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A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Instance batch0812
| Formatsⓘ | ams gms mod nl osil py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | 2687026.78400000 (ALPHAECP) 2687014.99200000 (ANTIGONE) 2687026.78400000 (BARON) 2687026.78400000 (BONMIN) 2687020.11400000 (COUENNE) 2687026.78400000 (LINDO) 2687026.78400000 (SCIP) 2686968.28500000 (SHOT) |
| Referencesⓘ | You, Fengqi and Grossmann, I E, Mixed-Integer Nonlinear Programming Models for the Optimal Design of Multi-product Batch Plant, 2009. |
| Sourceⓘ | convex2.gms from minlp.org model 48 |
| Applicationⓘ | Multi-Product Batch Plant Design |
| Added to libraryⓘ | 24 Sep 2013 |
| Problem typeⓘ | MBNLP |
| #Variablesⓘ | 100 |
| #Binary Variablesⓘ | 60 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 40 |
| #Nonlinear Binary Variablesⓘ | 0 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | nonlinear |
| Objective curvatureⓘ | convex |
| #Nonzeros in Objectiveⓘ | 24 |
| #Nonlinear Nonzeros in Objectiveⓘ | 24 |
| #Constraintsⓘ | 217 |
| #Linear Constraintsⓘ | 216 |
| #Quadratic Constraintsⓘ | 0 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 1 |
| Operands in Gen. Nonlin. Functionsⓘ | exp |
| Constraints curvatureⓘ | convex |
| #Nonzeros in Jacobianⓘ | 520 |
| #Nonlinear Nonzeros in Jacobianⓘ | 16 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 80 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 40 |
| #Blocks in Hessian of Lagrangianⓘ | 20 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 2 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 2 |
| Average blocksize in Hessian of Lagrangianⓘ | 2.0 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 6.0000e-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
* 218 25 192 1 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 101 41 60 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 545 505 40 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,b77,b78,b79,b80,b81,b82,b83,b84,b85,b86,b87
,b88,b89,b90,b91,b92,b93,b94,b95,b96,b97,b98,b99,b100,objvar;
Positive Variables x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12;
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,b77,b78,b79,b80,b81,b82,b83,b84,b85,b86,b87,b88,b89
,b90,b91,b92,b93,b94,b95,b96,b97,b98,b99,b100;
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,e215,e216,e217,e218;
e1.. -(250*exp(x1 + 0.6*x13) + 550*exp(x2 + 0.6*x14) + 250*exp(x3 + 0.6*x15) +
1000*exp(x4 + 0.6*x16) + 300*exp(x5 + 0.6*x17) + 800*exp(x6 + 0.6*x18) +
200*exp(x7 + 0.6*x19) + 1200*exp(x8 + 0.6*x20) + 250*exp(x9 + 0.6*x21) +
250*exp(x10 + 0.6*x22) + 450*exp(x11 + 0.6*x23) + 700*exp(x12 + 0.6*x24))
+ objvar =E= 0;
e2.. x13 - x25 =G= 2.06686275947298;
e3.. x14 - x25 =G= 0.693147180559945;
e4.. x15 - x25 =G= 1.64865862558738;
e5.. x16 - x25 =G= 1.58923520511658;
e6.. x17 - x25 =G= 1.80828877117927;
e7.. x18 - x25 =G= 1.43508452528932;
e8.. x19 - x25 =G= 1.02961941718116;
e9.. x20 - x25 =G= 1.19392246847243;
e10.. x21 - x25 =G= 1.41098697371026;
e11.. x22 - x25 =G= 1.33500106673234;
e12.. x23 - x25 =G= 1.02961941718116;
e13.. x24 - x25 =G= 1.3609765531356;
e14.. x13 - x26 =G= -0.356674943938732;
e15.. x14 - x26 =G= -0.22314355131421;
e16.. x15 - x26 =G= -0.105360515657826;
e17.. x16 - x26 =G= 1.22377543162212;
e18.. x17 - x26 =G= 0.741937344729377;
e19.. x18 - x26 =G= 0.916290731874155;
e20.. x19 - x26 =G= 1.19392246847243;
e21.. x20 - x26 =G= 1.09861228866811;
e22.. x21 - x26 =G= 0.993251773010283;
e23.. x22 - x26 =G= 0.8754687373539;
e24.. x23 - x26 =G= 0.78845736036427;
e25.. x24 - x26 =G= 1.1314021114911;
e26.. x13 - x27 =G= -0.356674943938732;
e27.. x14 - x27 =G= 0.955511445027436;
e28.. x15 - x27 =G= 0.470003629245736;
e29.. x16 - x27 =G= 1.28093384546206;
e30.. x17 - x27 =G= 1.16315080980568;
e31.. x18 - x27 =G= 1.06471073699243;
e32.. x19 - x27 =G= 0.955511445027436;
e33.. x20 - x27 =G= 0.78845736036427;
e34.. x21 - x27 =G= 1.52605630349505;
e35.. x22 - x27 =G= 1.45861502269952;
e36.. x23 - x27 =G= 1.43508452528932;
e37.. x24 - x27 =G= 1.52605630349505;
e38.. x13 - x28 =G= 1.54756250871601;
e39.. x14 - x28 =G= 0.832909122935104;
e40.. x15 - x28 =G= 0.470003629245736;
e41.. x16 - x28 =G= 0.993251773010283;
e42.. x17 - x28 =G= 0.182321556793955;
e43.. x18 - x28 =G= 0.916290731874155;
e44.. x19 - x28 =G= 0.405465108108164;
e45.. x20 - x28 =G= 0.405465108108164;
e46.. x21 - x28 =G= 0.262364264467491;
e47.. x22 - x28 =G= 0.53062825106217;
e48.. x23 - x28 =G= 0.405465108108164;
e49.. x24 - x28 =G= 0.587786664902119;
e50.. x13 - x29 =G= 0.182321556793955;
e51.. x14 - x29 =G= 1.28093384546206;
e52.. x15 - x29 =G= 0.8754687373539;
e53.. x16 - x29 =G= 1.50407739677627;
e54.. x17 - x29 =G= 0.470003629245736;
e55.. x18 - x29 =G= 0.741937344729377;
e56.. x19 - x29 =G= 0.8754687373539;
e57.. x20 - x29 =G= 0.993251773010283;
e58.. x21 - x29 =G= 1.02961941718116;
e59.. x22 - x29 =G= 1.25276296849537;
e60.. x23 - x29 =G= 1.25276296849537;
e61.. x24 - x29 =G= 1.45861502269952;
e62.. x13 - x30 =G= -0.356674943938732;
e63.. x14 - x30 =G= 0.8754687373539;
e64.. x15 - x30 =G= 1.1314021114911;
e65.. x16 - x30 =G= 0.78845736036427;
e66.. x17 - x30 =G= 1.30833281965018;
e67.. x18 - x30 =G= 1.56861591791385;
e68.. x19 - x30 =G= 1.50407739677627;
e69.. x20 - x30 =G= 1.64865862558738;
e70.. x21 - x30 =G= 1.85629799036563;
e71.. x22 - x30 =G= 1.7404661748405;
e72.. x23 - x30 =G= 1.85629799036563;
e73.. x24 - x30 =G= 1.91692261218206;
e74.. x13 - x31 =G= 0.832909122935104;
e75.. x14 - x31 =G= 1.54756250871601;
e76.. x15 - x31 =G= 1.64865862558738;
e77.. x16 - x31 =G= 1.25276296849537;
e78.. x17 - x31 =G= 1.06471073699243;
e79.. x18 - x31 =G= 1.28093384546206;
e80.. x19 - x31 =G= 1.19392246847243;
e81.. x20 - x31 =G= 1.16315080980568;
e82.. x21 - x31 =G= 1.41098697371026;
e83.. x22 - x31 =G= 1.30833281965018;
e84.. x23 - x31 =G= 1.22377543162212;
e85.. x24 - x31 =G= 1.30833281965018;
e86.. x13 - x32 =G= -0.916290731874155;
e87.. x14 - x32 =G= -0.105360515657826;
e88.. x15 - x32 =G= 0.0953101798043249;
e89.. x16 - x32 =G= 0.336472236621213;
e90.. x17 - x32 =G= 0.470003629245736;
e91.. x18 - x32 =G= 0.78845736036427;
e92.. x19 - x32 =G= 0.693147180559945;
e93.. x20 - x32 =G= 0.587786664902119;
e94.. x21 - x32 =G= 0.587786664902119;
e95.. x22 - x32 =G= 0.470003629245736;
e96.. x23 - x32 =G= 0.587786664902119;
e97.. x24 - x32 =G= 0.693147180559945;
e98.. x1 + x33 =G= 1.85629799036563;
e99.. x2 + x33 =G= 1.54756250871601;
e100.. x3 + x33 =G= 2.11625551480255;
e101.. x4 + x33 =G= 1.3609765531356;
e102.. x5 + x33 =G= 0.741937344729377;
e103.. x6 + x33 =G= 0.182321556793955;
e104.. x7 + x33 =G= -0.22314355131421;
e105.. x8 + x33 =G= 0.78845736036427;
e106.. x9 + x33 =G= 0.182321556793955;
e107.. x10 + x33 =G= 0.916290731874155;
e108.. x11 + x33 =G= 1.22377543162212;
e109.. x12 + x33 =G= 1.33500106673234;
e110.. x1 + x34 =G= 1.91692261218206;
e111.. x2 + x34 =G= 1.85629799036563;
e112.. x3 + x34 =G= 1.87180217690159;
e113.. x4 + x34 =G= 1.48160454092422;
e114.. x5 + x34 =G= 0.832909122935104;
e115.. x6 + x34 =G= 1.16315080980568;
e116.. x7 + x34 =G= -0.916290731874155;
e117.. x8 + x34 =G= -1.6094379124341;
e118.. x9 + x34 =G= -0.693147180559945;
e119.. x10 + x34 =G= 1.19392246847243;
e120.. x11 + x34 =G= -0.510825623765991;
e121.. x12 + x34 =G= 0.182321556793955;
e122.. x1 + x35 =G= 0;
e123.. x2 + x35 =G= 1.84054963339749;
e124.. x3 + x35 =G= 1.68639895357023;
e125.. x4 + x35 =G= 2.47653840011748;
e126.. x5 + x35 =G= 1.7404661748405;
e127.. x6 + x35 =G= 1.82454929205105;
e128.. x7 + x35 =G= 0.0953101798043249;
e129.. x8 + x35 =G= -0.510825623765991;
e130.. x9 + x35 =G= 0.182321556793955;
e131.. x10 + x35 =G= 1.45861502269952;
e132.. x11 + x35 =G= 1.02961941718116;
e133.. x12 + x35 =G= 1.64865862558738;
e134.. x1 + x36 =G= 1.16315080980568;
e135.. x2 + x36 =G= 1.09861228866811;
e136.. x3 + x36 =G= 1.25276296849537;
e137.. x4 + x36 =G= 1.19392246847243;
e138.. x5 + x36 =G= 1.02961941718116;
e139.. x6 + x36 =G= 1.22377543162212;
e140.. x7 + x36 =G= 0.53062825106217;
e141.. x8 + x36 =G= -0.105360515657826;
e142.. x9 + x36 =G= 0.78845736036427;
e143.. x10 + x36 =G= 0.765467842139571;
e144.. x11 + x36 =G= 0.587786664902119;
e145.. x12 + x36 =G= 0.916290731874155;
e146.. x1 + x37 =G= 0.741937344729377;
e147.. x2 + x37 =G= 0.916290731874155;
e148.. x3 + x37 =G= 1.43508452528932;
e149.. x4 + x37 =G= 1.28093384546206;
e150.. x5 + x37 =G= 1.7404661748405;
e151.. x6 + x37 =G= 0.78845736036427;
e152.. x7 + x37 =G= 0.182321556793955;
e153.. x8 + x37 =G= -0.510825623765991;
e154.. x9 + x37 =G= 0.139761942375159;
e155.. x10 + x37 =G= 1.1314021114911;
e156.. x11 + x37 =G= 1.43508452528932;
e157.. x12 + x37 =G= 0.470003629245736;
e158.. x1 + x38 =G= 0.0953101798043249;
e159.. x2 + x38 =G= -0.22314355131421;
e160.. x3 + x38 =G= -0.916290731874155;
e161.. x4 + x38 =G= 0.0953101798043249;
e162.. x5 + x38 =G= 0.587786664902119;
e163.. x6 + x38 =G= 0.916290731874155;
e164.. x7 + x38 =G= -0.693147180559945;
e165.. x8 + x38 =G= 0.262364264467491;
e166.. x9 + x38 =G= 0.336472236621213;
e167.. x10 + x38 =G= 1.44691898293633;
e168.. x11 + x38 =G= 0.993251773010283;
e169.. x12 + x38 =G= -0.105360515657826;
e170.. x1 + x39 =G= 1.43508452528932;
e171.. x2 + x39 =G= 1.38629436111989;
e172.. x3 + x39 =G= 0.78845736036427;
e173.. x4 + x39 =G= -0.693147180559945;
e174.. x5 + x39 =G= 1.22377543162212;
e175.. x6 + x39 =G= 0.78845736036427;
e176.. x7 + x39 =G= 0.336472236621213;
e177.. x8 + x39 =G= -0.105360515657826;
e178.. x9 + x39 =G= 0.741937344729377;
e179.. x10 + x39 =G= 1.48160454092422;
e180.. x11 + x39 =G= 0.78845736036427;
e181.. x12 + x39 =G= 1.16315080980568;
e182.. x1 + x40 =G= 0.993251773010283;
e183.. x2 + x40 =G= 1.45861502269952;
e184.. x3 + x40 =G= 0.641853886172395;
e185.. x4 + x40 =G= 0.693147180559945;
e186.. x5 + x40 =G= 0.53062825106217;
e187.. x6 + x40 =G= -0.356674943938732;
e188.. x7 + x40 =G= -1.20397280432594;
e189.. x8 + x40 =G= -1.6094379124341;
e190.. x9 + x40 =G= 0.470003629245736;
e191.. x10 + x40 =G= 1.25276296849537;
e192.. x11 + x40 =G= 1.22377543162212;
e193.. x12 + x40 =G= 0.741937344729377;
e194.. 485000*exp(x33 - x25) + 297000*exp(x34 - x26) + 320000*exp(x35 - x27) +
283000*exp(x36 - x28) + 363000*exp(x37 - x29) + 265000*exp(x38 - x30) +
288000*exp(x39 - x31) + 145000*exp(x40 - x32) =L= 6000;
e195.. x1 - 0.693147180559945*b53 - 1.09861228866811*b65
- 1.38629436111989*b77 - 1.6094379124341*b89 =E= 0;
e196.. x2 - 0.693147180559945*b54 - 1.09861228866811*b66
- 1.38629436111989*b78 - 1.6094379124341*b90 =E= 0;
e197.. x3 - 0.693147180559945*b55 - 1.09861228866811*b67
- 1.38629436111989*b79 - 1.6094379124341*b91 =E= 0;
e198.. x4 - 0.693147180559945*b56 - 1.09861228866811*b68
- 1.38629436111989*b80 - 1.6094379124341*b92 =E= 0;
e199.. x5 - 0.693147180559945*b57 - 1.09861228866811*b69
- 1.38629436111989*b81 - 1.6094379124341*b93 =E= 0;
e200.. x6 - 0.693147180559945*b58 - 1.09861228866811*b70
- 1.38629436111989*b82 - 1.6094379124341*b94 =E= 0;
e201.. x7 - 0.693147180559945*b59 - 1.09861228866811*b71
- 1.38629436111989*b83 - 1.6094379124341*b95 =E= 0;
e202.. x8 - 0.693147180559945*b60 - 1.09861228866811*b72
- 1.38629436111989*b84 - 1.6094379124341*b96 =E= 0;
e203.. x9 - 0.693147180559945*b61 - 1.09861228866811*b73
- 1.38629436111989*b85 - 1.6094379124341*b97 =E= 0;
e204.. x10 - 0.693147180559945*b62 - 1.09861228866811*b74
- 1.38629436111989*b86 - 1.6094379124341*b98 =E= 0;
e205.. x11 - 0.693147180559945*b63 - 1.09861228866811*b75
- 1.38629436111989*b87 - 1.6094379124341*b99 =E= 0;
e206.. x12 - 0.693147180559945*b64 - 1.09861228866811*b76
- 1.38629436111989*b88 - 1.6094379124341*b100 =E= 0;
e207.. b41 + b53 + b65 + b77 + b89 =E= 1;
e208.. b42 + b54 + b66 + b78 + b90 =E= 1;
e209.. b43 + b55 + b67 + b79 + b91 =E= 1;
e210.. b44 + b56 + b68 + b80 + b92 =E= 1;
e211.. b45 + b57 + b69 + b81 + b93 =E= 1;
e212.. b46 + b58 + b70 + b82 + b94 =E= 1;
e213.. b47 + b59 + b71 + b83 + b95 =E= 1;
e214.. b48 + b60 + b72 + b84 + b96 =E= 1;
e215.. b49 + b61 + b73 + b85 + b97 =E= 1;
e216.. b50 + b62 + b74 + b86 + b98 =E= 1;
e217.. b51 + b63 + b75 + b87 + b99 =E= 1;
e218.. b52 + b64 + b76 + b88 + b100 =E= 1;
* set non-default bounds
x1.up = 1.6094379124341;
x2.up = 1.6094379124341;
x3.up = 1.6094379124341;
x4.up = 1.6094379124341;
x5.up = 1.6094379124341;
x6.up = 1.6094379124341;
x7.up = 1.6094379124341;
x8.up = 1.6094379124341;
x9.up = 1.6094379124341;
x10.up = 1.6094379124341;
x11.up = 1.6094379124341;
x12.up = 1.6094379124341;
x13.lo = 5.7037824746562; x13.up = 8.00636756765025;
x14.lo = 5.7037824746562; x14.up = 8.00636756765025;
x15.lo = 5.7037824746562; x15.up = 8.00636756765025;
x16.lo = 5.7037824746562; x16.up = 8.00636756765025;
x17.lo = 5.7037824746562; x17.up = 8.00636756765025;
x18.lo = 5.7037824746562; x18.up = 8.00636756765025;
x19.lo = 5.7037824746562; x19.up = 8.00636756765025;
x20.lo = 5.7037824746562; x20.up = 8.00636756765025;
x21.lo = 5.7037824746562; x21.up = 8.00636756765025;
x22.lo = 5.7037824746562; x22.up = 8.00636756765025;
x23.lo = 5.7037824746562; x23.up = 8.00636756765025;
x24.lo = 5.7037824746562; x24.up = 8.00636756765025;
x25.lo = 4.89920702407788; x25.up = 5.93950480817727;
x26.lo = 4.2094573693226; x26.up = 6.78259213602813;
x27.lo = 4.8436620142491; x27.up = 6.4803112641552;
x28.lo = 3.49701248447645; x28.up = 6.45880505893423;
x29.lo = 4.2336716274432; x29.up = 6.50229017087397;
x30.lo = 3.62545142726039; x30.up = 6.08944495546819;
x31.lo = 3.74336763939801; x31.up = 6.35770894206286;
x32.lo = 3.03415138345794; x32.up = 7.21791020728598;
x33.lo = 0.506817602368452; x33.up = 2.11625551480255;
x34.lo = 0.307484699747961; x34.up = 1.91692261218206;
x35.lo = 0.867100487683383; x35.up = 2.47653840011748;
x36.lo = -0.356674943938732; x36.up = 1.25276296849537;
x37.lo = 0.131028262406404; x37.up = 1.7404661748405;
x38.lo = -0.162518929497775; x38.up = 1.44691898293633;
x39.lo = -0.127833371509885; x39.up = 1.48160454092422;
x40.lo = -0.150822889734584; x40.up = 1.45861502269952;
* set non-default levels
x36.l = -0.356674943938732;
x38.l = -0.162518929497775;
x39.l = -0.127833371509885;
x40.l = -0.150822889734584;
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