discrete pinene50 pollut popdynm100 popdynm200 popdynm25 popdynm50 prob06 prob07 prob09 process prolog qp1 qp2 qp3 qp4 qp5 ramsey rbrock rocket100 rocket200 rocket400 rocket50 sambal sample ship srcpm st bpaf1a st bpaf1b st bpk1 st bpv1 st bpv2 st bsj2 st bsj3 st bsj4 st cqpf st cqpjk1 st cqpjk2

2506 43 5616 11216 1416 2816 2 15 3 11 21 51 51 101 80 109 34 3 608 1208 2408 308 18 5 11 40 11 11 5 5 5 4 7 7 5 5 4

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

# Constraints

# Nonlinear Terms

2496 9 5593 11193 1393 2793 2 36 1 8 23 3 3 53 32 32 23 1 503 1003 2003 253 11 3 17 28 11 11 7 5 6 6 2 5 7 3 2

2860 40 7584 14984 2274 4044 4 63 2 11 14 50 50 100 29 0 22 2 1803 3603 7203 903 13 8 31 5 10 10 4 4 3 3 6 6 4 4 3


Table 4 (GLOBALLib) continued # Variables Problem Name Contin Discrete st st st st st st st st st st st st st st st st st st st st st st st st st st st st st st st st st st st st st

e01 e02 e03 e04 e05 e06 e07 e08 e09 e11 e12 e16 e17 e18 e19 e21 e22 e23 e24 e25 e26 e28 e30 e33 e34 e37 e41 e42 fp7a fp7b fp7c fp7d fp7e fp8 glmp fp1 glmp fp2 glmp fp3

3 4 11 5 6 4 11 3 3 4 5 13 3 3 3 7 3 3 3 5 3 10 15 10 7 5 5 8 21 21 21 21 21 25 5 5 5

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

# Constraints

# Nonlinear Terms

2 4 8 3 4 4 8 3 2 3 4 10 2 5 3 7 6 3 5 9 5 5 16 7 5 2 3 3 11 11 11 11 11 21 9 10 9

2 4 11 5 4 3 7 4 4 4 2 18 2 4 3 3 2 2 2 4 2 16 14 7 14 4 12 4 20 20 20 20 20 24 2 2 2


Table 4 (GLOBALLib) continued # Variables Problem Name Contin Discrete st glmp kk90 st glmp kk92 st glmp kky st glmp ss1 st glmp ss2 st ht st iqpbk1 st iqpbk2 st jcbpaf2 st m1 st m2 st pan1 st ph1 st ph2 st ph3 st phex st qpc-m0 st qpc-m1 st qpc-m3a st qpc-m3b st qpc-m3c st qpc-m4 st qpk1 st qpk2 st qpk3 st robot st rv1 st rv2 st rv3 st rv7 st rv8 st rv9 st z torsion100 torsion25 torsion50 torsion75

6 5 8 6 6 3 9 9 11 21 31 4 7 7 7 3 3 6 11 11 11 11 3 7 12 9 11 21 21 31 41 51 4 5309 1409 2709 4009

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

# Constraints

# Nonlinear Terms

8 9 14 12 9 4 8 8 14 12 22 5 6 6 6 6 3 6 11 11 11 11 5 13 23 9 6 11 21 21 21 21 6 5 5 5 5

2 2 4 2 2 2 8 8 10 20 30 3 6 6 4 2 2 5 10 10 10 10 2 6 11 16 10 20 20 30 40 50 3 10606 2806 5406 8006


Table 4 (GLOBALLib) continued # Variables Problem Name Contin Discrete turkey wall water weapons

519 6 42 66

0 0 0 0

# Constraints

# Nonlinear Terms

288 6 26 13

55 10 46 65

Table 5: 39 LINLib Case Studies; Accessed 11 http://www.gamsworld.org/performance/plib/linlib.zip Problem Name cl120a13l1 cl180a13l1 cl30a13l1 cl3a13l1 cl60a13l1 cl90a13l1 iair04 iair05 ibc1 ibienst1 icap6000 imas284 imisc07 ineos4 ineos5 iqiu iran13x13 iran8x32 iswath2 nql201 nql30 q18a13l1 q30a13l1

# Variables Contin

Discrete

# Constraints

72002 162002 4502 47 18002 40502 1 1 1500 478 1 2 2 3989 3989 793 170 257 4192 161606 3602 5478 14886

0 0 0 0 0 0 8904 7195 252 28 6000 150 259 17136 17136 48 169 256 2213 0 0 0 0

72321 162481 4581 54 18161 40741 824 427 1914 577 2172 69 213 36704 36703 1193 196 297 484 162141 3681 5501 14925

March

# Nonlinear Terms 28800 64800 1800 18 7200 16200 8904 7195 252 28 6000 150 259 17136 17136 48 169 256 2213 80802 1800 2738 7442


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Table 5 (LINLib) continued # Variables Problem Name Contin Discrete q60a13l1 q9a13l1 qssp120l1 qssp180l1 qssp18l1 qssp30l1 qssp60l1 qssp90l1 qt120a13l1 qt12a13l1 qt180a13l1 qt18a13l1 qt30a13l1 qt60a13l1 qt90a13l1 qt9a13l1

58566 1446 87848 196568 2168 5768 22328 49688 73207 847 163807 1807 4807 18607 41407 502

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

# Constraints

# Nonlinear Terms

58645 1457 72965 163445 1769 4745 18485 41225 73044 828 163564 1780 4764 18524 41284 487

29282 722 43923 98283 1083 2883 11163 24843 29282 338 65522 722 1922 7442 16562 200

Table 6: 12 MacMOOPLib Case Studies; Accessed 11 March http://www.gamsworld.org/performance/macmoop/macmooplib.zip Problem Name abc-comp ex001 ex002 ex003 ex005 hs05x liswetm molpg 1 molpg 2 molpg 3 moqp 1 moqp 2

# Variables Contin

Discrete

# Constraints

3 6 6 3 3 6 9 9 13 11 24 24

0 0 0 0 0 0 0 0 0 0 0 0

4 4 3 3 1 4 3 9 17 15 14 13

# Nonlinear Terms 4 11 3 5 2 5 7 0 0 0 60 60


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Table 6 (MacMOOPLib) continued # Variables Problem Name Contin Discrete moqp 3

24

0

# Constraints

# Nonlinear Terms

14

60

Table 7: 249 MINLPLib Case Studies [9, 24]; Accessed http://www.gamsworld.org/minlp/minlplib/minlplib.zip Problem Name 4stufen alan batch beuster cecil 13 chp partload contvar csched1 csched2 du-opt eg all s eg disc2 s eg disc s eg int s elf eniplac enpro48 enpro56 ex1221 ex1222 ex1223 ex1224 ex1225 ex1226 ex1233 ex1243

# Variables Contin

Discrete

# Constraints

102 5 23 106 679 2204 210 14 93 8 1 5 4 5 31 118 62 55 3 3 8 4 3 3 41 53

48 4 24 52 162 45 87 63 308 13 7 3 4 3 24 24 92 73 3 1 4 8 6 3 12 16

99 8 74 115 899 2517 285 23 138 10 28 28 28 28 39 190 215 192 6 4 14 8 11 6 65 97

11

# Nonlinear Terms 87 3 22 159 360 1916 530 8 58 20 196 196 196 196 30 48 29 24 2 2 17 6 2 2 28 36

March


32

2013

at

Table 7 (MINLPLib) continued # Variables Problem Name Contin Discrete ex1244 ex1252 ex1263 ex1264 ex1265 ex1266 ex3 ex4 fac1 fac2 fac3 feedtray fo7 fo8 fo9 fuel fuzzy gasnet gastrans gbd gear ghg 1veh ghg 2veh ghg 3veh gkocis hda hmittelman johnall lop97ic m3 m6 m7 mbtd meanvarx minlphix netmod dol1 netmod dol2

73 25 21 21 31 43 25 12 17 55 55 91 73 91 111 13 777 81 86 2 1 18 40 61 9 710 1 5 92 21 57 73 11 22 65 1537 1537

23 15 72 68 100 138 8 25 6 12 12 7 42 56 72 3 120 10 21 3 4 12 18 36 3 13 16 190 1662 6 30 42 200 14 20 462 462

# Constraints

# Nonlinear Terms

130 44 56 56 75 96 32 31 19 34 34 92 212 274 344 16 1057 70 150 5 1 38 63 120 9 719 8 193 92 44 158 212 71 45 93 3138 3081

52 36 32 32 50 72 5 127 16 54 54 282 14 16 18 6 79 130 45 1 4 91 154 307 2 464 122 573 8822 6 12 14 1400 7 40 6 6


Table 7 (MINLPLib) continued # Variables Problem Name Contin Discrete netmod kar1 netmod kar2 no7 ar2 1 no7 ar25 1 no7 ar3 1 no7 ar4 1 no7 ar5 1 nous1 nous2 nuclear104 nuclear10a nuclear10b nuclear14 nuclear25 nuclear49 nuclearva nuclearvb nuclearvc nuclearvd nuclearve nuclearvf nvs01 nvs02 nvs03 nvs04 nvs05 nvs06 nvs07 nvs08 nvs09 nvs10 nvs11 nvs12 nvs13 nvs14 nvs15 nvs16

321 321 71 71 71 71 71 49 49 12998 2091 12907 987 1054 3335 184 184 184 184 184 184 2 4 1 1 7 1 1 2 1 1 1 1 1 4 1 1

136 136 42 42 42 42 42 2 2 10816 10920 10920 576 625 2401 168 168 168 168 168 168 2 5 2 2 2 2 3 2 10 2 3 4 5 5 3 2

# Constraints

# Nonlinear Terms

667 667 270 270 270 270 270 44 44 14246 3340 24972 1227 1304 3874 318 318 318 318 318 318 4 4 3 1 10 1 3 4 1 3 4 5 6 4 2 1

4 4 14 14 14 14 14 122 122 61108 44884 23252 5520 5990 17539 2024 1988 1988 2864 2864 2864 7 16 3 2 24 2 3 7 10 6 12 20 30 16 3 2


Table 7 (MINLPLib) continued # Variables Problem Name Contin Discrete nvs17 nvs18 nvs19 nvs20 nvs21 nvs22 nvs23 nvs24 o7 o8 ar4 1 o9 ar4 1 oaer oil ortez parallel pb302035 pb302055 pb302075 pb302095 pb351535 pb351555 pb351575 pb351595 prob02 prob03 procsel product pump qap ravem risk2b saa 2 sep1 space25 space960 spectra2 spring

1 1 1 12 2 5 1 1 73 89 109 7 1517 70 181 1 1 1 1 1 1 1 1 1 1 8 1447 16 1 60 452 4008 28 144 4578 40 6

7 6 8 5 2 4 9 10 42 56 72 3 19 18 25 600 600 600 600 525 525 525 525 6 2 3 107 9 225 53 12 400 2 750 960 30 12

# Constraints

# Nonlinear Terms

8 7 9 9 3 10 10 11 212 348 436 8 1547 75 116 51 51 51 51 51 51 51 51 9 2 8 1926 35 31 187 581 6206 32 236 6498 73 9

56 42 72 16 7 24 90 110 14 16 18 2 759 54 155 600 600 600 600 525 525 525 525 10 2 2 264 36 225 28 3 15400 12 111 4700 240 14


Table 7 (MINLPLib) continued # Variables Problem Name Contin Discrete st e13 st e14 st e15 st e27 st e29 st e31 st e32 st e35 st e36 st e38 st e40 st miqp1 st miqp2 st miqp3 st miqp4 st miqp5 stockcycle st test1 st test2 st test3 st test4 st test5 st test6 st test8 st testgr1 st testgr3 st testph4 super1 super2 super3 synheat synthes1 synthes2 synthes3 tln12 tln2 tln4

2 8 3 3 4 89 18 26 2 3 2 1 1 1 4 6 49 1 1 1 1 1 1 1 1 1 1 1264 1264 1264 45 4 7 10 1 1 1

1 4 3 2 8 24 18 7 1 2 3 5 4 2 3 2 432 5 6 13 6 10 10 24 10 20 3 44 44 44 12 3 5 8 168 8 24

# Constraints

# Nonlinear Terms

3 14 6 7 8 136 19 40 3 4 9 2 4 2 5 14 98 2 3 11 6 12 6 21 6 21 11 1659 1659 1659 65 7 15 24 73 13 25

1 17 2 2 6 14 63 16 6 6 6 5 2 1 3 2 48 4 5 5 2 7 10 24 10 20 3 1201 1201 1201 28 6 8 12 288 8 32


Table 7 (MINLPLib) continued # Variables Problem Name Contin Discrete tln5 tln6 tln7 tloss tls12 tls2 tls4 tls5 tls6 tls7 tltr uselinear util waste water4 waterx waterz

1 1 1 1 145 5 17 26 37 50 1 6735 118 2085 70 57 70

# Constraints

# Nonlinear Terms

31 37 43 54 385 25 65 91 121 155 55 7031 168 1992 138 55 138

50 72 98 72 288 8 32 50 72 98 54 14091 10 2736 46 60 46

35 48 63 48 668 33 89 136 179 296 48 58 28 400 126 14 126

Table 8: 22 MPLLib Case Studies; Accessed 11 http://www.gamsworld.org/performance/mpllib/mpllib.zip # Variables

March

Contin

Discrete

# Constraints

3 3 3 3 3 10 7 22 15 6 8

0 0 0 0 0 0 0 0 0 0 0

3 4 4 4 4 13 4 29 22 11 8

Problem Name exmpl 13 2-1 nonlinearcons exmpl13 2-2 nonlinearobjective exmpl13 2-3 nonlinearobjective2 exmpl 3 1-1 wyndorglass exmpl 3 4-1 marysradiation exmpl 3 4-2 kibbutzim exmpl 3 4-3 noriandleets exmpl 3 4-4b saveitcomp exmpl 3 4-4 saveitcomp exmpl 3 4-5 unionairways exmpl 3 4-6 distrunlimited

2013

# Nonlinear Terms 2 2 2 0 0 0 0 0 0 0 0


37

at

Table 8 (MPLLib) continued # Variables Contin

Discrete

# Constraints

4 4 13 21 21 17 16 26 13 46 8

0 0 0 0 0 0 0 0 0 0 0

3 3 8 10 10 9 9 11 8 8 6

Problem Name exmpl exmpl exmpl exmpl exmpl exmpl exmpl exmpl exmpl exmpl exmpl

7 7 8 8 8 8 8 8 9 9 9

1-1 wyndorglassdual 3-1 upperbound 1-1 pandtcomp 1-2 northairplane 1-3 metrowater 3-1 jobshopco 3-2a betterprodco 3-2b betterprodco 3-1 shortestpath 5-1 maxflow 6-1 mincost

# Nonlinear Terms 0 0 0 0 0 0 0 0 0 0 0

Table 9: 1116 PrincetonLib Case Studies; Accessed 11 March 2013 http://www.gamsworld.org/performance/princetonlib/princeton.zip Problem Name 1 2 3 5 antenna antenna aopf4 bc4 bc5 bc7 blend braess branin camel1 catenary chemeq

# Variables Contin

Discrete

# Constraints

3010 322 3047 1552 353 372 1773 1026 2563 194 25 5 3 3 203 41

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

3003 304 3008 1508 599 488 1445 513 1537 129 15 5 1 1 102 15

# Nonlinear Terms 1501 243 4605 1177 297 314 1021 1024 1024 64 288 4 2 2 402 40


38

at

Table 9 (PrincetonLib) continued Problem Name chi dcopf dea emfl esfl esfl ex3 3 1a ex3 3 1b ex3 3 1c ex3 4 1 ex3 5 1 fekete fermat2 eps fermat2 eps fermat2 vareps fermat2 vareps fermat eps fermat eps fermat socp eps fermat socp eps fermat socp vareps fermat socp vareps fermat vareps fermat vareps fir convex fir exp fir linear fir socp gold grasp gridneta griewank growthopt hang midpt hang trap hs001 hs002

# Variables Contin

Discrete

# Constraints

3 49 7 51 3 3 1603 2403 2403 2402 1200 151 3 3 4 4 3 3 6 6 7 7 4 4 11 12 11 12 3 51 73 3 9 1200 359 3 3

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

1 34 101 1 1 1 1600 2399 2399 1600 897 51 1 1 1 1 1 1 4 4 4 4 1 1 305 306 304 306 1 51 1 1 2 897 355 1 1

# Nonlinear Terms 2 0 6 50 2 2 2 800 801 801 994 300 2 2 3 3 2 2 6 6 9 9 3 3 1001 2 0 2 2 20 72 2 8 3731 1008 2 2


Table 9 (PrincetonLib) continued # Variables Problem Name Contin Discrete hs003 hs004 hs005 hs006 hs007 hs008 hs009 hs010 hs011 hs012 hs013 hs014 hs015 hs016 hs017 hs018 hs019 hs020 hs021 hs022 hs023 hs024 hs025 hs026 hs027 hs028 hs029 hs030 hs031 hs032 hs033 hs034 hs035 hs036 hs037 hs038 hs039

3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 5 5

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

# Constraints

# Nonlinear Terms

1 1 1 2 2 3 2 2 2 2 2 3 4 3 3 3 3 4 2 3 6 4 1 2 2 2 2 2 2 3 3 3 2 2 3 1 3

2 1 2 2 3 4 2 2 3 4 3 4 5 4 4 6 6 6 2 3 8 2 3 6 3 3 6 5 5 4 7 2 3 3 3 4 4



5 5 5 5 5 6 6 6 6 6 6 6 6 6 7 7 8 3 3 4 4 4 4 4 4 4 11 8 8 25 5 5 5 5 5 5 6

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

# Constraints

# Nonlinear Terms

4 2 2 4 7 1 3 4 3 3 4 4 4 4 7 7 5 2 4 2 3 2 3 2 2 3 22 6 6 22 3 7 4 6 6 4 3

9 3 6 15 4 5 10 10 3 5 5 5 5 5 6 2 7 4 6 6 5 3 6 6 6 2 11 6 6 118 12 8 4 8 8 4 10



6 6 6 6 6 6 39 6 7 33 34 35 36 37 7 7 7 7 7 24 8 8 8 8 9 3 714 9 9 16 10 10 10 11 11 11 11

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

# Constraints

# Nonlinear Terms

4 4 4 4 7 7 38 11 5 32 32 32 32 32 3 5 5 5 5 15 5 7 7 7 7 1 707 7 7 13 14 11 11 1 4 4 4

16 10 16 16 29 35 54 5 14 92 123 154 185 216 18 14 14 14 14 21 16 45 45 45 22 2 3055 8 8 52 48 36 36 10 24 24 10


Table 9 (PrincetonLib) continued # Variables Problem Name Contin Discrete hs112 hs113 hs114 hs114 hs116 hs116 hs117 hs118 hs119 hs15 hs23 hs35 hs44 hs5 hs6 hs8 hydrothermal kowalik levy3 ljcluster logcheb lowpass markowitz masa maxcut maxmineig1 maxmineig2 median minsurf moonshot nnls opf4 optreward optrisk osborne1 pca pf4

11 11 15 15 14 14 16 16 17 3 3 4 5 3 3 3 53 5 3 66 353 333 9 9 51 201 201 2 1090 809 301 9730 9 9 6 10 239

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

# Constraints

# Nonlinear Terms

4 9 12 12 16 16 6 30 9 3 6 2 7 1 2 3 42 1 1 46 600 531 2 6 31 111 112 1 1 603 1 7476 3 3 1 5 3

10 21 11 11 31 31 10 15 16 5 8 3 4 2 2 4 28 4 2 225 298 0 8 4 68 588 588 1 1089 606 300 33521 8 8 5 27 580


Table 9 (PrincetonLib) continued # Variables Problem Name Contin Discrete pgon polygon powell price putt robotarm robust rocket rosenbr s201 s202 s203 s204 s205 s206 s207 s208 s209 s210 s211 s212 s213 s214 s215 s216 s217 s218 s219 s220 s221 s222 s223 s224 s225 s226 s227 s228

13 22 5 3 1137 563 25 303 5 3 3 6 6 3 3 3 3 3 3 3 3 3 3 3 3 3 3 5 3 3 3 3 3 3 3 3 3

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

# Constraints

# Nonlinear Terms

21 21 1 1 1132 712 10 201 3 1 1 4 4 1 1 1 1 1 1 1 1 1 1 2 2 3 2 3 2 2 2 3 5 6 3 3 3

72 21 4 2 2514 1161 129 400 3 2 2 9 9 2 2 2 2 2 2 2 2 2 2 1 3 2 1 4 1 1 1 2 2 8 6 4 3


Table 9 (PrincetonLib) continued # Variables Problem Name Contin Discrete s229 s230 s231 s232 s233 s234 s235 s236 s237 s238 s239 s240 s241 s242 s243 s244 s245 s246 s247 s248 s249 s250 s251 s252 s253 s254 s255 s256 s257 s258 s259 s260 s261 s262 s263 s264 s265

3 3 3 3 3 3 4 3 3 3 3 4 9 4 8 4 4 4 5 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

# Constraints

# Nonlinear Terms

1 3 3 4 2 2 2 3 4 4 2 1 6 1 5 1 1 1 2 3 2 3 2 2 2 3 1 1 1 1 1 1 1 5 5 4 3

2 2 2 2 4 4 3 5 6 6 4 3 14 3 13 3 3 3 6 3 5 3 3 3 3 4 4 4 4 4 4 4 4 0 6 15 4



16 6 6 6 6 7 7 7 3 5 7 5 7 9 11 11 11 11 16 16 21 21 21 31 3 11 31 51 7 11 17 31 51 101 21 51 101

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

# Constraints

# Nonlinear Terms

11 1 6 4 6 1 1 1 1 1 1 5 7 9 11 1 1 1 11 11 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

60 5 5 5 10 6 6 6 2 4 6 0 0 0 0 10 10 10 126 126 20 20 20 30 2 10 30 50 6 10 16 30 50 100 20 50 100



21 51 101 3 3 3 3 3 5 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

# Constraints

# Nonlinear Terms

1 1 1 1 1 1 1 1 3 4 2 2 2 2 2 2 2 3 3 3 4 3 2 1 4 2 2 1 1 1 3 3 2 3 2 2 2

20 50 100 2 2 2 2 2 6 4 4 4 4 4 4 4 4 3 6 6 4 5 4 2 8 4 2 2 3 3 4 3 5 6 6 3 6



4 4 4 4 4 7 21 5 5 5 6 5 9 10 322 6 6 6 6 410 10 8 8 9 9 7 10 10 10 46 11 11 11 11 12 13 14

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

# Constraints

# Nonlinear Terms

2 3 2 2 3 5 18 1 1 1 5 2 6 11 318 1 15 3 7 408 8 15 6 1 7 1 1 13 7 71 10 16 4 4 1 4 5

6 7 6 6 7 9 34 4 4 4 4 4 22 29 1124 5 0 15 35 1245 29 35 11 8 10 6 9 30 18 350 20 37 10 24 11 25 0


Table 9 (PrincetonLib) continued # Variables Problem Name Contin Discrete s382 s383 s383 s384 s385 s386 s387 s388 s389 s391 s392 s393 s394 s395 sawpath schwefel shear midpt shekel springs stableair midpt stableair trap steenbre structure trafequil tre weapon

14 15 15 16 16 3 16 16 16 961 34 134 21 51 594 6 1409 5 33 1349 1361 577 3651 2087 3 101

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

# Constraints

# Nonlinear Terms

5 2 2 11 11 1 12 26 26 961 31 113 2 2 785 1 1201 1 11 1195 1355 73 480 1710 1 13

28 14 14 126 126 2 141 141 141 1800 33 117 40 100 588 5 4802 4 50 4625 3763 72 0 76 2 65

Table 10: 115 minlp.org Case Studies Problem Name adhya1 adhya2 adhya3

# Variables Contin

Discrete

# Constraints

14 14 21

0 0 0

31 39 44

# Nonlinear Terms 153 209 328


49

Table 10 (minlp.org) continued # Variables Contin

Discrete

# Constraints

19 55 55 161 161 23 41 86 113 128 161 9 39 461 921 1181 2361 662 1322 1622 3242 1507 401 622 45 61 201 303 926 461 23 169 169 101 14 38 8

0 20 20 72 72 12 36 5 6 7 8 0 0 40 80 40 80 0 0 0 0 50 25 20 12 16 60 128 408 25 0 0 0 0 24 24 0

58 84 84 250 250 68 206 104 135 154 191 8 26 518 1038 1558 3118 439 879 1239 2479 1266 355 1129 65 91 251 273 838 415 13 49 49 41 73 81 7

Problem Name adhya4 ahmetovic Ex1 NoEps ahmetovic Ex1 WithEps ahmetovic Ex2 NoEps ahmetovic Ex2 WithEps batch plant nonconvex1 batch plant nonconvex2 bcp5 bcp6 bcp7 bcp8 bental4 bental5 CascadingTanks MINLP 1Tank 20FE CascadingTanks MINLP 1Tank 40FE CascadingTanks MINLP 3Tank 20FE CascadingTanks MINLP 3Tank 40FE CascadingTanks MPCC 1Tank 20FE CascadingTanks MPCC 1Tank 40FE CascadingTanks MPCC 3Tank 20FE CascadingTanks MPCC 3Tank 40FE caso-1-sc-v2 concbased Conventional Escobar HEN1 Escobar HEN2 Escobar HEN3 Ex1b WaterNetwokProblem-WOEps pw4 Ex 2 WaterNetwokProblem-NoEps flowbased pw4 foulds2 foulds3 foulds4 foulds5 GMA ethanol model BigM GMA ethanol model CH haverly1

# Nonlinear Terms 468 114 114 525 525 82 232 92 148 183 261 7 96 514 1034 1748 3508 714 1434 2188 4388 3116 520 1420 32 42 170 92 450 300 26 392 392 196 47 47 7


Table 10 (minlp.org) continued # Variables

Problem Name haverly2 haverly3 kg example1 kg example2 pw4 kg example3 pw4 kg example4 pw4 lee1 lee2 meyer04 meyer10 meyer15 MTG EX1 MTG EX2 MTG EX5 MTG EX6 ngw-r1-22020 ngw-r1-236 ngw-r1-3510 ngw-r1-53050 ngw-you-22020 ngw-you-236 ngw-you-33050 ngw-you-3510 rt2 ruiz concbased ruiz flowbased Scheduler LeeCrudeOil1 Scheduler LeeCrudeOil1 Scheduler LeeCrudeOil1 Scheduler LeeCrudeOil1 Scheduler LeeCrudeOil1 Scheduler LeeCrudeOil1 Scheduler LeeCrudeOil2 Scheduler LeeCrudeOil2 Scheduler LeeCrudeOil2 Scheduler LeeCrudeOil2 Scheduler LeeCrudeOil2

05 06 07 08 09 10 05 06 07 08 09

Contin

Discrete

# Constraints

8 8 78 325 268 557 41 45 64 208 383 77 118 113 174 981 67 161 3471 2481 124 13641 376 17 356 416 496 595 694 793 892 991 1086 1303 1520 1737 1954

0 0 0 84 56 108 9 9 55 187 352 48 112 78 176 460 27 70 1680 460 27 1680 70 0 5 5 40 48 56 64 72 80 70 84 98 112 126

7 7 65 211 179 385 83 93 142 424 769 196 307 309 481 1841 115 281 6581 5301 256 33191 836 29 320 380 1241 1504 1777 2060 2353 2656 2582 3118 3671 4241 4828

# Nonlinear Terms 7 7 92 184 180 450 128 192 156 930 2070 95 126 164 218 40 9 15 80 40 9 80 15 152 525 305 640 768 896 1024 1152 1280 1680 2016 2352 2688 3024


Table 10 (minlp.org) continued # Variables

Problem Name Scheduler LeeCrudeOil2 10 Scheduler LeeCrudeOil3 05 Scheduler LeeCrudeOil3 06 Scheduler LeeCrudeOil3 07 Scheduler LeeCrudeOil3 08 Scheduler LeeCrudeOil3 09 Scheduler LeeCrudeOil3 10 Scheduler LeeCrudeOil4 05 Scheduler LeeCrudeOil4 06 Scheduler LeeCrudeOil4 07 Scheduler LeeCrudeOil4 08 Scheduler LeeCrudeOil4 09 Scheduler LeeCrudeOil4 10 smith sahinidis M1 STG EX1 STG EX5 STG EX6 TCD MINLPorg wdn signvar blacksburg wdn signvar foss iron wdn signvar foss poly 0 wdn signvar foss poly 1 wdn signvar hanoi wdn signvar modena wdn signvar pescara wdn signvar shamir you supply chain design 1 you supply chain design 2 zondervan UC convex zondervan UC nonconvex

Contin

Discrete

# Constraints

2171 1211 1453 1695 1937 2179 2421 1861 2233 2605 2977 3349 3721 106 217 235 310 483 184 270 270 270 169 1541 468 40 7 25 241 241

140 70 84 98 112 126 140 95 114 133 152 171 190 23424 198 216 384 15 513 812 464 1334 238 4438 1386 120 21 3 720 720

5432 2787 3360 3950 4557 5181 5822 4242 5094 5966 6858 7770 8702 551 262 299 388 1311 381 617 617 617 372 3439 1059 87 28 31 5330 5330

Table 11: 482 MIQCQP from the Literature

52

# Nonlinear Terms 3360 1960 2352 2744 3136 3528 3920 3040 3648 4256 4864 5472 6080 105 175 127 166 840 175 290 290 290 170 1585 495 40 27 6 240 480

# Variables

Problem Name alkylation saxena alkyl saxena bur26a bur26b bur26e bur26f bur26g bur26h castro etal 2007 wts castro etal 2007 wts castro etal 2007 wts castro etal 2007 wts castro etal 2007 wts castro etal 2007 wts castro etal 2007 wts castro etal 2007 wts castro etal 2007 wts castro etal 2007 wts castro etal 2007 wts castro etal 2007 wts castro etal 2007 wts castro etal 2007 wts castro etal 2007 wts castro etal 2007 wts castro etal 2007 wts castro etal 2007 wts castro etal 2007 wts castro etal 2007 wts castro etal 2007 wts castro etal 2007 wts castro etal 2007 wts castro etal 2007 wts castro etal 2007 wts castro etal 2007 wts castro etal 2007 wts

Ex01 Ex01 Ex02 Ex02 Ex03 Ex03 Ex04 Ex04 Ex05 Ex05 Ex06 Ex06 Ex07 Ex07 Ex08 Ex08 Ex09 Ex09 Ex10 Ex10 Ex11 Ex11 Ex12 Ex12 Ex13 Ex13 Ex14

M1 M2 M1 M2 M1 M2 M1 M2 M1 M2 M1 M2 M1 M2 M1 M2 M1 M2 M1 M2 M1 M2 M1 M2 M1 M2 M1

Contin

Discrete

# Constraints

13 17 1 1 1 1 1 1 13 28 20 42 23 51 24 56 47 134 47 134 47 134 73 279 127 517 65 156 119 304 197 517 383 1040 75

0 0 676 676 676 676 676 676 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

14 10 53 53 53 53 53 53 11 34 15 45 16 54 22 66 41 152 41 152 41 152 73 335 113 573 31 138 43 252 58 408 84 783 47

# Nonlinear Terms 15 20 676 676 676 676 676 676 6 8 16 24 16 24 32 36 90 96 90 96 90 96 180 168 420 420 70 120 126 224 240 440 510 960 140


53

Table 11 (MIQCQP) continued # Variables

Problem Name castro etal 2007 wts Ex14 castro etal 2007 wts Ex15 castro etal 2007 wts Ex15 castro etal 2007 wts Ex16 castro etal 2007 wts Ex16 chr12a chr12b chr12c chr15a chr15b chr15c chr18a chr18b chr20a chr20b chr20c chr22a chr22b chr25a elf reformulated eniplac reformulated esc16b esc16c esc16d esc16e esc16g esc16h esc32a esc32b ex01 ex02 ex03 ex05 ex06 ex11 ex14 1 1 saxena ex14 1 2 saxena

M2 M1 M2 M1 M2

Contin

Discrete

# Constraints

209 47 134 88 244 1 1 1 1 1 1 1 1 1 1 1 1 1 1 31 142 1 1 1 1 1 1 1 1 297 1193 849 825 849 1046 8 8

0 0 0 0 0 144 144 144 225 225 225 324 324 400 400 400 484 484 625 24 24 256 256 256 256 256 256 1024 1024 48 105 116 116 116 132 0 0

205 41 152 54 234 25 25 25 31 31 31 37 37 41 41 41 45 45 51 39 214 33 33 33 33 33 33 65 65 696 5005 2443 1917 2437 3506 11 11

# Nonlinear Terms 180 90 96 192 252 144 144 144 225 225 225 324 324 400 400 400 484 484 625 30 90 240 240 224 144 128 256 800 768 112 108 384 384 384 384 20 33


Table 11 (MIQCQP) continued # Variables Contin

Discrete

# Constraints

1189 4 4 4 5 4 3 4 4 11 10 9 5 6 10 9 45 73 73 91 111 1 1 1 1 1 35 22 18 18 20 20 22 1110 158 43 43

160 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 42 42 56 72 144 196 256 324 400 0 0 0 0 0 0 0 0 0 0 0

4682 4 4 4 4 4 2 3 4 18 14 7 4 5 10 8 31 212 212 274 344 25 29 33 37 41 22 8 54 54 63 69 86 1134 174 48 48

Problem Name ex21 ex4 1 1 saxena ex4 1 3 saxena ex4 1 4 saxena ex4 1 5 saxena ex4 1 6 saxena ex4 1 7 saxena ex4 1 8 saxena ex4 1 9 saxena ex7 3 1 saxena ex7 3 2 saxena ex8 1 3 saxena ex8 1 4 saxena ex8 1 5 saxena ex8 1 7 saxena ex8 1 8 saxena ex8 4 2 saxena fo7 2 reformulated fo7 reformulated fo8 reformulated fo9 reformulated had12 had14 had16 had18 had20 harker saxena immun saxena kallrath packing 2009 kallrath packing 2009 kallrath packing 2009 kallrath packing 2009 kallrath packing 2009 kallrath packing 2009 kallrath packing 2009 kallrath packing 2009 kallrath packing 2009

circles.c6 circles.c6 circles.c6 circles.c7 circles.c8 circlespol circlespol circlespol circlespol

# Nonlinear Terms 384 9 9 8 10 9 3 3 5 33 13 14 10 12 23 10 110 28 28 32 36 144 196 256 324 400 48 6 86 86 114 114 146 1808 212 42 42


Table 11 (MIQCQP) continued # Variables Contin

Discrete

# Constraints

43 791 184 390 49 49 49 634 10 10 12 12 14 14 16 16 16 18 18 14 14 16 18 20 22 24 2425 1 21 57 73 4 4 67 136 136 136

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 448 1024 6 30 42 0 0 36 87 87 87

48 816 192 388 52 52 52 619 16 16 24 24 34 34 46 46 46 60 60 24 24 31 40 49 60 71 2507 65 44 158 212 4 6 214 625 607 628

Problem Name kallrath packing kallrath packing kallrath packing kallrath packing kallrath packing kallrath packing kallrath packing kallrath packing kallrath packing kallrath packing kallrath packing kallrath packing kallrath packing kallrath packing kallrath packing kallrath packing kallrath packing kallrath packing kallrath packing kallrath packing kallrath packing kallrath packing kallrath packing kallrath packing kallrath packing kallrath packing khor kra32 m3 reformulated m6 reformulated m7 reformulated mathopt1 saxena mathopt2 saxena MPBP 6T 3P 2Q 029 MPBP 8T 3P 2Q 146 MPBP 8T 3P 2Q 718 MPBP 8T 3P 2Q 721

2009 2009 2009 2009 2009 2009 2009 2009 2009 2009 2009 2009 2009 2009 2009 2009 2009 2009 2009 2009 2009 2009 2009 2009 2009 2009

circlespol circlespol circlesrec circlesrec circlesrec circlesrec circlesrec circlesrec congruentc congruentc congruentc congruentc congruentc congruentc congruentc congruentc congruentc congruentc congruentc diffcircle diffcircle diffcircle diffcircle diffcircle diffcircle diffcircle

# Nonlinear Terms 42 1262 298 600 48 48 48 968 14 14 26 26 42 42 62 62 62 86 86 42 42 62 86 114 146 182 232 960 12 24 28 6 5 64 256 244 256


Table 11 (MIQCQP) continued Problem Name MPBP 8T 4P 2Q 480 MPBP 8T 4P 2Q 531 MPBP 8T 4P 2Q 852 nug05 nug06 nug07 nug08 nug10 nug12 nug14 nug15 nug16a nug16b nug17 nug18 nug20 nug21 nug22 nug24 nug25 nug27 nug28 o7 2 reformulated o7 reformulated pnt pack 02.ORD pnt pack 03.ORD pnt pack 04.ORD pnt pack 05.ORD pnt pack 06.ORD pnt pack 07.ORD pnt pack 08.ORD pnt pack 09.ORD pnt pack 10.ORD pnt pack 11.ORD pnt pack 12.ORD pnt pack 13.ORD pnt pack 14.ORD

# Variables Contin

Discrete

# Constraints

185 169 185 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 73 73 6 8 10 12 14 16 18 20 22 24 26 28 30

120 104 120 25 36 49 64 100 144 196 225 256 256 289 324 400 441 484 576 625 729 784 42 42 0 0 0 0 0 0 0 0 0 0 0 0 0

857 737 861 11 13 15 17 21 25 29 31 33 33 35 37 41 43 45 49 51 55 57 212 212 4 7 11 16 22 29 37 46 56 67 79 92 106

# Nonlinear Terms 376 358 376 25 36 49 64 100 144 196 225 256 256 289 324 400 441 484 576 625 729 784 28 28 4 12 24 40 60 84 112 144 180 220 264 312 364


Table 11 (MIQCQP) continued Problem Name pnt pack 15.ORD prob09 saxena Problem 0030 75 Problem 0050 75 Problem 0100 01 Problem 0100 50 Problem 0100 75 Problem 0200 01 Problem 0200 50 Problem 0500 01 Problem 0500 25 Problem 1000 25 Problem Q030 Problem Q050 Problem Q100 Problem Q150 process saxena prolog saxena rbrock saxena rou12 rou15 rou20 Sarawak Scenario1 Sarawak Scenario81 scr12 scr15 spar020-100-1 spar020-100-2 spar020-100-3 spar030-060-1 spar030-060-2 spar030-060-3 spar030-070-1 spar030-070-2 spar030-070-3 spar030-080-1 spar030-080-2

# Variables Contin

Discrete

# Constraints

32 4 31 51 101 101 101 201 201 501 501 1001 31 51 101 151 13 21 4 1 1 1 94 7534 1 1 21 21 21 31 31 31 31 31 31 31 31

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 144 225 400 38 38 144 225 0 0 0 0 0 0 0 0 0 0 0

121 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 10 23 2 25 31 41 213 11093 25 31 1 1 1 1 1 1 1 1 1 1 1

# Nonlinear Terms 420 4 30 50 100 100 100 200 200 500 500 1000 30 50 100 150 13 14 4 144 225 400 68 5508 144 225 20 20 20 30 30 30 30 30 30 30 30


Table 11 (MIQCQP) continued # Variables Problem Name Contin Discrete spar030-080-3 spar030-090-1 spar030-090-2 spar030-090-3 spar030-100-1 spar030-100-2 spar030-100-3 spar040-030-1 spar040-030-2 spar040-030-3 spar040-040-1 spar040-040-2 spar040-040-3 spar040-050-1 spar040-050-2 spar040-050-3 spar040-060-1 spar040-060-2 spar040-060-3 spar040-070-1 spar040-070-2 spar040-070-3 spar040-080-1 spar040-080-2 spar040-080-3 spar040-090-1 spar040-090-2 spar040-090-3 spar040-100-1 spar040-100-2 spar040-100-3 spar050-030-1 spar050-030-2 spar050-030-3 spar050-040-1 spar050-040-2 spar050-040-3

31 31 31 31 31 31 31 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 51 51 51 51 51 51

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

# Constraints

# Nonlinear Terms

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

30 30 30 30 30 30 30 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 50 50 50 50 50 50


Table 11 (MIQCQP) continued # Variables Problem Name Contin Discrete spar050-050-1 spar050-050-2 spar050-050-3 spar060-020-1 spar060-020-2 spar060-020-3 spar070-025-1 spar070-025-2 spar070-025-3 spar070-050-1 spar070-050-2 spar070-050-3 spar070-075-1 spar070-075-2 spar070-075-3 spar080-025-1 spar080-025-2 spar080-025-3 spar080-050-1 spar080-050-2 spar080-050-3 spar080-075-1 spar080-075-2 spar080-075-3 spar090-025-1 spar090-025-2 spar090-025-3 spar090-050-1 spar090-050-2 spar090-050-3 spar090-075-1 spar090-075-2 spar090-075-3 spar100-025-1 spar100-025-2 spar100-025-3 spar100-050-1

51 51 51 61 61 61 71 71 71 71 71 71 71 71 71 81 81 81 81 81 81 81 81 81 91 91 91 91 91 91 91 91 91 101 101 101 101

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

# Constraints

# Nonlinear Terms

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

50 50 50 60 60 60 70 70 70 70 70 70 70 70 70 80 80 80 80 80 80 80 80 80 90 90 90 90 90 90 90 90 90 100 100 100 100



Problem Name spar100-050-2 spar100-050-3 spar100-075-1 spar100-075-2 spar100-075-3 st e03 saxena st e05 saxena st e10 saxena st e17 saxena st e19 saxena st e20 saxena st qpc-m0 saxena st qpk1 saxena st z saxena tai10a tai12a tai15a tai17a tai20a tai25a tai30a tai35a teles etal 2009 WUN teles etal 2009 WUN teles etal 2009 WUN teles etal 2009 WUN teles etal 2009 WUN teles etal 2009 WUN teles etal 2009 WUN teles etal 2009 WUN teles etal 2009 WUN teles etal 2009 WUN teles etal 2009 WUN teles etal 2009 WUN teles etal 2009 WUN teles etal 2009 WUN teles etal 2009 WUN

Ex01 Ex02 Ex03 Ex04 Ex05 Ex06 Ex07 Ex08 Ex09 Ex10 Ex11 Ex12 Ex13 Ex14 Ex16

Contin

Discrete

# Constraints

101 101 101 101 101 15 6 5 3 5 9 3 3 4 1 1 1 1 1 1 1 1 41 69 65 71 94 106 111 91 133 51 65 53 99 126 83

0 0 0 0 0 0 0 0 0 0 0 0 0 0 100 144 225 289 400 625 900 1225 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

1 1 1 1 1 14 4 4 2 5 8 3 5 6 21 25 31 35 41 51 61 71 39 77 77 55 60 116 136 96 163 52 65 45 91 136 84

# Nonlinear Terms 100 100 100 100 100 27 4 3 2 5 10 2 2 3 100 144 225 289 400 625 900 1225 78 208 208 136 152 375 450 300 612 117 156 104 272 456 240


Table 11 (MIQCQP) continued Problem Name teles etal 2009 WUN Ex17 teles etal 2009 WUN Ex18 teles etal 2009 WUN Ex19 teles etal 2009 WUN Ex20 teles etal 2009 WUN Ex21 teles etal 2009 WUN Ex22 teles etal 2009 WUN Ex23 teles etal 2009 WUN Ex24 teles etal 2009 WUN Ex25 teles etal 2009 WUN Ex26 teles etal 2009 WUN Ex27 teles etal 2009 WUN Ex28 teles etal 2009 WUN Ex29 teles etal 2009 WUN Ex30 teles etal 2009 WUN Ex31 teles etal 2009 WUN Ex32 teles etal 2009 WUN Ex33 teles etal 2009 WUN Ex34 teles etal 2009 WUN Ex35 teles etal 2009 WUN Ex36 unitbox c 10 10 1 100 unitbox c 10 10 1 50 unitbox c 10 10 2 100 unitbox c 10 10 2 50 unitbox c 10 10 3 100 unitbox c 10 10 3 50 unitbox c 10 15 1 100 unitbox c 10 15 1 50 unitbox c 10 15 2 100 unitbox c 10 15 2 50 unitbox c 10 15 3 100 unitbox c 10 15 3 50 unitbox c 10 20 1 100 unitbox c 10 20 1 50 unitbox c 10 20 2 100 unitbox c 10 20 2 50 unitbox c 10 20 3 100

# Variables Contin

Discrete

# Constraints

75 61 69 176 121 147 159 140 122 337 433 761 669 721 781 661 425 489 483 325 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

67 65 77 133 127 136 154 136 88 289 209 541 433 451 541 381 245 269 324 240 11 11 11 11 11 11 16 16 16 16 16 16 21 21 21 21 21

# Nonlinear Terms 180 156 208 460 408 456 570 456 285 1740 1184 5400 3780 4050 5400 3600 1628 1924 2405 1395 110 110 110 110 110 110 160 160 160 160 160 160 210 210 210 210 210



Problem Name unitbox unitbox unitbox unitbox unitbox unitbox unitbox unitbox unitbox unitbox unitbox unitbox unitbox unitbox unitbox unitbox unitbox unitbox unitbox unitbox unitbox unitbox unitbox unitbox unitbox unitbox unitbox unitbox unitbox unitbox unitbox unitbox unitbox unitbox unitbox unitbox unitbox

c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c

10 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 28 28 28 28 28 28 28 28 28

20 20 20 20 20 20 20 20 20 20 30 30 30 30 30 30 30 30 30 40 40 40 40 40 40 40 40 40 28 28 28 42 42 42 56 56 56

3 1 1 1 2 2 2 3 3 3 1 1 1 2 2 2 3 3 3 1 1 1 2 2 2 3 3 3 1 2 3 1 2 3 1 2 3

50 100 25 50 100 25 50 100 25 50 100 25 50 100 25 50 100 25 50 100 25 50 100 25 50 100 25 50 25 25 25 25 25 25 25 25 25

Contin

Discrete

# Constraints

11 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 29 29 29 29 29 29 29 29 29

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

21 21 21 21 21 21 21 21 21 21 31 31 31 31 31 31 31 31 31 41 41 41 41 41 41 41 41 41 29 29 29 43 43 43 57 57 57

# Nonlinear Terms 210 420 419 420 420 420 420 420 420 420 620 619 620 620 620 620 620 620 620 820 819 820 820 820 820 820 820 820 811 812 812 1203 1204 1204 1595 1596 1596



Problem Name unitbox unitbox unitbox unitbox unitbox unitbox unitbox unitbox unitbox unitbox unitbox unitbox unitbox unitbox unitbox unitbox unitbox unitbox unitbox unitbox unitbox unitbox unitbox unitbox unitbox unitbox unitbox unitbox unitbox unitbox unitbox unitbox unitbox unitbox unitbox unitbox unitbox


30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40

30 30 30 30 30 30 45 45 45 45 45 45 60 60 60 60 60 60 40 40 40 40 40 40 40 40 40 60 60 60 60 60 60 60 60 60 80

1 1 2 2 3 3 1 1 2 2 3 3 1 1 2 2 3 3 1 1 1 2 2 2 3 3 3 1 1 1 2 2 2 3 3 3 1

100 50 100 50 100 50 100 50 100 50 100 50 100 50 100 50 100 50 100 25 50 100 25 50 100 25 50 100 25 50 100 25 50 100 25 50 100

Contin

Discrete

# Constraints

31 31 31 31 31 31 31 31 31 31 31 31 31 31 31 31 31 31 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

31 31 31 31 31 31 46 46 46 46 46 46 61 61 61 61 61 61 41 41 41 41 41 41 41 41 41 61 61 61 61 61 61 61 61 61 81

# Nonlinear Terms 930 930 930 930 930 930 1380 1380 1380 1380 1380 1380 1830 1830 1830 1830 1830 1830 1640 1640 1640 1640 1640 1640 1640 1640 1640 2440 2440 2440 2440 2440 2440 2440 2440 2440 3240


Table 11 (MIQCQP) continued Problem Name unitbox unitbox unitbox unitbox unitbox unitbox unitbox unitbox unitbox unitbox unitbox unitbox unitbox unitbox unitbox unitbox unitbox unitbox unitbox unitbox unitbox unitbox unitbox unitbox unitbox unitbox unitbox unitbox unitbox unitbox unitbox unitbox unitbox unitbox unitbox unitbox unitbox


40 80 1 25 40 80 1 50 40 80 2 100 40 80 2 25 40 80 2 50 40 80 3 100 40 80 3 25 40 80 3 50 48 48 1 25 48 48 2 25 48 48 3 25 48 72 1 25 48 72 2 25 48 72 3 25 48 96 1 25 48 96 2 25 48 96 3 25 50 100 1 100 50 100 1 50 50 100 2 100 50 100 2 50 50 100 3 100 50 100 3 50 50 50 1 100 50 50 1 50 50 50 2 100 50 50 2 50 50 50 3 100 50 50 3 50 50 75 1 100 50 75 1 50 50 75 2 100 50 75 2 50 50 75 3 100 50 75 3 50 8 12 1 25 8 12 2 25

# Variables Contin

Discrete

# Constraints

41 41 41 41 41 41 41 41 49 49 49 49 49 49 49 49 49 51 51 51 51 51 51 51 51 51 51 51 51 51 51 51 51 51 51 9 9

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

81 81 81 81 81 81 81 81 49 49 49 73 73 73 97 97 97 101 101 101 101 101 101 51 51 51 51 51 51 76 76 76 76 76 76 13 13

# Nonlinear Terms 3240 3240 3240 3240 3240 3240 3240 3240 2352 2352 2351 3504 3504 3503 4656 4656 4655 5050 5050 5050 5050 5050 5050 2550 2550 2550 2550 2550 2550 3800 3800 3800 3800 3800 3800 99 98



Problem Name unitbox unitbox unitbox unitbox unitbox unitbox unitbox wil50

c c c c c c c

8 8 8 8 8 8 8

12 3 25 16 1 25 16 2 25 16 3 25 8 1 25 8 2 25 8 3 25

Contin

Discrete

# Constraints

9 9 9 9 9 9 9 1

0 0 0 0 0 0 0 2500

13 17 17 17 9 9 9 101

66

# Nonlinear Terms 100 129 130 131 69 68 69 2500