MINLPLib
A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Removed Instance clay0303h
Non overlapping rectangular units must be placed within the confines of certain designated areas such that the cost of connecting these units is minimized.
| Formatsⓘ | ams gms mod nl osil py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | 26669.13374000 (ALPHAECP) 19413.15701000 (ANTIGONE) 26669.13370000 (BARON) 26669.13374000 (BONMIN) 26669.13363000 (COUENNE) 26669.13374000 (LINDO) 26669.13370000 (SCIP) 2400.00000000 (SHOT) |
| Referencesⓘ | Sawaya, Nicolas W, Reformulations, relaxations and cutting planes for generalized disjunctive programming, PhD thesis, Carnegie Mellon University, 2006. |
| Sourceⓘ | CLay0303H.gms from CMU-IBM MINLP solver project page |
| Applicationⓘ | Layout |
| Added to libraryⓘ | 28 Sep 2013 |
| Removed from libraryⓘ | 16 Feb 2022 |
| Removed becauseⓘ | Superseded by clay0303hfsg |
| Problem typeⓘ | MBNLP |
| #Variablesⓘ | 99 |
| #Binary Variablesⓘ | 21 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 27 |
| #Nonlinear Binary Variablesⓘ | 9 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | linear |
| Objective curvatureⓘ | linear |
| #Nonzeros in Objectiveⓘ | 6 |
| #Nonlinear Nonzeros in Objectiveⓘ | 0 |
| #Constraintsⓘ | 150 |
| #Linear Constraintsⓘ | 114 |
| #Quadratic Constraintsⓘ | 0 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 36 |
| Operands in Gen. Nonlin. Functionsⓘ | div mul sqr |
| Constraints curvatureⓘ | convex |
| #Nonzeros in Jacobianⓘ | 417 |
| #Nonlinear Nonzeros in Jacobianⓘ | 108 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 63 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 27 |
| #Blocks in Hessian of Lagrangianⓘ | 9 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 3 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 3 |
| Average blocksize in Hessian of Lagrangianⓘ | 3.0 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 1.0000e-06 |
| Maximal coefficientⓘ | 6.8890e+03 |
| Infeasibility of initial pointⓘ | 12.5 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 151 25 12 114 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 100 79 21 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 424 316 108 0
*
* Solve m using MINLP minimizing objvar;
Variables x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,x17,x18,x19
,x20,x21,x22,x23,x24,x25,x26,x27,x28,x29,x30,x31,x32,x33,x34,x35,x36
,x37,x38,x39,x40,x41,x42,x43,x44,x45,x46,x47,x48,x49,x50,x51,x52,x53
,x54,x55,x56,x57,x58,x59,x60,x61,x62,x63,x64,x65,x66,x67,x68,x69,x70
,x71,x72,b73,b74,b75,b76,b77,b78,b79,b80,b81,b82,b83,b84,b85,b86,b87
,b88,b89,b90,b91,b92,b93,x94,x95,x96,x97,x98,x99,objvar;
Positive Variables x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,x17,x18,x19,x20,x21
,x22,x23,x24,x25,x26,x27,x28,x29,x30,x31,x32,x33,x34,x35,x36,x37,x38
,x39,x40,x41,x42,x43,x44,x45,x46,x47,x48,x49,x50,x51,x52,x53,x54,x55
,x56,x57,x58,x59,x60,x61,x62,x63,x64,x65,x66,x67,x68,x69,x70,x71,x72
,x94,x95,x96,x97,x98,x99;
Binary Variables b73,b74,b75,b76,b77,b78,b79,b80,b81,b82,b83,b84,b85,b86,b87
,b88,b89,b90,b91,b92,b93;
Equations e1,e2,e3,e4,e5,e6,e7,e8,e9,e10,e11,e12,e13,e14,e15,e16,e17,e18,e19
,e20,e21,e22,e23,e24,e25,e26,e27,e28,e29,e30,e31,e32,e33,e34,e35,e36
,e37,e38,e39,e40,e41,e42,e43,e44,e45,e46,e47,e48,e49,e50,e51,e52,e53
,e54,e55,e56,e57,e58,e59,e60,e61,e62,e63,e64,e65,e66,e67,e68,e69,e70
,e71,e72,e73,e74,e75,e76,e77,e78,e79,e80,e81,e82,e83,e84,e85,e86,e87
,e88,e89,e90,e91,e92,e93,e94,e95,e96,e97,e98,e99,e100,e101,e102,e103
,e104,e105,e106,e107,e108,e109,e110,e111,e112,e113,e114,e115,e116
,e117,e118,e119,e120,e121,e122,e123,e124,e125,e126,e127,e128,e129
,e130,e131,e132,e133,e134,e135,e136,e137,e138,e139,e140,e141,e142
,e143,e144,e145,e146,e147,e148,e149,e150,e151;
e1.. - 300*x94 - 240*x95 - 100*x96 - 300*x97 - 240*x98 - 100*x99 + objvar
=E= 0;
e2.. - x1 + x2 + x94 =G= 0;
e3.. - x1 + x3 + x95 =G= 0;
e4.. - x2 + x3 + x96 =G= 0;
e5.. x1 - x2 + x94 =G= 0;
e6.. x1 - x3 + x95 =G= 0;
e7.. x2 - x3 + x96 =G= 0;
e8.. - x4 + x5 + x97 =G= 0;
e9.. - x4 + x6 + x98 =G= 0;
e10.. - x5 + x6 + x99 =G= 0;
e11.. x4 - x5 + x97 =G= 0;
e12.. x4 - x6 + x98 =G= 0;
e13.. x5 - x6 + x99 =G= 0;
e14.. x1 - x7 - x9 - x11 - x13 =E= 0;
e15.. x1 - x8 - x10 - x12 - x14 =E= 0;
e16.. x2 - x15 - x17 - x19 - x21 =E= 0;
e17.. x2 - x16 - x18 - x20 - x22 =E= 0;
e18.. x3 - x23 - x25 - x27 - x29 =E= 0;
e19.. x3 - x24 - x26 - x28 - x30 =E= 0;
e20.. x4 - x31 - x33 - x35 - x37 =E= 0;
e21.. x4 - x32 - x34 - x36 - x38 =E= 0;
e22.. x5 - x39 - x41 - x43 - x45 =E= 0;
e23.. x5 - x40 - x42 - x44 - x46 =E= 0;
e24.. x6 - x47 - x49 - x51 - x53 =E= 0;
e25.. x6 - x48 - x50 - x52 - x54 =E= 0;
e26.. x7 - 52.5*b73 =L= 0;
e27.. x8 - 52.5*b74 =L= 0;
e28.. x9 - 52.5*b76 =L= 0;
e29.. x10 - 52.5*b77 =L= 0;
e30.. x11 - 52.5*b79 =L= 0;
e31.. x12 - 52.5*b80 =L= 0;
e32.. x13 - 52.5*b82 =L= 0;
e33.. x14 - 52.5*b83 =L= 0;
e34.. x15 - 52.5*b73 =L= 0;
e35.. x16 - 51.5*b75 =L= 0;
e36.. x17 - 52.5*b76 =L= 0;
e37.. x18 - 51.5*b78 =L= 0;
e38.. x19 - 52.5*b79 =L= 0;
e39.. x20 - 51.5*b81 =L= 0;
e40.. x21 - 52.5*b82 =L= 0;
e41.. x22 - 51.5*b84 =L= 0;
e42.. x23 - 52.5*b74 =L= 0;
e43.. x24 - 51.5*b75 =L= 0;
e44.. x25 - 52.5*b77 =L= 0;
e45.. x26 - 51.5*b78 =L= 0;
e46.. x27 - 52.5*b80 =L= 0;
e47.. x28 - 51.5*b81 =L= 0;
e48.. x29 - 52.5*b83 =L= 0;
e49.. x30 - 51.5*b84 =L= 0;
e50.. x31 - 82*b73 =L= 0;
e51.. x32 - 82*b74 =L= 0;
e52.. x33 - 82*b76 =L= 0;
e53.. x34 - 82*b77 =L= 0;
e54.. x35 - 82*b79 =L= 0;
e55.. x36 - 82*b80 =L= 0;
e56.. x37 - 82*b82 =L= 0;
e57.. x38 - 82*b83 =L= 0;
e58.. x39 - 82*b73 =L= 0;
e59.. x40 - 82.5*b75 =L= 0;
e60.. x41 - 82*b76 =L= 0;
e61.. x42 - 82.5*b78 =L= 0;
e62.. x43 - 82*b79 =L= 0;
e63.. x44 - 82.5*b81 =L= 0;
e64.. x45 - 82*b82 =L= 0;
e65.. x46 - 82.5*b84 =L= 0;
e66.. x47 - 82*b74 =L= 0;
e67.. x48 - 82.5*b75 =L= 0;
e68.. x49 - 82*b77 =L= 0;
e69.. x50 - 82.5*b78 =L= 0;
e70.. x51 - 82*b80 =L= 0;
e71.. x52 - 82.5*b81 =L= 0;
e72.. x53 - 82*b83 =L= 0;
e73.. x54 - 82.5*b84 =L= 0;
e74.. x7 - x15 + 6*b73 =L= 0;
e75.. x8 - x23 + 4*b74 =L= 0;
e76.. x16 - x24 + 5*b75 =L= 0;
e77.. - x9 + x17 + 6*b76 =L= 0;
e78.. - x10 + x25 + 4*b77 =L= 0;
e79.. - x18 + x26 + 5*b78 =L= 0;
e80.. x35 - x43 + 5.5*b79 =L= 0;
e81.. x36 - x51 + 4.5*b80 =L= 0;
e82.. x44 - x52 + 4*b81 =L= 0;
e83.. - x37 + x45 + 5.5*b82 =L= 0;
e84.. - x38 + x53 + 4.5*b83 =L= 0;
e85.. - x46 + x54 + 4*b84 =L= 0;
e86.. b73 + b76 + b79 + b82 =E= 1;
e87.. b74 + b77 + b80 + b83 =E= 1;
e88.. b75 + b78 + b81 + b84 =E= 1;
e89.. x1 - x55 - x58 - x61 =E= 0;
e90.. x2 - x56 - x59 - x62 =E= 0;
e91.. x3 - x57 - x60 - x63 =E= 0;
e92.. x4 - x64 - x67 - x70 =E= 0;
e93.. x5 - x65 - x68 - x71 =E= 0;
e94.. x6 - x66 - x69 - x72 =E= 0;
e95.. x55 - 18.5*b85 =L= 0;
e96.. x56 - 17.5*b86 =L= 0;
e97.. x57 - 19.5*b87 =L= 0;
e98.. x58 - 52.5*b88 =L= 0;
e99.. x59 - 51.5*b89 =L= 0;
e100.. x60 - 53.5*b90 =L= 0;
e101.. x61 - 31.5*b91 =L= 0;
e102.. x62 - 30.5*b92 =L= 0;
e103.. x63 - 32.5*b93 =L= 0;
e104.. x64 - 13*b85 =L= 0;
e105.. x65 - 13.5*b86 =L= 0;
e106.. x66 - 14.5*b87 =L= 0;
e107.. x67 - 82*b88 =L= 0;
e108.. x68 - 82.5*b89 =L= 0;
e109.. x69 - 83.5*b90 =L= 0;
e110.. x70 - 51*b91 =L= 0;
e111.. x71 - 51.5*b92 =L= 0;
e112.. x72 - 52.5*b93 =L= 0;
e113.. (sqr(x55/(1e-6 + b85)) - 35*x55/(1e-6 + b85) + 306.25*b85 + sqr(x64/(
1e-6 + b85)) - 14*x64/(1e-6 + b85) + 49*b85 - 36*b85)*(1e-6 + b85) =L= 0
;
e114.. (sqr(x56/(1e-6 + b86)) - 37*x56/(1e-6 + b86) + 342.25*b86 + sqr(x65/(
1e-6 + b86)) - 15*x65/(1e-6 + b86) + 56.25*b86 - 36*b86)*(1e-6 + b86)
=L= 0;
e115.. (sqr(x57/(1e-6 + b87)) - 33*x57/(1e-6 + b87) + 272.25*b87 + sqr(x66/(
1e-6 + b87)) - 17*x66/(1e-6 + b87) + 72.25*b87 - 36*b87)*(1e-6 + b87)
=L= 0;
e116.. (sqr(x58/(1e-6 + b88)) - 105*x58/(1e-6 + b88) + 2756.25*b88 + sqr(x67/(
1e-6 + b88)) - 154*x67/(1e-6 + b88) + 5929*b88 - 25*b88)*(1e-6 + b88)
=L= 0;
e117.. (sqr(x59/(1e-6 + b89)) - 107*x59/(1e-6 + b89) + 2862.25*b89 + sqr(x68/(
1e-6 + b89)) - 155*x68/(1e-6 + b89) + 6006.25*b89 - 25*b89)*(1e-6 + b89)
=L= 0;
e118.. (sqr(x60/(1e-6 + b90)) - 103*x60/(1e-6 + b90) + 2652.25*b90 + sqr(x69/(
1e-6 + b90)) - 157*x69/(1e-6 + b90) + 6162.25*b90 - 25*b90)*(1e-6 + b90)
=L= 0;
e119.. (sqr(x61/(1e-6 + b91)) - 65*x61/(1e-6 + b91) + 1056.25*b91 + sqr(x70/(
1e-6 + b91)) - 94*x70/(1e-6 + b91) + 2209*b91 - 16*b91)*(1e-6 + b91)
=L= 0;
e120.. (sqr(x62/(1e-6 + b92)) - 67*x62/(1e-6 + b92) + 1122.25*b92 + sqr(x71/(
1e-6 + b92)) - 95*x71/(1e-6 + b92) + 2256.25*b92 - 16*b92)*(1e-6 + b92)
=L= 0;
e121.. (sqr(x63/(1e-6 + b93)) - 63*x63/(1e-6 + b93) + 992.25*b93 + sqr(x72/(
1e-6 + b93)) - 97*x72/(1e-6 + b93) + 2352.25*b93 - 16*b93)*(1e-6 + b93)
=L= 0;
e122.. (sqr(x55/(1e-6 + b85)) - 35*x55/(1e-6 + b85) + 306.25*b85 + sqr(x64/(
1e-6 + b85)) - 26*x64/(1e-6 + b85) + 169*b85 - 36*b85)*(1e-6 + b85)
=L= 0;
e123.. (sqr(x56/(1e-6 + b86)) - 37*x56/(1e-6 + b86) + 342.25*b86 + sqr(x65/(
1e-6 + b86)) - 25*x65/(1e-6 + b86) + 156.25*b86 - 36*b86)*(1e-6 + b86)
=L= 0;
e124.. (sqr(x57/(1e-6 + b87)) - 33*x57/(1e-6 + b87) + 272.25*b87 + sqr(x66/(
1e-6 + b87)) - 23*x66/(1e-6 + b87) + 132.25*b87 - 36*b87)*(1e-6 + b87)
=L= 0;
e125.. (sqr(x58/(1e-6 + b88)) - 105*x58/(1e-6 + b88) + 2756.25*b88 + sqr(x67/(
1e-6 + b88)) - 166*x67/(1e-6 + b88) + 6889*b88 - 25*b88)*(1e-6 + b88)
=L= 0;
e126.. (sqr(x59/(1e-6 + b89)) - 107*x59/(1e-6 + b89) + 2862.25*b89 + sqr(x68/(
1e-6 + b89)) - 165*x68/(1e-6 + b89) + 6806.25*b89 - 25*b89)*(1e-6 + b89)
=L= 0;
e127.. (sqr(x60/(1e-6 + b90)) - 103*x60/(1e-6 + b90) + 2652.25*b90 + sqr(x69/(
1e-6 + b90)) - 163*x69/(1e-6 + b90) + 6642.25*b90 - 25*b90)*(1e-6 + b90)
=L= 0;
e128.. (sqr(x61/(1e-6 + b91)) - 65*x61/(1e-6 + b91) + 1056.25*b91 + sqr(x70/(
1e-6 + b91)) - 106*x70/(1e-6 + b91) + 2809*b91 - 16*b91)*(1e-6 + b91)
=L= 0;
e129.. (sqr(x62/(1e-6 + b92)) - 67*x62/(1e-6 + b92) + 1122.25*b92 + sqr(x71/(
1e-6 + b92)) - 105*x71/(1e-6 + b92) + 2756.25*b92 - 16*b92)*(1e-6 + b92)
=L= 0;
e130.. (sqr(x63/(1e-6 + b93)) - 63*x63/(1e-6 + b93) + 992.25*b93 + sqr(x72/(
1e-6 + b93)) - 103*x72/(1e-6 + b93) + 2652.25*b93 - 16*b93)*(1e-6 + b93)
=L= 0;
e131.. (sqr(x55/(1e-6 + b85)) - 25*x55/(1e-6 + b85) + 156.25*b85 + sqr(x64/(
1e-6 + b85)) - 14*x64/(1e-6 + b85) + 49*b85 - 36*b85)*(1e-6 + b85) =L= 0
;
e132.. (sqr(x56/(1e-6 + b86)) - 23*x56/(1e-6 + b86) + 132.25*b86 + sqr(x65/(
1e-6 + b86)) - 15*x65/(1e-6 + b86) + 56.25*b86 - 36*b86)*(1e-6 + b86)
=L= 0;
e133.. (sqr(x57/(1e-6 + b87)) - 27*x57/(1e-6 + b87) + 182.25*b87 + sqr(x66/(
1e-6 + b87)) - 17*x66/(1e-6 + b87) + 72.25*b87 - 36*b87)*(1e-6 + b87)
=L= 0;
e134.. (sqr(x58/(1e-6 + b88)) - 95*x58/(1e-6 + b88) + 2256.25*b88 + sqr(x67/(
1e-6 + b88)) - 154*x67/(1e-6 + b88) + 5929*b88 - 25*b88)*(1e-6 + b88)
=L= 0;
e135.. (sqr(x59/(1e-6 + b89)) - 93*x59/(1e-6 + b89) + 2162.25*b89 + sqr(x68/(
1e-6 + b89)) - 155*x68/(1e-6 + b89) + 6006.25*b89 - 25*b89)*(1e-6 + b89)
=L= 0;
e136.. (sqr(x60/(1e-6 + b90)) - 97*x60/(1e-6 + b90) + 2352.25*b90 + sqr(x69/(
1e-6 + b90)) - 157*x69/(1e-6 + b90) + 6162.25*b90 - 25*b90)*(1e-6 + b90)
=L= 0;
e137.. (sqr(x61/(1e-6 + b91)) - 55*x61/(1e-6 + b91) + 756.25*b91 + sqr(x70/(
1e-6 + b91)) - 94*x70/(1e-6 + b91) + 2209*b91 - 16*b91)*(1e-6 + b91)
=L= 0;
e138.. (sqr(x62/(1e-6 + b92)) - 53*x62/(1e-6 + b92) + 702.25*b92 + sqr(x71/(
1e-6 + b92)) - 95*x71/(1e-6 + b92) + 2256.25*b92 - 16*b92)*(1e-6 + b92)
=L= 0;
e139.. (sqr(x63/(1e-6 + b93)) - 57*x63/(1e-6 + b93) + 812.25*b93 + sqr(x72/(
1e-6 + b93)) - 97*x72/(1e-6 + b93) + 2352.25*b93 - 16*b93)*(1e-6 + b93)
=L= 0;
e140.. (sqr(x55/(1e-6 + b85)) - 25*x55/(1e-6 + b85) + 156.25*b85 + sqr(x64/(
1e-6 + b85)) - 26*x64/(1e-6 + b85) + 169*b85 - 36*b85)*(1e-6 + b85)
=L= 0;
e141.. (sqr(x56/(1e-6 + b86)) - 23*x56/(1e-6 + b86) + 132.25*b86 + sqr(x65/(
1e-6 + b86)) - 25*x65/(1e-6 + b86) + 156.25*b86 - 36*b86)*(1e-6 + b86)
=L= 0;
e142.. (sqr(x57/(1e-6 + b87)) - 27*x57/(1e-6 + b87) + 182.25*b87 + sqr(x66/(
1e-6 + b87)) - 23*x66/(1e-6 + b87) + 132.25*b87 - 36*b87)*(1e-6 + b87)
=L= 0;
e143.. (sqr(x58/(1e-6 + b88)) - 95*x58/(1e-6 + b88) + 2256.25*b88 + sqr(x67/(
1e-6 + b88)) - 166*x67/(1e-6 + b88) + 6889*b88 - 25*b88)*(1e-6 + b88)
=L= 0;
e144.. (sqr(x59/(1e-6 + b89)) - 93*x59/(1e-6 + b89) + 2162.25*b89 + sqr(x68/(
1e-6 + b89)) - 165*x68/(1e-6 + b89) + 6806.25*b89 - 25*b89)*(1e-6 + b89)
=L= 0;
e145.. (sqr(x60/(1e-6 + b90)) - 97*x60/(1e-6 + b90) + 2352.25*b90 + sqr(x69/(
1e-6 + b90)) - 163*x69/(1e-6 + b90) + 6642.25*b90 - 25*b90)*(1e-6 + b90)
=L= 0;
e146.. (sqr(x61/(1e-6 + b91)) - 55*x61/(1e-6 + b91) + 756.25*b91 + sqr(x70/(
1e-6 + b91)) - 106*x70/(1e-6 + b91) + 2809*b91 - 16*b91)*(1e-6 + b91)
=L= 0;
e147.. (sqr(x62/(1e-6 + b92)) - 53*x62/(1e-6 + b92) + 702.25*b92 + sqr(x71/(
1e-6 + b92)) - 105*x71/(1e-6 + b92) + 2756.25*b92 - 16*b92)*(1e-6 + b92)
=L= 0;
e148.. (sqr(x63/(1e-6 + b93)) - 57*x63/(1e-6 + b93) + 812.25*b93 + sqr(x72/(
1e-6 + b93)) - 103*x72/(1e-6 + b93) + 2652.25*b93 - 16*b93)*(1e-6 + b93)
=L= 0;
e149.. b85 + b88 + b91 =E= 1;
e150.. b86 + b89 + b92 =E= 1;
e151.. b87 + b90 + b93 =E= 1;
* set non-default bounds
x1.lo = 11.5; x1.up = 52.5;
x2.lo = 12.5; x2.up = 51.5;
x3.lo = 10.5; x3.up = 53.5;
x4.lo = 7; x4.up = 82;
x5.lo = 6.5; x5.up = 82.5;
x6.lo = 5.5; x6.up = 83.5;
Model m / all /;
m.limrow=0; m.limcol=0;
m.tolproj=0.0;
$if NOT '%gams.u1%' == '' $include '%gams.u1%'
$if not set MINLP $set MINLP MINLP
Solve m using %MINLP% minimizing objvar;
Last updated: 2025-08-07 Git hash: e62cedfc