MINLPLib
A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Removed Instance bchoco08
| Formatsⓘ | ams gms mod nl osil py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | 0.96248654 (ANTIGONE) 0.99983736 (BARON) 0.98480691 (COUENNE) 0.96514011 (LINDO) 0.99996523 (SCIP) 0.95006052 (SHOT) |
| Referencesⓘ | Chang, YoungJung and Sahinidis, N V, Stabilizing controller design and the Belgian chocolate problem, 2009. |
| Sourceⓘ | bcp8.gms from minlp.org model 57 |
| Applicationⓘ | Belgian chocolate problem |
| Added to libraryⓘ | 24 Sep 2013 |
| Removed from libraryⓘ | 01 Mar 2022 |
| Removed becauseⓘ | Numerically difficult formulation (coefficient of order 1E-10 and 1E10) |
| Problem typeⓘ | MBNLP |
| #Variablesⓘ | 168 |
| #Binary Variablesⓘ | 9 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 101 |
| #Nonlinear Binary Variablesⓘ | 2 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | max |
| Objective typeⓘ | linear |
| Objective curvatureⓘ | linear |
| #Nonzeros in Objectiveⓘ | 1 |
| #Nonlinear Nonzeros in Objectiveⓘ | 0 |
| #Constraintsⓘ | 190 |
| #Linear Constraintsⓘ | 111 |
| #Quadratic Constraintsⓘ | 10 |
| #Polynomial Constraintsⓘ | 5 |
| #Signomial Constraintsⓘ | 64 |
| #General Nonlinear Constraintsⓘ | 0 |
| Operands in Gen. Nonlin. Functionsⓘ | |
| Constraints curvatureⓘ | indefinite |
| #Nonzeros in Jacobianⓘ | 693 |
| #Nonlinear Nonzeros in Jacobianⓘ | 261 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 421 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 23 |
| #Blocks in Hessian of Lagrangianⓘ | 4 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 10 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 49 |
| Average blocksize in Hessian of Lagrangianⓘ | 25.25 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 1.0000e-10 |
| Maximal coefficientⓘ | 1.0000e+10 |
| Infeasibility of initial pointⓘ | 1e+07 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 191 141 14 36 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 169 160 9 0 0 0 0 0
* FX 1
*
* Nonzero counts
* Total const NL DLL
* 695 434 261 0
*
* Solve m using MINLP maximizing 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,x73,x74,x75,x76,x77,x78,x79,x80,x81,x82,x83,x84,x85,x86,x87
,x88,x89,x90,x91,x92,x93,x94,x95,x96,x97,x98,x99,x100,x101,x102,x103
,x104,x105,x106,x107,x108,x109,x110,x111,x112,x113,x114,x115,x116
,x117,x118,x119,x120,x121,x122,x123,x124,x125,x126,x127,x128,x129
,x130,x131,x132,x133,x134,x135,x136,x137,x138,x139,x140,x141,x142
,x143,x144,x145,x146,x147,x148,x149,x150,x151,x152,x153,x154,x155
,x156,x157,x158,x159,b160,b161,b162,b163,b164,b165,b166,b167,b168
,objvar;
Positive Variables x11,x12,x13,x14,x15,x16,x17,x18,x19,x40,x41,x42,x43,x44
,x45,x46,x47,x48,x69,x111;
Binary Variables b160,b161,b162,b163,b164,b165,b166,b167,b168;
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;
e1.. - x1 + objvar =E= 0;
e2.. - x11 + 0.001*b160 =L= 0;
e3.. - x12 + 0.001*b161 =L= 0;
e4.. - x13 + 0.001*b162 =L= 0;
e5.. - x14 + 0.001*b163 =L= 0;
e6.. - x15 + 0.001*b164 =L= 0;
e7.. - x16 + 0.001*b165 =L= 0;
e8.. - x17 + 0.001*b166 =L= 0;
e9.. - x18 + 0.001*b167 =L= 0;
e10.. - x19 + 0.001*b168 =L= 0;
e11.. x11 - 10*b160 =L= 0;
e12.. x12 - 10*b161 =L= 0;
e13.. x13 - 10*b162 =L= 0;
e14.. x14 - 10*b163 =L= 0;
e15.. x15 - 10*b164 =L= 0;
e16.. x16 - 10*b165 =L= 0;
e17.. x17 - 10*b166 =L= 0;
e18.. x18 - 10*b167 =L= 0;
e19.. x19 - 10*b168 =L= 0;
e20.. - x40 + 0.001*b160 =L= 0;
e21.. - x41 + 0.001*b161 =L= 0;
e22.. - x42 + 0.001*b162 =L= 0;
e23.. - x43 + 0.001*b163 =L= 0;
e24.. - x44 + 0.001*b164 =L= 0;
e25.. - x45 + 0.001*b165 =L= 0;
e26.. - x46 + 0.001*b166 =L= 0;
e27.. - x47 + 0.001*b167 =L= 0;
e28.. - x48 + 0.001*b168 =L= 0;
e29.. x40 - 10*b160 =L= 0;
e30.. x41 - 10*b161 =L= 0;
e31.. x42 - 10*b162 =L= 0;
e32.. x43 - 10*b163 =L= 0;
e33.. x44 - 10*b164 =L= 0;
e34.. x45 - 10*b165 =L= 0;
e35.. x46 - 10*b166 =L= 0;
e36.. x47 - 10*b167 =L= 0;
e37.. x48 - 10*b168 =L= 0;
e38.. b160 - b161 =G= 0;
e39.. b161 - b162 =G= 0;
e40.. b162 - b163 =G= 0;
e41.. b163 - b164 =G= 0;
e42.. b164 - b165 =G= 0;
e43.. b165 - b166 =G= 0;
e44.. b166 - b167 =G= 0;
e45.. b167 - b168 =G= 0;
e46.. - 10000000000*x2 + 10000000000*x11 + x20 =E= 0;
e47.. 2000000000.00001*x1*x2 - 1000000000*x3 + 1000000000*x12 + x21 =E= 0;
e48.. 200000000*x1*x3 - 100000000*x2 - 100000000*x4 - 100000000*x11
+ 100000000*x13 + x22 =E= 0;
e49.. 20000000*x1*x4 - 10000000*x3 - 10000000*x5 - 10000000*x12 + 10000000*x14
+ x23 =E= 0;
e50.. 2000000*x1*x5 - 1000000*x4 - 1000000*x6 - 1000000*x13 + 1000000*x15 + x24
=E= 0;
e51.. 200000*x1*x6 - 100000*x5 - 100000*x7 - 100000*x14 + 100000*x16 + x25
=E= 0;
e52.. 20000*x1*x7 - 10000*x6 - 10000*x8 - 10000*x15 + 10000*x17 + x26 =E= 0;
e53.. 2000*x1*x8 - 1000*x7 - 1000*x9 - 1000*x16 + 1000*x18 + x27 =E= 0;
e54.. 200*x1*x9 - 100*x8 - 100*x10 - 100*x17 + 100*x19 + x28 =E= 0;
e55.. 20*x1*x10 - 10*x9 - 10*x18 + x29 =E= 0;
e56.. - x10 - x19 + x30 =E= 0;
e57.. - x2 + 1E-5*x3 - 1E-10*x4 + x31 =E= 0;
e58.. - x3 + 2E-5*x4 - 3E-10*x5 + x32 =E= 0;
e59.. - x4 + 3E-5*x5 - 6E-10*x6 + x33 =E= 0;
e60.. - x5 + 4E-5*x6 - 1E-9*x7 + x34 =E= 0;
e61.. - x6 + 5E-5*x7 - 1.5E-9*x8 + x35 =E= 0;
e62.. - x7 + 6E-5*x8 - 2.1E-9*x9 + x36 =E= 0;
e63.. - x8 + 7E-5*x9 - 2.8E-9*x10 + x37 =E= 0;
e64.. - x9 + 8E-5*x10 + x38 =E= 0;
e65.. - x10 + x39 =E= 0;
e66.. - x11 + 1E-5*x12 - 1E-10*x13 + x40 =E= 0;
e67.. - x12 + 2E-5*x13 - 3E-10*x14 + x41 =E= 0;
e68.. - x13 + 3E-5*x14 - 6E-10*x15 + x42 =E= 0;
e69.. - x14 + 4E-5*x15 - 1E-9*x16 + x43 =E= 0;
e70.. - x15 + 5E-5*x16 - 1.5E-9*x17 + x44 =E= 0;
e71.. - x16 + 6E-5*x17 - 2.1E-9*x18 + x45 =E= 0;
e72.. - x17 + 7E-5*x18 - 2.8E-9*x19 + x46 =E= 0;
e73.. - x18 + 8E-5*x19 + x47 =E= 0;
e74.. - x19 + x48 =E= 0;
e75.. - x20 + 1E-5*x21 - 1E-10*x22 + x49 =E= 0;
e76.. - x21 + 2E-5*x22 - 3E-10*x23 + x50 =E= 0;
e77.. - x22 + 3E-5*x23 - 6E-10*x24 + x51 =E= 0;
e78.. - x23 + 4E-5*x24 - 1E-9*x25 + x52 =E= 0;
e79.. - x24 + 5E-5*x25 - 1.5E-9*x26 + x53 =E= 0;
e80.. - x25 + 6E-5*x26 - 2.1E-9*x27 + x54 =E= 0;
e81.. - x26 + 7E-5*x27 - 2.8E-9*x28 + x55 =E= 0;
e82.. - x27 + 8E-5*x28 - 3.6E-9*x29 + x56 =E= 0;
e83.. - x28 + 9E-5*x29 - 4.5E-9*x30 + x57 =E= 0;
e84.. - x29 + 0.0001*x30 + x58 =E= 0;
e85.. - x30 + x59 =E= 0;
e86.. - x39 + x60 =E= 0;
e87.. - x37 + x61 =E= 0;
e88.. - x35 + x62 =E= 0;
e89.. - x33 + x63 =E= 0;
e90.. - x31 + x64 =E= 0;
e91.. - x38 + x65 =E= 0;
e92.. - x36 + x66 =E= 0;
e93.. - x34 + x67 =E= 0;
e94.. - x32 + x68 =E= 0;
e95.. x69 =E= 0;
e96.. x60*x66/x65 - x61 + x70 =E= 0;
e97.. x60*x67/x65 - x62 + x71 =E= 0;
e98.. x60*x68/x65 - x63 + x72 =E= 0;
e99.. x60*x69/x65 - x64 + x73 =E= 0;
e100.. x65*x71/x70 - x66 + x75 =E= 0;
e101.. x65*x72/x70 - x67 + x76 =E= 0;
e102.. x65*x73/x70 - x68 + x77 =E= 0;
e103.. x65*x74/x70 - x69 + x78 =E= 0;
e104.. x70*x76/x75 - x71 + x80 =E= 0;
e105.. x70*x77/x75 - x72 + x81 =E= 0;
e106.. x70*x78/x75 - x73 + x82 =E= 0;
e107.. x70*x79/x75 - x74 + x83 =E= 0;
e108.. x75*x81/x80 - x76 + x85 =E= 0;
e109.. x75*x82/x80 - x77 + x86 =E= 0;
e110.. x75*x83/x80 - x78 + x87 =E= 0;
e111.. x75*x84/x80 - x79 + x88 =E= 0;
e112.. x80*x86/x85 - x81 + x90 =E= 0;
e113.. x80*x87/x85 - x82 + x91 =E= 0;
e114.. x80*x88/x85 - x83 + x92 =E= 0;
e115.. x80*x89/x85 - x84 + x93 =E= 0;
e116.. x85*x91/x90 - x86 + x95 =E= 0;
e117.. x85*x92/x90 - x87 + x96 =E= 0;
e118.. x85*x93/x90 - x88 + x97 =E= 0;
e119.. x85*x94/x90 - x89 + x98 =E= 0;
e120.. x74 =E= 0;
e121.. x79 =E= 0;
e122.. x84 =E= 0;
e123.. x89 =E= 0;
e124.. x94 =E= 0;
e125.. x99 =E= 0;
e126.. - x59 + x100 =E= 0;
e127.. - x57 + x101 =E= 0;
e128.. - x55 + x102 =E= 0;
e129.. - x53 + x103 =E= 0;
e130.. - x51 + x104 =E= 0;
e131.. - x49 + x105 =E= 0;
e132.. - x58 + x106 =E= 0;
e133.. - x56 + x107 =E= 0;
e134.. - x54 + x108 =E= 0;
e135.. - x52 + x109 =E= 0;
e136.. - x50 + x110 =E= 0;
e137.. x111 =E= 0;
e138.. x100*x107/x106 - x101 + x112 =E= 0;
e139.. x100*x108/x106 - x102 + x113 =E= 0;
e140.. x100*x109/x106 - x103 + x114 =E= 0;
e141.. x100*x110/x106 - x104 + x115 =E= 0;
e142.. x100*x111/x106 - x105 + x116 =E= 0;
e143.. x106*x113/x112 - x107 + x118 =E= 0;
e144.. x106*x114/x112 - x108 + x119 =E= 0;
e145.. x106*x115/x112 - x109 + x120 =E= 0;
e146.. x106*x116/x112 - x110 + x121 =E= 0;
e147.. x106*x117/x112 - x111 + x122 =E= 0;
e148.. x112*x119/x118 - x113 + x124 =E= 0;
e149.. x112*x120/x118 - x114 + x125 =E= 0;
e150.. x112*x121/x118 - x115 + x126 =E= 0;
e151.. x112*x122/x118 - x116 + x127 =E= 0;
e152.. x112*x123/x118 - x117 + x128 =E= 0;
e153.. x118*x125/x124 - x119 + x130 =E= 0;
e154.. x118*x126/x124 - x120 + x131 =E= 0;
e155.. x118*x127/x124 - x121 + x132 =E= 0;
e156.. x118*x128/x124 - x122 + x133 =E= 0;
e157.. x118*x129/x124 - x123 + x134 =E= 0;
e158.. x124*x131/x130 - x125 + x136 =E= 0;
e159.. x124*x132/x130 - x126 + x137 =E= 0;
e160.. x124*x133/x130 - x127 + x138 =E= 0;
e161.. x124*x134/x130 - x128 + x139 =E= 0;
e162.. x124*x135/x130 - x129 + x140 =E= 0;
e163.. x130*x137/x136 - x131 + x142 =E= 0;
e164.. x130*x138/x136 - x132 + x143 =E= 0;
e165.. x130*x139/x136 - x133 + x144 =E= 0;
e166.. x130*x140/x136 - x134 + x145 =E= 0;
e167.. x130*x141/x136 - x135 + x146 =E= 0;
e168.. x136*x143/x142 - x137 + x148 =E= 0;
e169.. x136*x144/x142 - x138 + x149 =E= 0;
e170.. x136*x145/x142 - x139 + x150 =E= 0;
e171.. x136*x146/x142 - x140 + x151 =E= 0;
e172.. x136*x147/x142 - x141 + x152 =E= 0;
e173.. x142*x149/x148 - x143 + x154 =E= 0;
e174.. x142*x150/x148 - x144 + x155 =E= 0;
e175.. x142*x151/x148 - x145 + x156 =E= 0;
e176.. x142*x152/x148 - x146 + x157 =E= 0;
e177.. x142*x153/x148 - x147 + x158 =E= 0;
e178.. x117 =E= 0;
e179.. x123 =E= 0;
e180.. x129 =E= 0;
e181.. x135 =E= 0;
e182.. x141 =E= 0;
e183.. x147 =E= 0;
e184.. x153 =E= 0;
e185.. x159 =E= 0;
e186.. x46*x47 - x45*x48 - 1E-5*b168 =G= 0;
e187.. x45*x46*x47 - x45*x45*x48 + x43*x47*x48 - x44*x47*x47 - 1E-5*b167 =G= 0;
e188.. x44*x45*x46*x47 - x45**2*x44*x48 - x44**2*x47**2 + 2*x43*x44*x47*x48 +
x43*x45*x46*x48 - x43**2*x48**2 - x46**2*x43*x47 + x42*x46*x47**2 - x42*
x45*x47*x48 - x41*x46*x47*x48 + x41*x45*x48**2 + (x44*x45 - x43*x46)*(1
- b167) - 1E-5*b166 =G= 0;
e189.. x41*x45*x46**2*x47 - x43**2*x46**2*x47 + 2*x42*x43*x46*x47**2 - x41*x44*
x46*x47**2 - x40*x45*x46*x47**2 + x43*x44*x45*x46*x47 - x41*x43*x46*x47*
x48 - x45**2*x42*x46*x47 + x43**2*x45*x46*x48 - x45**2*x41*x46*x48 + x40
*x44*x47**3 - x42**2*x47**3 + x42*x44*x45*x47**2 + 2*x41*x42*x47**2*x48
- x40*x43*x47**2*x48 - x44**2*x43*x47**2 - 3*x42*x43*x45*x47*x48 - x41
**2*x47*x48**2 + 2*x43**2*x44*x47*x48 + x45**2*x40*x47*x48 - x43**3*x48
**2 - x43*x44*x45**2*x48 + 2*x41*x43*x45*x48**2 + x45**3*x42*x48 + (x43*
x44*x45 - x43**2*x46 - x45**2*x42 + x41*x45*x46)*(1 - b167) - 1E-5*b165
=G= 0;
e190.. x41**3*x48**3 - x40*x42*x45*x46*x47**2 + 2*x41*x42*x45*x46**2*x47 - x40
**2*x46*x47**3 + x44**3*x41*x47**2 - x43**3*x42*x48**2 - x41**2*x46**3*
x47 + 2*x40*x42*x44*x47**3 - x44**2*x40*x45*x47**2 + 2*x40*x41*x46**2*
x47**2 + x42**2*x44*x45*x47**2 - x42**2*x45**2*x46*x47 - 3*x41**2*x42*
x47*x48**2 + x40*x41*x45**2*x48**2 - 2*x41**2*x44*x45*x48**2 + x40**2*
x45*x47**2*x48 + 3*x42**2*x41*x47**2*x48 + x41**2*x45*x46**2*x48 - x40*
x44*x45**3*x48 + x44**2*x41*x45**2*x48 - 3*x41*x42*x44*x46*x47**2 + x40*
x44*x45**2*x46*x47 - x44**2*x41*x45*x46*x47 + x42**2*x45**3*x48 - 2*x40*
x41*x44*x47**2*x48 + x40*x42*x45**2*x47*x48 + x41*x42*x44*x45*x47*x48 -
3*x40*x41*x45*x46*x47*x48 + 3*x41**2*x44*x46*x47*x48 - 2*x41*x42*x45**2*
x46*x48 - x41**2*x43*x46*x48**2 - x42*x43*x44**2*x47**2 + 2*x42**2*x43*
x46*x47**2 + x43**2*x41*x44*x48**2 - x43**2*x40*x45*x48**2 - x43**2*x42*
x46**2*x47 + x40*x43*x45**2*x46*x48 - x41*x43*x44*x45*x46*x48 - x40*x43*
x45*x46**2*x47 + x42*x43*x44*x45*x46*x47 + x41*x43*x44*x46**2*x47 + 2*
x43**2*x42*x44*x47*x48 + x43**2*x42*x45*x46*x48 + 2*x40*x41*x43*x47*x48
**2 + 3*x41*x42*x43*x45*x48**2 - 2*x40*x42*x43*x47**2*x48 + 2*x40*x43*
x44*x45*x47*x48 - 3*x42**2*x43*x45*x47*x48 - 2*x41*x43*x44**2*x47*x48 -
x41*x42*x43*x46*x47*x48 - x42*x43*x44*x45**2*x48 - x47**3*x42**3 + (x42*
x43*x44*x45 - x43**2*x42*x46 - x42**2*x45**2 + 2*x41*x42*x45*x46 + x41*
x43*x44*x46 - x41**2*x46**2 - x44**2*x41*x45 + x40*x44*x45**2 - x40*x43*
x45*x46)*(1 - b167) + (x42*x43 - x41*x44)*(1 - b165) - 1E-5*b164 =G= 0;
e191.. 4*x41**2*x40*x43*x47*x48**2 - 2*x40*x41*x44*x45**3*x48 - 2*x43**3*x40*
x44*x47*x48 - 4*x40**2*x43*x45**2*x47*x48 + 3*x40**2*x43*x45*x46*x47**2
+ 4*x40**2*x41*x45*x47**2*x48 + x40**2*x44*x45**2*x47**2 - x42**3*x41*
x47**3 + x43**4*x40*x48**2 + x40**2*x48*x45**4 - 2*x40*x42*x43**2*x46*
x47**2 - x43**3*x40*x45*x46*x48 + x43**2*x40*x44*x45**2*x48 - x40*x42*
x43*x45**3*x48 - 4*x40*x41*x43**2*x45*x48**2 - 2*x40*x41*x44**2*x45*x47
**2 + 3*x40*x41*x42*x44*x47**3 - 3*x41**2*x40*x44*x47**2*x48 + 4*x40*x41
*x43*x44*x45*x47*x48 - x41**3*x43*x46*x48**2 - x41*x42*x43*x44*x45**2*
x48 + x41**2*x44**3*x47**2 + 2*x41**2*x42*x45*x46**2*x47 + x41**2*x43*
x44*x46**2*x47 - x41**2*x42*x43*x46*x47*x48 - x41**2*x43*x44*x45*x46*x48
- 2*x41**2*x42*x45**2*x46*x48 - 3*x41**2*x42*x44*x46*x47**2 - x41**2*
x44**2*x45*x46*x47 + 3*x41**2*x42*x43*x45*x48**2 + x41**2*x42*x44*x45*
x47*x48 - 2*x41**2*x43*x44**2*x47*x48 + x42**2*x41*x44*x45*x47**2 - x42
**2*x41*x45**2*x46*x47 + x42**2*x41*x45**3*x48 - x41*x42*x43*x44**2*x47
**2 + 2*x42**2*x41*x43*x46*x47**2 - x41*x42*x43**2*x46**2*x47 + x41*x42*
x43*x44*x45*x46*x47 + 2*x41*x42*x43**2*x44*x47*x48 + x41*x42*x43**2*x45*
x46*x48 - 3*x42**2*x41*x43*x45*x47*x48 + 2*x41**2*x40*x45**2*x48**2 +
x48**3*x41**4 + 3*x41**2*x40*x46**2*x47**2 + x40*x42*x43*x45**2*x46*x47
- x43**2*x40*x44*x45*x46*x47 - 5*x40*x41*x42*x43*x47**2*x48 + 3*x40*x41
*x43*x45**2*x46*x48 + x40*x41*x42*x45**2*x47*x48 + 2*x40*x41*x44*x45**2*
x46*x47 - 5*x41**2*x40*x45*x46*x47*x48 - x40*x42*x43*x44*x45*x47**2 +
x40*x41*x43*x44*x46*x47**2 + 3*x40*x42*x43**2*x45*x47*x48 + x40*x41*x43
**2*x46*x47*x48 - x40*x41*x42*x45*x46*x47**2 - 3*x40*x41*x43*x45*x46**2*
x47 - 2*x40**2*x43*x44*x47**3 - x40**2*x42*x45*x47**3 - 3*x40**2*x41*x46
*x47**3 + 2*x40**2*x43**2*x47**2*x48 - x40**2*x45**3*x46*x47 + x42**2*
x40*x43*x47**3 + x43**2*x40*x44**2*x47**2 + x43**3*x40*x46**2*x47 - 2*
x41**3*x44*x45*x48**2 + x40**3*x47**4 + 3*x41**3*x44*x46*x47*x48 - 3*x41
**3*x42*x47*x48**2 + x41**2*x43**2*x44*x48**2 + 3*x41**2*x42**2*x47**2*
x48 + x41**2*x44**2*x45**2*x48 - x41*x42*x43**3*x48**2 + x41**3*x45*x46
**2*x48 - x41**3*x47*x46**3 + (x43**3*x40*x46 - x41*x42*x43**2*x46 - x43
**2*x40*x44*x45 - 3*x40*x41*x43*x45*x46 + x41**2*x43*x46*x44 + x41*x42*
x43*x44*x45 + x40*x42*x43*x45**2 - x41**3*x46**2 + 2*x41**2*x42*x45*x46
- x41**2*x44**2*x45 - x42**2*x41*x45**2 + 2*x40*x41*x44*x45**2 - x40**2
*x45**3)*(1 - b167) + (x41*x42*x43 - x41**2*x44 - x43**2*x40)*(1 - b165)
- 1E-5*b163 =G= 0;
* set non-default bounds
x1.lo = 0.95; x1.up = 1;
x2.lo = 0.001; x2.up = 10;
x3.lo = 0.001; x3.up = 10;
x4.lo = 0.001; x4.up = 10;
x5.lo = 0.001; x5.up = 10;
x6.lo = 0.001; x6.up = 10;
x7.lo = 0.001; x7.up = 10;
x8.lo = 0.001; x8.up = 10;
x9.lo = 0.001; x9.up = 10;
x10.lo = 0.001; x10.up = 10;
x20.lo = 0.001; x20.up = 10;
x21.lo = 0.001; x21.up = 10;
x22.lo = 0.001; x22.up = 10;
x23.lo = 0.001; x23.up = 10;
x24.lo = 0.001; x24.up = 10;
x25.lo = 0.001; x25.up = 10;
x26.lo = 0.001; x26.up = 10;
x27.lo = 0.001; x27.up = 10;
x28.lo = 0.001; x28.up = 10;
x29.lo = 0.001; x29.up = 10;
x30.lo = 0.001; x30.up = 10;
x31.lo = 0.001; x31.up = 10;
x32.lo = 0.001; x32.up = 10;
x33.lo = 0.001; x33.up = 10;
x34.lo = 0.001; x34.up = 10;
x35.lo = 0.001; x35.up = 10;
x36.lo = 0.001; x36.up = 10;
x37.lo = 0.001; x37.up = 10;
x38.lo = 0.001; x38.up = 10;
x39.lo = 0.001; x39.up = 10;
x49.lo = 0.001; x49.up = 10;
x50.lo = 0.001; x50.up = 10;
x51.lo = 0.001; x51.up = 10;
x52.lo = 0.001; x52.up = 10;
x53.lo = 0.001; x53.up = 10;
x54.lo = 0.001; x54.up = 10;
x55.lo = 0.001; x55.up = 10;
x56.lo = 0.001; x56.up = 10;
x57.lo = 0.001; x57.up = 10;
x58.lo = 0.001; x58.up = 10;
x59.lo = 0.001; x59.up = 10;
x60.lo = 0.001; x60.up = 10;
x61.lo = 0.001; x61.up = 10;
x62.lo = 0.001; x62.up = 10;
x63.lo = 0.001; x63.up = 10;
x64.lo = 0.001; x64.up = 10;
x65.lo = 0.001; x65.up = 10;
x66.lo = 0.001; x66.up = 10;
x67.lo = 0.001; x67.up = 10;
x68.lo = 0.001; x68.up = 10;
x69.up = 10;
x70.lo = 1E-5; x70.up = 10;
x71.lo = -10; x71.up = 10;
x72.lo = -10; x72.up = 10;
x73.lo = -10; x73.up = 10;
x74.lo = -10; x74.up = 10;
x75.lo = 1E-5; x75.up = 10;
x76.lo = -10; x76.up = 10;
x77.lo = -10; x77.up = 10;
x78.lo = -10; x78.up = 10;
x79.lo = -10; x79.up = 10;
x80.lo = 1E-5; x80.up = 10;
x81.lo = -10; x81.up = 10;
x82.lo = -10; x82.up = 10;
x83.lo = -10; x83.up = 10;
x84.lo = -10; x84.up = 10;
x85.lo = 1E-5; x85.up = 10;
x86.lo = -10; x86.up = 10;
x87.lo = -10; x87.up = 10;
x88.lo = -10; x88.up = 10;
x89.lo = -10; x89.up = 10;
x90.lo = 1E-5; x90.up = 10;
x91.lo = -10; x91.up = 10;
x92.lo = -10; x92.up = 10;
x93.lo = -10; x93.up = 10;
x94.lo = -10; x94.up = 10;
x95.lo = 1E-5; x95.up = 10;
x96.lo = -10; x96.up = 10;
x97.lo = -10; x97.up = 10;
x98.lo = -10; x98.up = 10;
x99.lo = -10; x99.up = 10;
x100.lo = 0.001; x100.up = 10;
x101.lo = 0.001; x101.up = 10;
x102.lo = 0.001; x102.up = 10;
x103.lo = 0.001; x103.up = 10;
x104.lo = 0.001; x104.up = 10;
x105.lo = 0.001; x105.up = 10;
x106.lo = 0.001; x106.up = 10;
x107.lo = 0.001; x107.up = 10;
x108.lo = 0.001; x108.up = 10;
x109.lo = 0.001; x109.up = 10;
x110.lo = 0.001; x110.up = 10;
x111.up = 10;
x112.lo = 1E-5; x112.up = 10;
x113.lo = -10; x113.up = 10;
x114.lo = -10; x114.up = 10;
x115.lo = -10; x115.up = 10;
x116.lo = -10; x116.up = 10;
x117.lo = -10; x117.up = 10;
x118.lo = 1E-5; x118.up = 10;
x119.lo = -10; x119.up = 10;
x120.lo = -10; x120.up = 10;
x121.lo = -10; x121.up = 10;
x122.lo = -10; x122.up = 10;
x123.lo = -10; x123.up = 10;
x124.lo = 1E-5; x124.up = 10;
x125.lo = -10; x125.up = 10;
x126.lo = -10; x126.up = 10;
x127.lo = -10; x127.up = 10;
x128.lo = -10; x128.up = 10;
x129.lo = -10; x129.up = 10;
x130.lo = 1E-5; x130.up = 10;
x131.lo = -10; x131.up = 10;
x132.lo = -10; x132.up = 10;
x133.lo = -10; x133.up = 10;
x134.lo = -10; x134.up = 10;
x135.lo = -10; x135.up = 10;
x136.lo = 1E-5; x136.up = 10;
x137.lo = -10; x137.up = 10;
x138.lo = -10; x138.up = 10;
x139.lo = -10; x139.up = 10;
x140.lo = -10; x140.up = 10;
x141.lo = -10; x141.up = 10;
x142.lo = 1E-5; x142.up = 10;
x143.lo = -10; x143.up = 10;
x144.lo = -10; x144.up = 10;
x145.lo = -10; x145.up = 10;
x146.lo = -10; x146.up = 10;
x147.lo = -10; x147.up = 10;
x148.lo = 1E-5; x148.up = 10;
x149.lo = -10; x149.up = 10;
x150.lo = -10; x150.up = 10;
x151.lo = -10; x151.up = 10;
x152.lo = -10; x152.up = 10;
x153.lo = -10; x153.up = 10;
x154.lo = 1E-5; x154.up = 10;
x155.lo = -10; x155.up = 10;
x156.lo = -10; x156.up = 10;
x157.lo = -10; x157.up = 10;
x158.lo = -10; x158.up = 10;
x159.lo = -10; x159.up = 10;
b160.fx = 1;
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