MINLPLib
A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Instance blend029
| Formatsⓘ | ams gms lp mod nl osil pip py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | 13.35940000 (ANTIGONE) 13.35940000 (BARON) 21.41190000 (COUENNE) 13.35940000 (GUROBI) 13.35940000 (LINDO) 13.35940000 (SCIP) 19.68940000 (SHOT) |
| Referencesⓘ | Trespalacios, Francisco, Kolodziej, Scott P, Furman, Kevin C, and Sawaya, Nicolas W, Multiperiod Blend Scheduling Problem, 2013. |
| Sourceⓘ | MPBP-029.gms from minlp.org model 168 |
| Applicationⓘ | Multiperiod Blend Scheduling |
| Added to libraryⓘ | 25 Sep 2013 |
| Problem typeⓘ | MBQCP |
| #Variablesⓘ | 102 |
| #Binary Variablesⓘ | 36 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 26 |
| #Nonlinear Binary Variablesⓘ | 0 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | max |
| Objective typeⓘ | linear |
| Objective curvatureⓘ | linear |
| #Nonzeros in Objectiveⓘ | 72 |
| #Nonlinear Nonzeros in Objectiveⓘ | 0 |
| #Constraintsⓘ | 213 |
| #Linear Constraintsⓘ | 201 |
| #Quadratic Constraintsⓘ | 12 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 0 |
| Operands in Gen. Nonlin. Functionsⓘ | |
| Constraints curvatureⓘ | indefinite |
| #Nonzeros in Jacobianⓘ | 470 |
| #Nonlinear Nonzeros in Jacobianⓘ | 64 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 56 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 0 |
| #Blocks in Hessian of Lagrangianⓘ | 6 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 3 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 6 |
| Average blocksize in Hessian of Lagrangianⓘ | 4.333333 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 5.0000e-02 |
| Maximal coefficientⓘ | 7.7400e+00 |
| Infeasibility of initial pointⓘ | 1.55 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 214 31 78 105 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 103 67 36 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 543 479 64 0
*
* Solve m using MINLP maximizing objvar;
Variables objvar,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,b68,b69
,b70,b71,b72,b73,b74,b75,b76,b77,b78,b79,b80,b81,b82,b83,b84,b85,b86
,b87,b88,b89,b90,b91,b92,b93,b94,b95,b96,b97,b98,b99,b100,b101,b102
,b103;
Positive Variables 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;
Binary Variables b68,b69,b70,b71,b72,b73,b74,b75,b76,b77,b78,b79,b80,b81,b82
,b83,b84,b85,b86,b87,b88,b89,b90,b91,b92,b93,b94,b95,b96,b97,b98,b99
,b100,b101,b102,b103;
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,e152,e153,e154,e155
,e156,e157,e158,e159,e160,e161,e162,e163,e164,e165,e166,e167,e168
,e169,e170,e171,e172,e173,e174,e175,e176,e177,e178,e179,e180,e181
,e182,e183,e184,e185,e186,e187,e188,e189,e190,e191,e192,e193,e194
,e195,e196,e197,e198,e199,e200,e201,e202,e203,e204,e205,e206,e207
,e208,e209,e210,e211,e212,e213,e214;
e1.. objvar + 1.74*x2 + 1.74*x3 + 1.74*x4 + 1.45*x5 + 1.45*x6 + 1.45*x7
- 7.38*x8 - 7.38*x9 - 7.38*x10 - 5.6*x11 - 5.6*x12 - 5.6*x13 + 1.7*x14
+ 1.7*x15 + 1.7*x16 + 1.18*x17 + 1.18*x18 + 1.18*x19 - 7.21*x20
- 7.21*x21 - 7.21*x22 - 5.45*x23 - 5.45*x24 - 5.45*x25 + 0.3*x26
+ 0.3*x27 + 0.3*x28 - 7.71*x29 - 7.71*x30 - 7.71*x31 - 6.28*x32
- 6.28*x33 - 6.28*x34 - 7.74*x35 - 7.74*x36 - 7.74*x37 + 0.84*b68
+ 0.84*b69 + 0.84*b70 + 0.05*b71 + 0.05*b72 + 0.05*b73 + 0.94*b74
+ 0.94*b75 + 0.94*b76 + 0.81*b77 + 0.81*b78 + 0.81*b79 + 0.79*b80
+ 0.79*b81 + 0.79*b82 + 0.05*b83 + 0.05*b84 + 0.05*b85 + 0.65*b86
+ 0.65*b87 + 0.65*b88 + 0.97*b89 + 0.97*b90 + 0.97*b91 + 0.57*b92
+ 0.57*b93 + 0.57*b94 + 0.26*b95 + 0.26*b96 + 0.26*b97 + 0.45*b98
+ 0.45*b99 + 0.45*b100 + 0.1*b101 + 0.1*b102 + 0.1*b103 =E= 0;
e2.. x2 + x5 + x8 + x11 + x50 =E= 1;
e3.. x14 + x17 + x20 + x23 + x53 =E= 1.1;
e4.. - x2 - x14 + x26 + x29 + x32 + x56 =E= 0.2;
e5.. - x5 - x17 - x26 + x35 + x59 =E= 0.1;
e6.. - x8 - x20 - x29 - x35 + x62 =E= 1.55;
e7.. - x11 - x23 - x32 + x65 =E= 0.49;
e8.. x38*x56 - 0.6*x2 - 0.2*x14 + 0.2*x26 + 0.2*x29 + 0.2*x32 =E= 0.04;
e9.. x41*x59 - 0.6*x5 - 0.2*x17 - 0.2*x26 + 0.7*x35 =E= 0.07;
e10.. x44*x56 - 0.4*x2 - 0.4*x14 + 0.5*x26 + 0.5*x29 + 0.5*x32 =E= 0.1;
e11.. x47*x59 - 0.4*x5 - 0.4*x17 - 0.5*x26 + 0.6*x35 =E= 0.06;
e12.. x3 + x6 + x9 + x12 - x50 + x51 =E= 1;
e13.. x4 + x7 + x10 + x13 - x51 + x52 =E= 0;
e14.. x15 + x18 + x21 + x24 - x53 + x54 =E= 0.1;
e15.. x16 + x19 + x22 + x25 - x54 + x55 =E= 0.9;
e16.. - x3 - x15 + x27 + x30 + x33 - x56 + x57 =E= 0;
e17.. - x4 - x16 + x28 + x31 + x34 - x57 + x58 =E= 0;
e18.. - x6 - x18 - x27 + x36 - x59 + x60 =E= 0;
e19.. - x7 - x19 - x28 + x37 - x60 + x61 =E= 0;
e20.. - x9 - x21 - x30 - x36 - x62 + x63 =E= -0.81;
e21.. - x10 - x22 - x31 - x37 - x63 + x64 =E= -0.88;
e22.. - x12 - x24 - x33 - x65 + x66 =E= -0.14;
e23.. - x13 - x25 - x34 - x66 + x67 =E= -0.1;
e24.. x39*x57 - (x38*x56 - (x38*x27 + x38*x30 + x38*x33)) - 0.6*x3 - 0.2*x15
=E= 0;
e25.. x40*x58 - (x39*x57 - (x39*x28 + x39*x31 + x39*x34)) - 0.6*x4 - 0.2*x16
=E= 0;
e26.. x42*x60 - (x41*x59 + x38*x27 - x41*x36) - 0.6*x6 - 0.2*x18 =E= 0;
e27.. x43*x61 - (x42*x60 + x39*x28 - x42*x37) - 0.6*x7 - 0.2*x19 =E= 0;
e28.. x45*x57 - (x44*x56 - (x44*x27 + x44*x30 + x44*x33)) - 0.4*x3 - 0.4*x15
=E= 0;
e29.. x46*x58 - (x45*x57 - (x45*x28 + x45*x31 + x45*x34)) - 0.4*x4 - 0.4*x16
=E= 0;
e30.. x48*x60 - (x47*x59 + x44*x27 - x47*x36) - 0.4*x6 - 0.4*x18 =E= 0;
e31.. x49*x61 - (x48*x60 + x45*x28 - x48*x37) - 0.4*x7 - 0.4*x19 =E= 0;
e32.. x2 - b68 =L= 0;
e33.. x3 - b69 =L= 0;
e34.. x4 - b70 =L= 0;
e35.. x5 - b71 =L= 0;
e36.. x6 - b72 =L= 0;
e37.. x7 - b73 =L= 0;
e38.. x8 - b74 =L= 0;
e39.. x9 - b75 =L= 0;
e40.. x10 - b76 =L= 0;
e41.. x11 - b77 =L= 0;
e42.. x12 - b78 =L= 0;
e43.. x13 - b79 =L= 0;
e44.. x14 - b80 =L= 0;
e45.. x15 - b81 =L= 0;
e46.. x16 - b82 =L= 0;
e47.. x17 - b83 =L= 0;
e48.. x18 - b84 =L= 0;
e49.. x19 - b85 =L= 0;
e50.. x20 - b86 =L= 0;
e51.. x21 - b87 =L= 0;
e52.. x22 - b88 =L= 0;
e53.. x23 - b89 =L= 0;
e54.. x24 - b90 =L= 0;
e55.. x25 - b91 =L= 0;
e56.. x26 - b92 =L= 0;
e57.. x27 - b93 =L= 0;
e58.. x28 - b94 =L= 0;
e59.. x29 - b95 =L= 0;
e60.. x30 - b96 =L= 0;
e61.. x31 - b97 =L= 0;
e62.. x32 - b98 =L= 0;
e63.. x33 - b99 =L= 0;
e64.. x34 - b100 =L= 0;
e65.. x35 - b101 =L= 0;
e66.. x36 - b102 =L= 0;
e67.. x37 - b103 =L= 0;
e68.. x2 =G= 0;
e69.. x3 =G= 0;
e70.. x4 =G= 0;
e71.. x5 =G= 0;
e72.. x6 =G= 0;
e73.. x7 =G= 0;
e74.. x8 =G= 0;
e75.. x9 =G= 0;
e76.. x10 =G= 0;
e77.. x11 =G= 0;
e78.. x12 =G= 0;
e79.. x13 =G= 0;
e80.. x14 =G= 0;
e81.. x15 =G= 0;
e82.. x16 =G= 0;
e83.. x17 =G= 0;
e84.. x18 =G= 0;
e85.. x19 =G= 0;
e86.. x20 =G= 0;
e87.. x21 =G= 0;
e88.. x22 =G= 0;
e89.. x23 =G= 0;
e90.. x24 =G= 0;
e91.. x25 =G= 0;
e92.. x26 =G= 0;
e93.. x27 =G= 0;
e94.. x28 =G= 0;
e95.. x29 =G= 0;
e96.. x30 =G= 0;
e97.. x31 =G= 0;
e98.. x32 =G= 0;
e99.. x33 =G= 0;
e100.. x34 =G= 0;
e101.. x35 =G= 0;
e102.. x36 =G= 0;
e103.. x37 =G= 0;
e104.. b74 =L= 1.5;
e105.. b75 =L= 1.5;
e106.. b76 =L= 1.5;
e107.. b77 =L= 0.6;
e108.. b78 =L= 0.6;
e109.. b79 =L= 0.6;
e110.. b86 =L= 1.1;
e111.. b87 =L= 1.1;
e112.. b88 =L= 1.1;
e113.. b89 =L= 0.2;
e114.. b90 =L= 0.2;
e115.. b91 =L= 0.2;
e116.. b74 =L= 1;
e117.. b75 =L= 1;
e118.. b76 =L= 1;
e119.. b77 =L= 0.8;
e120.. b78 =L= 0.8;
e121.. b79 =L= 0.8;
e122.. b86 =L= 1;
e123.. b87 =L= 1;
e124.. b88 =L= 1;
e125.. b89 =L= 0.8;
e126.. b90 =L= 0.8;
e127.. b91 =L= 0.8;
e128.. - b74 =G= -1.3;
e129.. - b75 =G= -1.3;
e130.. - b76 =G= -1.3;
e131.. - b77 =G= -1.4;
e132.. - b78 =G= -1.4;
e133.. - b79 =G= -1.4;
e134.. - b86 =G= -1.7;
e135.. - b87 =G= -1.7;
e136.. - b88 =G= -1.7;
e137.. - b89 =G= -1.8;
e138.. - b90 =G= -1.8;
e139.. - b91 =G= -1.8;
e140.. - b74 =G= -1;
e141.. - b75 =G= -1;
e142.. - b76 =G= -1;
e143.. - b77 =G= -1.4;
e144.. - b78 =G= -1.4;
e145.. - b79 =G= -1.4;
e146.. - b86 =G= -1;
e147.. - b87 =G= -1;
e148.. - b88 =G= -1;
e149.. - b89 =G= -1.4;
e150.. - b90 =G= -1.4;
e151.. - b91 =G= -1.4;
e152.. - x38 + b96 =L= 0.9;
e153.. - x39 + b97 =L= 0.9;
e154.. - x38 + b99 =L= 0;
e155.. - x39 + b100 =L= 0;
e156.. - x41 + b102 =L= 0.9;
e157.. - x42 + b103 =L= 0.9;
e158.. - x44 + b96 =L= 0.6;
e159.. - x45 + b97 =L= 0.6;
e160.. - x44 + b99 =L= 0.4;
e161.. - x45 + b100 =L= 0.4;
e162.. - x47 + b102 =L= 0.6;
e163.. - x48 + b103 =L= 0.6;
e164.. - x38 - b96 =G= -1.9;
e165.. - x39 - b97 =G= -1.9;
e166.. - x38 - b99 =G= -2;
e167.. - x39 - b100 =G= -2;
e168.. - x41 - b102 =G= -1.9;
e169.. - x42 - b103 =G= -1.9;
e170.. - x44 - b96 =G= -1.4;
e171.. - x45 - b97 =G= -1.4;
e172.. - x44 - b99 =G= -1.8;
e173.. - x45 - b100 =G= -1.8;
e174.. - x47 - b102 =G= -1.4;
e175.. - x48 - b103 =G= -1.4;
e176.. b95 =L= 1.1;
e177.. b98 =L= 0.2;
e178.. b101 =L= 1.6;
e179.. b95 =L= 1.1;
e180.. b98 =L= 0.9;
e181.. b101 =L= 1.2;
e182.. - b95 =G= -1.7;
e183.. - b98 =G= -1.8;
e184.. - b101 =G= -1.2;
e185.. - b95 =G= -0.9;
e186.. - b98 =G= -1.3;
e187.. - b101 =G= -0.8;
e188.. b68 + b92 =L= 1;
e189.. b69 + b93 =L= 1;
e190.. b70 + b94 =L= 1;
e191.. b68 + b95 =L= 1;
e192.. b69 + b96 =L= 1;
e193.. b70 + b97 =L= 1;
e194.. b68 + b98 =L= 1;
e195.. b69 + b99 =L= 1;
e196.. b70 + b100 =L= 1;
e197.. b80 + b92 =L= 1;
e198.. b81 + b93 =L= 1;
e199.. b82 + b94 =L= 1;
e200.. b80 + b95 =L= 1;
e201.. b81 + b96 =L= 1;
e202.. b82 + b97 =L= 1;
e203.. b80 + b98 =L= 1;
e204.. b81 + b99 =L= 1;
e205.. b82 + b100 =L= 1;
e206.. b71 + b101 =L= 1;
e207.. b72 + b102 =L= 1;
e208.. b73 + b103 =L= 1;
e209.. b83 + b101 =L= 1;
e210.. b84 + b102 =L= 1;
e211.. b85 + b103 =L= 1;
e212.. b92 + b101 =L= 1;
e213.. b93 + b102 =L= 1;
e214.. b94 + b103 =L= 1;
* set non-default bounds
x2.up = 1;
x3.up = 1;
x4.up = 1;
x5.up = 1;
x6.up = 1;
x7.up = 1;
x8.up = 1;
x9.up = 1;
x10.up = 1;
x11.up = 1;
x12.up = 1;
x13.up = 1;
x14.up = 1;
x15.up = 1;
x16.up = 1;
x17.up = 1;
x18.up = 1;
x19.up = 1;
x20.up = 1;
x21.up = 1;
x22.up = 1;
x23.up = 1;
x24.up = 1;
x25.up = 1;
x26.up = 1;
x27.up = 1;
x28.up = 1;
x29.up = 1;
x30.up = 1;
x31.up = 1;
x32.up = 1;
x33.up = 1;
x34.up = 1;
x35.up = 1;
x36.up = 1;
x37.up = 1;
x38.up = 1;
x39.up = 1;
x40.up = 1;
x41.up = 1;
x42.up = 1;
x43.up = 1;
x44.up = 1;
x45.up = 1;
x46.up = 1;
x47.up = 1;
x48.up = 1;
x49.up = 1;
x50.up = 2;
x51.up = 2;
x52.up = 2;
x53.up = 2;
x54.up = 2;
x55.up = 2;
x56.up = 2;
x57.up = 2;
x58.up = 2;
x59.up = 2;
x60.up = 2;
x61.up = 2;
x62.up = 2;
x63.up = 2;
x64.up = 2;
x65.up = 2;
x66.up = 2;
x67.up = 2;
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% maximizing objvar;
Last updated: 2025-08-07 Git hash: e62cedfc