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A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Instance batch0812_nc
Nonconvex variant of batch0812
| Formatsⓘ | ams gms mod nl osil py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | 2687025.65800000 (ANTIGONE) 2687026.77700000 (BARON) 2687025.95500000 (COUENNE) 2687026.78400000 (LINDO) 2687026.68200000 (SCIP) 189960.99790000 (SHOT) |
| Referencesⓘ | You, Fengqi and Grossmann, I E, Mixed-Integer Nonlinear Programming Models for the Optimal Design of Multi-product Batch Plant, 2009. |
| Sourceⓘ | nonconvex2.gms from minlp.org model 48 |
| Applicationⓘ | Multi-Product Batch Plant Design |
| Added to libraryⓘ | 24 Sep 2013 |
| Problem typeⓘ | MBNLP |
| #Variablesⓘ | 76 |
| #Binary Variablesⓘ | 36 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 40 |
| #Nonlinear Binary Variablesⓘ | 0 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | signomial |
| Objective curvatureⓘ | indefinite |
| #Nonzeros in Objectiveⓘ | 24 |
| #Nonlinear Nonzeros in Objectiveⓘ | 24 |
| #Constraintsⓘ | 205 |
| #Linear Constraintsⓘ | 108 |
| #Quadratic Constraintsⓘ | 96 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 1 |
| #General Nonlinear Constraintsⓘ | 0 |
| Operands in Gen. Nonlin. Functionsⓘ | |
| Constraints curvatureⓘ | indefinite |
| #Nonzeros in Jacobianⓘ | 448 |
| #Nonlinear Nonzeros in Jacobianⓘ | 208 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 252 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 20 |
| #Blocks in Hessian of Lagrangianⓘ | 1 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 40 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 40 |
| Average blocksize in Hessian of Lagrangianⓘ | 40.0 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 4.0000e-01 |
| Maximal coefficientⓘ | 4.8500e+05 |
| Infeasibility of initial pointⓘ | 4.2e+04 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 206 13 192 1 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 77 41 36 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 473 241 232 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,b41,b42,b43,b44,b45,b46,b47,b48,b49,b50,b51,b52,b53
,b54,b55,b56,b57,b58,b59,b60,b61,b62,b63,b64,b65,b66,b67,b68,b69,b70
,b71,b72,b73,b74,b75,b76,objvar;
Binary Variables b41,b42,b43,b44,b45,b46,b47,b48,b49,b50,b51,b52,b53,b54,b55
,b56,b57,b58,b59,b60,b61,b62,b63,b64,b65,b66,b67,b68,b69,b70,b71,b72
,b73,b74,b75,b76;
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;
e1.. -(250*x13**0.6*x1 + 550*x14**0.6*x2 + 250*x15**0.6*x3 + 1000*x16**0.6*x4
+ 300*x17**0.6*x5 + 800*x18**0.6*x6 + 200*x19**0.6*x7 + 1200*x20**0.6*x8
+ 250*x21**0.6*x9 + 250*x22**0.6*x10 + 450*x23**0.6*x11 + 700*x24**0.6*
x12) + objvar =E= 0;
e2.. x13 - 7.9*x25 =G= 0;
e3.. x14 - 2*x25 =G= 0;
e4.. x15 - 5.2*x25 =G= 0;
e5.. x16 - 4.9*x25 =G= 0;
e6.. x17 - 6.1*x25 =G= 0;
e7.. x18 - 4.2*x25 =G= 0;
e8.. x19 - 2.8*x25 =G= 0;
e9.. x20 - 3.3*x25 =G= 0;
e10.. x21 - 4.1*x25 =G= 0;
e11.. x22 - 3.8*x25 =G= 0;
e12.. x23 - 2.8*x25 =G= 0;
e13.. x24 - 3.9*x25 =G= 0;
e14.. x13 - 0.7*x26 =G= 0;
e15.. x14 - 0.8*x26 =G= 0;
e16.. x15 - 0.9*x26 =G= 0;
e17.. x16 - 3.4*x26 =G= 0;
e18.. x17 - 2.1*x26 =G= 0;
e19.. x18 - 2.5*x26 =G= 0;
e20.. x19 - 3.3*x26 =G= 0;
e21.. x20 - 3*x26 =G= 0;
e22.. x21 - 2.7*x26 =G= 0;
e23.. x22 - 2.4*x26 =G= 0;
e24.. x23 - 2.2*x26 =G= 0;
e25.. x24 - 3.1*x26 =G= 0;
e26.. x13 - 0.7*x27 =G= 0;
e27.. x14 - 2.6*x27 =G= 0;
e28.. x15 - 1.6*x27 =G= 0;
e29.. x16 - 3.6*x27 =G= 0;
e30.. x17 - 3.2*x27 =G= 0;
e31.. x18 - 2.9*x27 =G= 0;
e32.. x19 - 2.6*x27 =G= 0;
e33.. x20 - 2.2*x27 =G= 0;
e34.. x21 - 4.6*x27 =G= 0;
e35.. x22 - 4.3*x27 =G= 0;
e36.. x23 - 4.2*x27 =G= 0;
e37.. x24 - 4.6*x27 =G= 0;
e38.. x13 - 4.7*x28 =G= 0;
e39.. x14 - 2.3*x28 =G= 0;
e40.. x15 - 1.6*x28 =G= 0;
e41.. x16 - 2.7*x28 =G= 0;
e42.. x17 - 1.2*x28 =G= 0;
e43.. x18 - 2.5*x28 =G= 0;
e44.. x19 - 1.5*x28 =G= 0;
e45.. x20 - 1.5*x28 =G= 0;
e46.. x21 - 1.3*x28 =G= 0;
e47.. x22 - 1.7*x28 =G= 0;
e48.. x23 - 1.5*x28 =G= 0;
e49.. x24 - 1.8*x28 =G= 0;
e50.. x13 - 1.2*x29 =G= 0;
e51.. x14 - 3.6*x29 =G= 0;
e52.. x15 - 2.4*x29 =G= 0;
e53.. x16 - 4.5*x29 =G= 0;
e54.. x17 - 1.6*x29 =G= 0;
e55.. x18 - 2.1*x29 =G= 0;
e56.. x19 - 2.4*x29 =G= 0;
e57.. x20 - 2.7*x29 =G= 0;
e58.. x21 - 2.8*x29 =G= 0;
e59.. x22 - 3.5*x29 =G= 0;
e60.. x23 - 3.5*x29 =G= 0;
e61.. x24 - 4.3*x29 =G= 0;
e62.. x13 - 0.7*x30 =G= 0;
e63.. x14 - 2.4*x30 =G= 0;
e64.. x15 - 3.1*x30 =G= 0;
e65.. x16 - 2.2*x30 =G= 0;
e66.. x17 - 3.7*x30 =G= 0;
e67.. x18 - 4.8*x30 =G= 0;
e68.. x19 - 4.5*x30 =G= 0;
e69.. x20 - 5.2*x30 =G= 0;
e70.. x21 - 6.4*x30 =G= 0;
e71.. x22 - 5.7*x30 =G= 0;
e72.. x23 - 6.4*x30 =G= 0;
e73.. x24 - 6.8*x30 =G= 0;
e74.. x13 - 2.3*x31 =G= 0;
e75.. x14 - 4.7*x31 =G= 0;
e76.. x15 - 5.2*x31 =G= 0;
e77.. x16 - 3.5*x31 =G= 0;
e78.. x17 - 2.9*x31 =G= 0;
e79.. x18 - 3.6*x31 =G= 0;
e80.. x19 - 3.3*x31 =G= 0;
e81.. x20 - 3.2*x31 =G= 0;
e82.. x21 - 4.1*x31 =G= 0;
e83.. x22 - 3.7*x31 =G= 0;
e84.. x23 - 3.4*x31 =G= 0;
e85.. x24 - 3.7*x31 =G= 0;
e86.. x13 - 0.4*x32 =G= 0;
e87.. x14 - 0.9*x32 =G= 0;
e88.. x15 - 1.1*x32 =G= 0;
e89.. x16 - 1.4*x32 =G= 0;
e90.. x17 - 1.6*x32 =G= 0;
e91.. x18 - 2.2*x32 =G= 0;
e92.. x19 - 2*x32 =G= 0;
e93.. x20 - 1.8*x32 =G= 0;
e94.. x21 - 1.8*x32 =G= 0;
e95.. x22 - 1.6*x32 =G= 0;
e96.. x23 - 1.8*x32 =G= 0;
e97.. x24 - 2*x32 =G= 0;
e98.. x1*x33 =G= 6.4;
e99.. x2*x33 =G= 4.7;
e100.. x3*x33 =G= 8.3;
e101.. x4*x33 =G= 3.9;
e102.. x5*x33 =G= 2.1;
e103.. x6*x33 =G= 1.2;
e104.. x7*x33 =G= 0.8;
e105.. x8*x33 =G= 2.2;
e106.. x9*x33 =G= 1.2;
e107.. x10*x33 =G= 2.5;
e108.. x11*x33 =G= 3.4;
e109.. x12*x33 =G= 3.8;
e110.. x1*x34 =G= 6.8;
e111.. x2*x34 =G= 6.4;
e112.. x3*x34 =G= 6.5;
e113.. x4*x34 =G= 4.4;
e114.. x5*x34 =G= 2.3;
e115.. x6*x34 =G= 3.2;
e116.. x7*x34 =G= 0.4;
e117.. x8*x34 =G= 0.2;
e118.. x9*x34 =G= 0.5;
e119.. x10*x34 =G= 3.3;
e120.. x11*x34 =G= 0.6;
e121.. x12*x34 =G= 1.2;
e122.. x1*x35 =G= 1;
e123.. x2*x35 =G= 6.3;
e124.. x3*x35 =G= 5.4;
e125.. x4*x35 =G= 11.9;
e126.. x5*x35 =G= 5.7;
e127.. x6*x35 =G= 6.2;
e128.. x7*x35 =G= 1.1;
e129.. x8*x35 =G= 0.6;
e130.. x9*x35 =G= 1.2;
e131.. x10*x35 =G= 4.3;
e132.. x11*x35 =G= 2.8;
e133.. x12*x35 =G= 5.2;
e134.. x1*x36 =G= 3.2;
e135.. x2*x36 =G= 3;
e136.. x3*x36 =G= 3.5;
e137.. x4*x36 =G= 3.3;
e138.. x5*x36 =G= 2.8;
e139.. x6*x36 =G= 3.4;
e140.. x7*x36 =G= 1.7;
e141.. x8*x36 =G= 0.9;
e142.. x9*x36 =G= 2.2;
e143.. x10*x36 =G= 2.15;
e144.. x11*x36 =G= 1.8;
e145.. x12*x36 =G= 2.5;
e146.. x1*x37 =G= 2.1;
e147.. x2*x37 =G= 2.5;
e148.. x3*x37 =G= 4.2;
e149.. x4*x37 =G= 3.6;
e150.. x5*x37 =G= 5.7;
e151.. x6*x37 =G= 2.2;
e152.. x7*x37 =G= 1.2;
e153.. x8*x37 =G= 0.6;
e154.. x9*x37 =G= 1.15;
e155.. x10*x37 =G= 3.1;
e156.. x11*x37 =G= 4.2;
e157.. x12*x37 =G= 1.6;
e158.. x1*x38 =G= 1.1;
e159.. x2*x38 =G= 0.8;
e160.. x3*x38 =G= 0.4;
e161.. x4*x38 =G= 1.1;
e162.. x5*x38 =G= 1.8;
e163.. x6*x38 =G= 2.5;
e164.. x7*x38 =G= 0.5;
e165.. x8*x38 =G= 1.3;
e166.. x9*x38 =G= 1.4;
e167.. x10*x38 =G= 4.25;
e168.. x11*x38 =G= 2.7;
e169.. x12*x38 =G= 0.9;
e170.. x1*x39 =G= 4.2;
e171.. x2*x39 =G= 4;
e172.. x3*x39 =G= 2.2;
e173.. x4*x39 =G= 0.5;
e174.. x5*x39 =G= 3.4;
e175.. x6*x39 =G= 2.2;
e176.. x7*x39 =G= 1.4;
e177.. x8*x39 =G= 0.9;
e178.. x9*x39 =G= 2.1;
e179.. x10*x39 =G= 4.4;
e180.. x11*x39 =G= 2.2;
e181.. x12*x39 =G= 3.2;
e182.. x1*x40 =G= 2.7;
e183.. x2*x40 =G= 4.3;
e184.. x3*x40 =G= 1.9;
e185.. x4*x40 =G= 2;
e186.. x5*x40 =G= 1.7;
e187.. x6*x40 =G= 0.7;
e188.. x7*x40 =G= 0.3;
e189.. x8*x40 =G= 0.2;
e190.. x9*x40 =G= 1.6;
e191.. x10*x40 =G= 3.5;
e192.. x11*x40 =G= 3.4;
e193.. x12*x40 =G= 2.1;
e194.. 485000*x33/x25 + 297000*x34/x26 + 320000*x35/x27 + 283000*x36/x28 +
363000*x37/x29 + 265000*x38/x30 + 288000*x39/x31 + 145000*x40/x32
=L= 6000;
e195.. x1 - b41 - 2*b53 - 4*b65 =E= 1;
e196.. x2 - b42 - 2*b54 - 4*b66 =E= 1;
e197.. x3 - b43 - 2*b55 - 4*b67 =E= 1;
e198.. x4 - b44 - 2*b56 - 4*b68 =E= 1;
e199.. x5 - b45 - 2*b57 - 4*b69 =E= 1;
e200.. x6 - b46 - 2*b58 - 4*b70 =E= 1;
e201.. x7 - b47 - 2*b59 - 4*b71 =E= 1;
e202.. x8 - b48 - 2*b60 - 4*b72 =E= 1;
e203.. x9 - b49 - 2*b61 - 4*b73 =E= 1;
e204.. x10 - b50 - 2*b62 - 4*b74 =E= 1;
e205.. x11 - b51 - 2*b63 - 4*b75 =E= 1;
e206.. x12 - b52 - 2*b64 - 4*b76 =E= 1;
* set non-default bounds
x1.lo = 1; x1.up = 5;
x2.lo = 1; x2.up = 5;
x3.lo = 1; x3.up = 5;
x4.lo = 1; x4.up = 5;
x5.lo = 1; x5.up = 5;
x6.lo = 1; x6.up = 5;
x7.lo = 1; x7.up = 5;
x8.lo = 1; x8.up = 5;
x9.lo = 1; x9.up = 5;
x10.lo = 1; x10.up = 5;
x11.lo = 1; x11.up = 5;
x12.lo = 1; x12.up = 5;
x13.lo = 300; x13.up = 3000;
x14.lo = 300; x14.up = 3000;
x15.lo = 300; x15.up = 3000;
x16.lo = 300; x16.up = 3000;
x17.lo = 300; x17.up = 3000;
x18.lo = 300; x18.up = 3000;
x19.lo = 300; x19.up = 3000;
x20.lo = 300; x20.up = 3000;
x21.lo = 300; x21.up = 3000;
x22.lo = 300; x22.up = 3000;
x23.lo = 300; x23.up = 3000;
x24.lo = 300; x24.up = 3000;
x25.lo = 134.183333333333; x25.up = 379.746835443038;
x26.lo = 67.32; x26.up = 882.352941176471;
x27.lo = 126.933333333333; x27.up = 652.173913043478;
x28.lo = 33.0166666666667; x28.up = 638.297872340426;
x29.lo = 68.97; x29.up = 666.666666666667;
x30.lo = 37.5416666666667; x30.up = 441.176470588235;
x31.lo = 42.24; x31.up = 576.923076923077;
x32.lo = 20.7833333333333; x32.up = 1363.63636363636;
x33.lo = 1.66; x33.up = 8.3;
x34.lo = 1.36; x34.up = 6.8;
x35.lo = 2.38; x35.up = 11.9;
x36.lo = 0.7; x36.up = 3.5;
x37.lo = 1.14; x37.up = 5.7;
x38.lo = 0.85; x38.up = 4.25;
x39.lo = 0.88; x39.up = 4.4;
x40.lo = 0.86; x40.up = 4.3;
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: 2024-08-26 Git hash: 6cc1607f