MINLPLib
A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Instance primary
| Formatsⓘ | ams gms mod nl osil py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | -1.28796692 (ANTIGONE) -2.12194828 (BARON) -1.28796692 (GUROBI) -100.00000000 (LINDO) -100.00000000 (SCIP) -100.00000000 (SHOT) -1.28800307 (XPRESS) |
| Referencesⓘ | Sahinidis, N V, Tawarmalani, M, and Yu, Minrui, Design of alternative refrigerants via global optimization, AIChE Journal, 49:7, 2003, 1761-1775. Tawarmalani, M and Sahinidis, N V, Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming: Theory, Algorithms, Software, and Applications, Kluwer, 2002. |
| Sourceⓘ | BARON book instance refrigerant/primary |
| Applicationⓘ | Molecular Design |
| Added to libraryⓘ | 07 Mar 2014 |
| Problem typeⓘ | MINLP |
| #Variablesⓘ | 81 |
| #Binary Variablesⓘ | 8 |
| #Integer Variablesⓘ | 52 |
| #Nonlinear Variablesⓘ | 64 |
| #Nonlinear Binary Variablesⓘ | 1 |
| #Nonlinear Integer Variablesⓘ | 46 |
| Objective Senseⓘ | min |
| Objective typeⓘ | signomial |
| Objective curvatureⓘ | indefinite |
| #Nonzeros in Objectiveⓘ | 2 |
| #Nonlinear Nonzeros in Objectiveⓘ | 2 |
| #Constraintsⓘ | 163 |
| #Linear Constraintsⓘ | 139 |
| #Quadratic Constraintsⓘ | 9 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 4 |
| #General Nonlinear Constraintsⓘ | 11 |
| Operands in Gen. Nonlin. Functionsⓘ | div exp log mul vcpower |
| Constraints curvatureⓘ | indefinite |
| #Nonzeros in Jacobianⓘ | 1634 |
| #Nonlinear Nonzeros in Jacobianⓘ | 241 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 2129 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 55 |
| #Blocks in Hessian of Lagrangianⓘ | 6 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 1 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 47 |
| Average blocksize in Hessian of Lagrangianⓘ | 10.666667 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 4.0000e-04 |
| Maximal coefficientⓘ | 5.2500e+02 |
| Infeasibility of initial pointⓘ | 1.558e+04 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 164 30 30 104 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 82 22 8 52 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 1637 1394 243 0
*
* Solve m using MINLP minimizing objvar;
Variables i1,i2,i3,i4,i5,i6,i7,i8,i9,i10,i11,i12,i13,i14,i15,i16,i17,i18,i19
,i20,i21,i22,i23,i24,i25,i26,i27,i28,i29,i30,i31,i32,i33,i34,i35,i36
,i37,i38,i39,i40,i41,i42,i43,i44,i45,i46,i47,i48,i49,i50,i51,i52,b53
,b54,b55,b56,b57,b58,b59,b60,x61,x62,x63,x64,x65,x66,x67,x68,x69,x70
,x71,x72,x73,x74,x75,x76,x77,x78,x79,x80,x81,objvar;
Negative Variables x80;
Positive Variables x73;
Binary Variables b53,b54,b55,b56,b57,b58,b59,b60;
Integer Variables i1,i2,i3,i4,i5,i6,i7,i8,i9,i10,i11,i12,i13,i14,i15,i16,i17
,i18,i19,i20,i21,i22,i23,i24,i25,i26,i27,i28,i29,i30,i31,i32,i33,i34
,i35,i36,i37,i38,i39,i40,i41,i42,i43,i44,i45,i46,i47,i48,i49,i50,i51
,i52;
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;
e1.. - 23.58*i1 - 22.88*i2 - 21.74*i3 - 18.25*i4 - 18.18*i5 - 24.96*i6
- 24.14*i7 - 26.15*i8 - 9.2*i9 - 27.38*i10 - 27.15*i11 - 21.78*i12
- 21.78*i13 - 21.32*i14 - 21.32*i15 - 21.32*i16 - 26.73*i17 - 31.01*i18
- 31.01*i19 - 31.01*i20 + 0.03*i21 - 38.13*i22 - 66.86*i23 - 93.84*i24
- 92.88*i25 - 22.42*i26 - 31.22*i27 - 76.75*i28 - 94.97*i29 - 72.24*i30
- 169.09*i31 - 81.1*i32 + 10.5*i33 - 73.23*i34 - 50.17*i35 - 52.82*i36
- 11.74*i37 - 74.6*i38 - 57.55*i39 - 125.66*i40 - 152.54*i41 - 63.56*i42
- 68.78*i43 - 52.1*i44 + x61 =E= 198.2;
e2.. -x61/(0.584 + 0.0136065*i1 - (0.0141*i1 + 0.0189*i2 + 0.0164*i3 + 0.0067*
i4 + 0.0113*i5 + 0.0129*i6 + 0.0117*i7 + 0.0026*i8 + 0.0027*i9 + 0.002*i10
+ 0.01*i11 + 0.0122*i12 + 0.0122*i13 + 0.0042*i14 + 0.0042*i15 + 0.0042*
i16 + 0.0082*i17 + 0.0143*i18 + 0.0143*i19 + 0.0143*i20 + 0.0111*i21 +
0.0105*i22 + 0.0133*i23 + 0.0068*i24 + 0.0741*i25 + 0.0168*i26 + 0.0098*
i27 + 0.038*i28 + 0.0284*i29 + 0.0379*i30 + 0.0791*i31 + 0.0481*i32 +
0.0143*i33 + 0.0243*i34 + 0.0295*i35 + 0.013*i36 + 0.0169*i37 + 0.0255*i38
+ 0.0085*i39 + 0.0496*i40 + 0.0437*i41 + 0.0031*i42 + 0.0119*i43 + 0.0019
*i44)**2 + 0.0182385*i2 + 0.015826*i3 + 0.0064655*i4 + 0.0109045*i5 +
0.0124485*i6 + 0.0112905*i7 + 0.002509*i8 + 0.0026055*i9 + 0.00193*i10 +
0.00965*i11 + 0.011773*i12 + 0.011773*i13 + 0.004053*i14 + 0.004053*i15 +
0.004053*i16 + 0.007913*i17 + 0.0137995*i18 + 0.0137995*i19 + 0.0137995*
i20 + 0.0107115*i21 + 0.0101325*i22 + 0.0128345*i23 + 0.006562*i24 +
0.0715065*i25 + 0.016212*i26 + 0.009457*i27 + 0.03667*i28 + 0.027406*i29
+ 0.0365735*i30 + 0.0763315*i31 + 0.0464165*i32 + 0.0137995*i33 +
0.0234495*i34 + 0.0284675*i35 + 0.012545*i36 + 0.0163085*i37 + 0.0246075*
i38 + 0.0082025*i39 + 0.047864*i40 + 0.0421705*i41 + 0.0029915*i42 +
0.0114835*i43 + 0.0018335*i44) + x62 =E= 0;
e3.. -1/(0.113 + 0.014*i1 + 0.0096*i2 + 0.0044*i3 - 0.0011*i4 + 0.0124*i5 +
0.007*i6 + 0.0021*i7 + 0.0004*i8 + 0.0072*i9 + 0.0016*i10 + 0.0071*i11 +
0.006*i12 + 0.006*i13 - 0.0029*i14 - 0.0029*i15 - 0.0029*i16 + 0.0053*i17
+ 0.0024*i18 + 0.0024*i19 + 0.0024*i20 + 0.0089*i21 + 0.0081*i22 - 0.0025
*i23 + 0.0066*i24 - 0.0048*i25 + 0.0017*i26 - 0.0016*i27 + 0.0033*i28 +
0.0036*i29 + 0.0066*i30 + 0.0051*i31 + 0.0091*i32 - 0.0069*i33 - 0.0013*
i34 - 0.0013*i35 - 0.005*i36 - 0.0042*i37 + 0.0131*i38 - 0.0044*i39 +
0.0165*i40 + 0.0032*i41 - 0.002*i42 - 0.0017*i43 - 0.0019*i44)**2 + x63
=E= 0;
e4.. - 27.9060362667016*i1 - 22.6378084870734*i2 - 17.139736374375*i3
- 11.6136038458281*i4 - 24.6572239375156*i5 - 15.4652846358562*i6
- 10.3292345315312*i7 - 18.4762155922406*i8 - 24.4091998531656*i9
- 13.0986012113105*i10 - 17.9476983094687*i11 - 14.904978927175*i12
- 14.904978927175*i13 - 7.02123776995307*i14 - 7.02123776995307*i15
- 7.02123776995307*i16 - 14.2028684258641*i17 - 10.9018002093344*i18
- 10.9018002093344*i19 - 10.9018002093344*i20 - 13.5482021250156*i21
- 18.6172418998938*i22 - 19.3804300725235*i23 - 22.3977664311391*i24
- 18.1753929278063*i25 - 15.1179767129938*i26 - 12.7299939157219*i27
- 23.1465990779122*i28 - 23.1027820855781*i29 - 32.3493558653063*i30
- 41.8754787811391*i31 - 38.6579257229438*i32 - 13.2334131164469*i33
- 26.489960594675*i34 - 17.2714223569766*i35 - 12.6966779338688*i36
- 11.7078216565312*i37 - 10.8040394990938*i39 - 28.2386206875156*i40
- 33.7063565892125*i41 - 26.3895787500156*i42 - 20.7267295870188*i43
- 19.9761272356828*i44 + x64 =E= -4.74320181253128;
e5.. -x61/x62 + x65 =E= 0;
e6.. -294.25/x62 + x66 =E= 0;
e7.. -316.45/x62 + x67 =E= 0;
e8.. -272.05/x62 + x68 =E= 0;
e9.. log(0.987166831194472*x63) - 6.09648/x65 - 1.28862*log(x65) + 0.169347*x65
**6 + x79 =E= -5.97214;
e10.. 15.6875/x65 + 13.4721*log(x65) - 0.43577*x65**6 + x80 =E= 15.2518;
e11.. x69*x80 - x79 =E= 0;
e12.. -(3.7413/(1 - x66) + 52.3782*(1 - x66)**0.333333333333333*x69/x66 +
35.563135*x69 + 3.620747*x69/(1 - x66)) - x64 + 4.1868*x70 =E= 12.0553;
e13.. - 2.373*i1 - 2.226*i2 - 1.691*i3 - 0.636*i4 - 1.724*i5 - 2.205*i6
- 2.138*i7 - 2.661*i8 - 1.155*i9 - 3.302*i10 - 2.398*i11 - 1.942*i12
- 1.942*i13 - 0.664*i14 - 0.664*i15 - 0.664*i16 - 2.544*i17 - 3.059*i18
- 3.059*i19 - 3.059*i20 + 0.67*i21 - 4.532*i22 - 6.582*i23 - 9.52*i24
- 16.826*i25 - 2.41*i26 - 4.682*i27 - 8.972*i28 - 6.645*i29 - 9.093*i30
- 19.537*i31 - 9.633*i32 - 5.909*i33 - 10.788*i34 - 6.436*i35 - 6.93*i36
- 1.896*i37 - 3.335*i38 - 6.528*i39 - 12.851*i40 - 16.738*i41
- 6.884*i42 - 6.817*i43 - 5.984*i44 + x71 =E= 15.3;
e14.. -((1 - x68)/(1 - x65))**0.38*x71 + x72 =E= 0;
e15.. -log(0.987166831194472*x63)*x65/(1 - x65) + x73 =E= 0;
e16.. - 0.4605*x73 + x74 =E= 0.4835;
e17.. -(x73 - (1 + x65)*x74)/x74/(3 + x65)/(1 - x65)**2 + x81 =E= 0;
e18.. -exp(-(1 + x81*(3 + x67)*(1 - x67)**3 - x67**2)*x74/x67) + x75 =E= 0;
e19.. -x75*x63 + x76 =E= 0;
e20.. -exp(-(1 + x81*(3 + x68)*(1 - x68)**3 - x68**2)*x74/x68) + x77 =E= 0;
e21.. -x77*x63 + x78 =E= 0;
e22.. i1 + i2 + i3 + i4 + i5 + i6 + i7 + i8 + i9 + i10 + i11 + i12 + i13
+ i14 + i15 + i16 + i17 + i18 + i19 + i20 + i21 + i22 + i23 + i24 + i25
+ i26 + i27 + i28 + i29 + i30 + i31 + i32 + i33 + i34 + i35 + i36 + i37
+ i38 + i39 + i40 + i41 + i42 + i43 + i44 =G= 2;
e23.. i1 + i2 + i3 + i4 + i5 + i6 + i7 + i8 + i9 + i10 + i21 + i22 + i23
+ i24 + i25 + i26 + i28 + i30 + i31 + i32 + i33 + i34 + i35 + i37 + i38
+ i40 + i41 + i42 + i43 - b53 =G= 0;
e24.. i1 - 15*b53 =L= 0;
e25.. i2 - 15*b53 =L= 0;
e26.. i3 - 15*b53 =L= 0;
e27.. i4 - 15*b53 =L= 0;
e28.. i5 - 15*b53 =L= 0;
e29.. i6 - 15*b53 =L= 0;
e30.. i7 - 15*b53 =L= 0;
e31.. i8 - 15*b53 =L= 0;
e32.. i9 - 15*b53 =L= 0;
e33.. i10 - 15*b53 =L= 0;
e34.. i21 - 15*b53 =L= 0;
e35.. i22 - 15*b53 =L= 0;
e36.. i23 - 15*b53 =L= 0;
e37.. i24 - 15*b53 =L= 0;
e38.. i25 - 15*b53 =L= 0;
e39.. i26 - 15*b53 =L= 0;
e40.. i28 - 15*b53 =L= 0;
e41.. i30 - 15*b53 =L= 0;
e42.. i31 - 15*b53 =L= 0;
e43.. i32 - 15*b53 =L= 0;
e44.. i33 - 15*b53 =L= 0;
e45.. i34 - 15*b53 =L= 0;
e46.. i35 - 15*b53 =L= 0;
e47.. i37 - 15*b53 =L= 0;
e48.. i38 - 15*b53 =L= 0;
e49.. i40 - 15*b53 =L= 0;
e50.. i41 - 15*b53 =L= 0;
e51.. i42 - 15*b53 =L= 0;
e52.. i43 - 15*b53 =L= 0;
e53.. i11 + i12 + i14 + i17 + i18 + i27 + i29 + i36 + i39 + i44 - b54 =G= 0;
e54.. i11 - 15*b54 =L= 0;
e55.. i12 - 15*b54 =L= 0;
e56.. i14 - 15*b54 =L= 0;
e57.. i17 - 15*b54 =L= 0;
e58.. i18 - 15*b54 =L= 0;
e59.. i27 - 15*b54 =L= 0;
e60.. i29 - 15*b54 =L= 0;
e61.. i36 - 15*b54 =L= 0;
e62.. i29 - 15*b54 =L= 0;
e63.. i44 - 15*b54 =L= 0;
e64.. i13 + i15 + i16 + i19 + i20 - b55 =G= 0;
e65.. i13 - 15*b55 =L= 0;
e66.. i15 - 15*b55 =L= 0;
e67.. i16 - 15*b55 =L= 0;
e68.. i19 - 15*b55 =L= 0;
e69.. i20 - 15*b55 =L= 0;
e70.. - b53 - b54 + b55 =G= -1;
e71.. - b53 - b54 + b55 =L= 0;
e72.. i11 + i12 + i13 + i14 + i15 + i16 + i17 + i18 + i19 + i20 + i27 + i29
+ i36 + i39 + i44 - 3*b56 =G= 0;
e73.. i11 - 15*b56 =L= 0;
e74.. i12 - 15*b56 =L= 0;
e75.. i13 - 15*b56 =L= 0;
e76.. i14 - 15*b56 =L= 0;
e77.. i15 - 15*b56 =L= 0;
e78.. i16 - 15*b56 =L= 0;
e79.. i17 - 15*b56 =L= 0;
e80.. i18 - 15*b56 =L= 0;
e81.. i19 - 15*b56 =L= 0;
e82.. i20 - 15*b56 =L= 0;
e83.. i27 - 15*b56 =L= 0;
e84.. i29 - 15*b56 =L= 0;
e85.. i36 - 15*b56 =L= 0;
e86.. i39 - 15*b56 =L= 0;
e87.. i44 - 15*b56 =L= 0;
e88.. i1 + i3 + i5 + i7 + i9 + i12 + i13 + i18 + i19 + i20 + i21 + i22 + i23
+ i24 + i25 + i30 + i31 + i33 + i34 + i37 + i40 + i41 + i42 - 2*i45
=E= 0;
e89.. - i1 + i3 + 2*i4 - i5 + i7 - i9 + i12 + i13 + 2*i14 + 2*i15 + 2*i16
+ i18 + i19 + i20 - i21 - i22 - i23 - i24 - i25 - i30 - i31 - i33 - i34
+ i37 - i40 - i41 - i42 =G= -2;
e90.. i1 - (i1 + i2 + i3 + i4 + i5 + i6 + i7 + i8 + i9 + i10 + i11 + i12 + i13
+ i14 + i15 + i16 + i17 + i18 + i19 + i20 + i21 + i22 + i23 + i24 + i25
+ i26 + i27 + i28 + i29 + i30 + i31 + i32 + i33 + i34 + i35 + i36 + i37
+ i38 + i39 + i40 + i41 + i42 + i43 + i44)**2 + 2*i2 + 3*i3 + 4*i4 + i5
+ 2*i6 + 3*i7 + 2*i8 + i9 + 2*i10 + 2*i11 + 3*i12 + 3*i13 + 4*i14 + 4*
i15 + 4*i16 + 2*i17 + 3*i18 + 3*i19 + 3*i20 + i21 + i22 + i23 + i24 + i25
+ 2*i26 + 2*i27 + 2*i28 + 2*i29 + i30 + i31 + 2*i32 + i33 + i34 + 2*i35
+ 2*i36 + 3*i37 + 2*i38 + 2*i39 + i40 + i41 + i42 + 2*i43 + 2*i44 + i1
+ i2 + i3 + i4 + i5 + i6 + i7 + i8 + i9 + i10 + i11 + i12 + i13 + i14 +
i15 + i16 + i17 + i18 + i19 + i20 + i21 + i22 + i23 + i24 + i25 + i26 +
i27 + i28 + i29 + i30 + i31 + i32 + i33 + i34 + i35 + i36 + i37 + i38 +
i39 + i40 + i41 + i42 + i43 + i44 =L= 0;
e91.. i13 + i15 + i16 + i19 + i20 - b58 =G= 0;
e92.. i13 - 15*b58 =L= 0;
e93.. i15 - 15*b58 =L= 0;
e94.. i16 - 15*b58 =L= 0;
e95.. i19 - 15*b58 =L= 0;
e96.. i20 - 15*b58 =L= 0;
e97.. i1 - i3 - 2*i4 + i5 - i7 + i9 - i13 - 2*i15 - 2*i16 - i19 - i20 + i21
+ i22 + i23 + i24 + i25 + i30 + i31 + i33 + i34 - i37 + i40 + i41 + i42
+ 225*b58 =L= 225;
e98.. i11 + i12 + i13 + i14 + i15 + i16 + i17 + i18 + i19 + i20 + i27 + i29
+ i36 + i39 + i44 - b57 =G= 0;
e99.. i11 - 15*b57 =L= 0;
e100.. i12 - 15*b57 =L= 0;
e101.. i13 - 15*b57 =L= 0;
e102.. i14 - 15*b57 =L= 0;
e103.. i15 - 15*b57 =L= 0;
e104.. i16 - 15*b57 =L= 0;
e105.. i17 - 15*b57 =L= 0;
e106.. i18 - 15*b57 =L= 0;
e107.. i19 - 15*b57 =L= 0;
e108.. i20 - 15*b57 =L= 0;
e109.. i27 - 15*b57 =L= 0;
e110.. i29 - 15*b57 =L= 0;
e111.. i36 - 15*b57 =L= 0;
e112.. i39 - 15*b57 =L= 0;
e113.. i44 - 15*b57 =L= 0;
e114.. i1 - i3 - 2*i4 + i5 - i7 + i9 + i21 + i22 + i23 + i24 + i25 + i30
+ i31 + i33 + i34 - i37 + i40 + i41 + i42 + 77*b57 =G= 2;
e115.. i1 - i3 - 2*i4 + i5 - i7 + i9 + i21 + i22 + i23 + i24 + i25 + i30
+ i31 + i33 + i34 - i37 + i40 + i41 + i42 - 223*b57 =L= 2;
e116.. i1 + 2*i2 + 3*i3 + 4*i4 + i6 + 2*i7 + i10 + i13 + i15 + 2*i16 + i19
+ i21 + i22 + i23 + i24 + i25 + 2*i26 + 2*i28 + i30 + i31 + 2*i32 + i34
+ 2*i35 + 3*i37 + i38 + i40 + i41 + i42 + 2*i43 - 2*i46 =E= 0;
e117.. 2*i11 + 3*i12 + 2*i13 + 4*i14 + 3*i15 + 2*i16 + i17 + 2*i18 + i19
+ 2*i20 + 2*i27 + 2*i29 + 2*i36 + i39 + 2*i44 - 2*i47 =E= 0;
e118.. i5 + i6 + i7 + 2*i8 + i20 + i33 + i38 - 2*i48 =E= 0;
e119.. i17 + i18 + i19 + i39 - 2*i49 =E= 0;
e120.. i9 + i10 - 2*i50 =E= 0;
e121.. i1 + i3 + i4 + i5 + i6 + i7 + i8 + i9 + i10 + i11 + i12 + i13 + i14
+ i15 + i16 + i17 + i18 + i19 + i20 + i21 + i22 + i23 + i24 + i25 + i26
+ i27 + i28 + i29 + i30 + i31 + i32 + i33 + i34 + i35 + i36 + i37 + i38
+ i39 + i40 + i41 + i42 + i43 + i44 =G= 2;
e122.. i1 + i2 - i3 + i4 + i5 + i6 + i7 + i8 + i9 + i10 + i11 + i12 + i13
+ i14 + i15 + i16 + i17 + i18 + i19 + i20 + i21 + i22 + i23 + i24 + i25
+ i26 + i27 + i28 + i29 + i30 + i31 + i32 + i33 + i34 + i35 + i36 + i37
+ i38 + i39 + i40 + i41 + i42 + i43 + i44 =G= 2;
e123.. i1 + i2 + i3 - 2*i4 + i5 + i6 + i7 + i8 + i9 + i10 + i11 + i12 + i13
+ i14 + i15 + i16 + i17 + i18 + i19 + i20 + i21 + i22 + i23 + i24 + i25
+ i26 + i27 + i28 + i29 + i30 + i31 + i32 + i33 + i34 + i35 + i36 + i37
+ i38 + i39 + i40 + i41 + i42 + i43 + i44 =G= 2;
e124.. i1 + i2 + i3 + i4 + i5 + i7 + i8 + i9 + i10 + i11 + i12 + i13 + i14
+ i15 + i16 + i17 + i18 + i19 + i20 + i21 + i22 + i23 + i24 + i25 + i26
+ i27 + i28 + i29 + i30 + i31 + i32 + i33 + i34 + i35 + i36 + i37 + i38
+ i39 + i40 + i41 + i42 + i43 + i44 =G= 2;
e125.. i1 + i2 + i3 + i4 + i5 + i6 - i7 + i8 + i9 + i10 + i11 + i12 + i13
+ i14 + i15 + i16 + i17 + i18 + i19 + i20 + i21 + i22 + i23 + i24 + i25
+ i26 + i27 + i28 + i29 + i30 + i31 + i32 + i33 + i34 + i35 + i36 + i37
+ i38 + i39 + i40 + i41 + i42 + i43 + i44 =G= 2;
e126.. i1 + i2 + i3 + i4 + i5 + i6 + i7 + i9 + i10 + i11 + i12 + i13 + i14
+ i15 + i16 + i17 + i18 + i19 + i20 + i21 + i22 + i23 + i24 + i25 + i26
+ i27 + i28 + i29 + i30 + i31 + i32 + i33 + i34 + i35 + i36 + i37 + i38
+ i39 + i40 + i41 + i42 + i43 + i44 =G= 2;
e127.. i1 + i2 + i3 + i4 + i5 + i6 + i7 + i8 + i9 + i11 + i12 + i13 + i14
+ i15 + i16 + i17 + i18 + i19 + i20 + i21 + i22 + i23 + i24 + i25 + i26
+ i27 + i28 + i29 + i30 + i31 + i32 + i33 + i34 + i35 + i36 + i37 + i38
+ i39 + i40 + i41 + i42 + i43 + i44 =G= 2;
e128.. i1 + i2 + i3 + i4 + i5 + i6 + i7 + i8 + i9 + i10 + i11 + i12 + i13
+ i14 + i15 + i16 + i17 + i18 + i19 + i20 + i21 + i22 + i23 + i24 + i25
+ i27 + i28 + i29 + i30 + i31 + i32 + i33 + i34 + i35 + i36 + i37 + i38
+ i39 + i40 + i41 + i42 + i43 + i44 =G= 2;
e129.. i1 + i2 + i3 + i4 + i5 + i6 + i7 + i8 + i9 + i10 + i11 + i12 + i13
+ i14 + i15 + i16 + i17 + i18 + i19 + i20 + i21 + i22 + i23 + i24 + i25
+ i26 + i27 + i29 + i30 + i31 + i32 + i33 + i34 + i35 + i36 + i37 + i38
+ i39 + i40 + i41 + i42 + i43 + i44 =G= 2;
e130.. i1 + i2 + i3 + i4 + i5 + i6 + i7 + i8 + i9 + i10 + i11 + i12 + i13
+ i14 + i15 + i16 + i17 + i18 + i19 + i20 + i21 + i22 + i23 + i24 + i25
+ i26 + i27 + i28 + i29 + i30 + i31 + i33 + i34 + i35 + i36 + i37 + i38
+ i39 + i40 + i41 + i42 + i43 + i44 =G= 2;
e131.. i1 + i2 + i3 + i4 + i5 + i6 + i7 + i8 + i9 + i10 + i11 + i12 + i13
+ i14 + i15 + i16 + i17 + i18 + i19 + i20 + i21 + i22 + i23 + i24 + i25
+ i26 + i27 + i28 + i29 + i30 + i31 + i32 + i33 + i34 + i36 + i37 + i38
+ i39 + i40 + i41 + i42 + i43 + i44 =G= 2;
e132.. i1 + i2 + i3 + i4 + i5 + i6 + i7 + i8 + i9 + i10 + i11 + i12 + i13
+ i14 + i15 + i16 + i17 + i18 + i19 + i20 + i21 + i22 + i23 + i24 + i25
+ i26 + i27 + i28 + i29 + i30 + i31 + i32 + i33 + i34 + i35 + i36 - i37
+ i38 + i39 + i40 + i41 + i42 + i43 + i44 =G= 2;
e133.. i1 + i2 + i3 + i4 + i5 + i6 + i7 + i8 + i9 + i10 + i11 + i12 + i13
+ i14 + i15 + i16 + i17 + i18 + i19 + i20 + i21 + i22 + i23 + i24 + i25
+ i26 + i27 + i28 + i29 + i30 + i31 + i32 + i33 + i34 + i35 + i36 + i37
+ i39 + i40 + i41 + i42 + i43 + i44 =G= 2;
e134.. i1 + i2 + i3 + i4 + i5 + i6 + i7 + i8 + i9 + i10 + i11 + i12 + i13
+ i14 + i15 + i16 + i17 + i18 + i19 + i20 + i21 + i22 + i23 + i24 + i25
+ i26 + i27 + i28 + i29 + i30 + i31 + i32 + i33 + i34 + i35 + i36 + i37
+ i38 + i39 + i40 + i41 + i42 + i44 =G= 2;
e135.. i2 + i3 + i4 + i6 + i7 + i8 + i10 + i16 + i26 + i28 + i32 + i35 + i37
+ i38 + i43 - b59 =G= 0;
e136.. i2 - 15*b59 =L= 0;
e137.. i3 - 15*b59 =L= 0;
e138.. i4 - 15*b59 =L= 0;
e139.. i6 - 15*b59 =L= 0;
e140.. i7 - 15*b59 =L= 0;
e141.. i8 - 15*b59 =L= 0;
e142.. i10 - 15*b59 =L= 0;
e143.. i16 - 15*b59 =L= 0;
e144.. i26 - 15*b59 =L= 0;
e145.. i28 - 15*b59 =L= 0;
e146.. i32 - 15*b59 =L= 0;
e147.. i35 - 15*b59 =L= 0;
e148.. i37 - 15*b59 =L= 0;
e149.. i38 - 15*b59 =L= 0;
e150.. i43 - 15*b59 =L= 0;
e151.. i1 - 2*i2 - 3*i3 - 4*i4 - i6 - 2*i7 - i10 + i13 + i15 - 2*i16 + i19
+ i21 + i22 + i23 + i24 + i25 - 2*i26 - 2*i28 + i30 + i31 - 2*i32 + i34
- 2*i35 - 3*i37 - i38 + i40 + i41 + i42 - 2*i43 - 225*b56 + 225*b59
=L= 225;
e152.. i5 - i6 - i7 - 2*i8 + i20 + i33 - i38 - 45*b56 + 45*b59 =L= 45;
e153.. i9 - i10 - 15*b56 + 15*b59 =L= 15;
e154.. - i1 + i3 + 2*i4 - i5 + i7 - i9 - i13 - i15 - i19 - i20 - i21 - i22
- i23 - i24 - i25 - i30 - i31 - i33 - i34 + i37 - i40 - i41 - i42
- 525*b56 =L= -2;
e155.. - i1 + i3 + 2*i4 - i5 + i7 - i9 - i13 - i15 - i19 - i20 - i21 - i22
- i23 - i24 - i25 - i30 - i31 - i33 - i34 + i37 - i40 - i41 - i42
+ 525*b56 =G= -2;
e156.. i11 + i12 + i13 + i14 + i15 + i16 + i17 + i18 + i19 + i20 + i27 + i29
+ i36 + i39 + i44 - i51 =E= 0;
e157.. i17 + i18 + i19 + i39 - i52 =E= 0;
e158.. i51 - i51**2 + 2*i47 - b60 =L= -1;
e159.. i52 - i52**2 + 2*i49 =L= 0;
e160.. b60*i1 + 2*b60*i2 + 3*b60*i3 + 4*b60*i4 + b60*i6 + 2*b60*i7 + b60*i10 +
b60*i21 + b60*i22 + b60*i23 + b60*i24 + b60*i25 + 2*b60*i26 + 2*b60*i28
+ b60*i30 + b60*i31 + 2*b60*i32 + b60*i34 + 2*b60*i35 + 3*b60*i37 + b60
*i38 + b60*i40 + b60*i41 + b60*i42 + 2*b60*i43 - b60*i13 - b60*i15 - 2*
b60*i16 - b60*i19 =G= 0;
e161.. i7*i8 + i6*i8 + i20*i8 + i7*i38 + i6*i38 + i20*i38 - i7*i33 - i6*i33 -
i20*i33 =G= 0;
e162.. i28*i1 + i28*i2 + i28*i3 + i28*i4 + i28*i6 + i28*i7 + i28*i10 + i28*i13
+ i28*i15 + i28*i16 + i28*i19 + i28*i21 + i28*i22 + i28*i23 + i28*i24
+ i28*i26 + i28*i30 + i28*i31 + i28*i32 + i28*i34 + i28*i35 + i28*i37
+ i28*i38 + i28*i40 + i28*i41 + i28*i42 + i28*i43 - i28*i25 =G= 0;
e163.. i2*i28*i26 + i3*i28*i26 + i4*i28*i26 + i7*i28*i26 + i16*i28*i26 + i32*
i28*i26 + i35*i28*i26 + i37*i28*i26 + i43*i28*i26 - 0.5*i28*i26*i26 -
0.5*i28*i26*i28 + 0.5*i28*i26*((i26 - i28)*(i26 - i28))**0.5 =G= 0;
e164.. x72/x70 + objvar =E= 0;
* set non-default bounds
i1.up = 15;
i2.up = 15;
i3.up = 15;
i4.up = 15;
i5.up = 15;
i6.up = 15;
i7.up = 15;
i8.up = 15;
i9.up = 15;
i10.up = 15;
i11.up = 15;
i12.up = 15;
i13.up = 15;
i14.up = 15;
i15.up = 15;
i16.up = 15;
i17.up = 15;
i18.up = 15;
i19.up = 15;
i20.up = 15;
i21.up = 15;
i22.up = 15;
i23.up = 15;
i24.up = 15;
i25.up = 15;
i26.up = 15;
i27.up = 15;
i28.up = 15;
i29.up = 15;
i30.up = 15;
i31.up = 15;
i32.up = 15;
i33.up = 15;
i34.up = 15;
i35.up = 15;
i36.up = 15;
i37.up = 15;
i38.up = 15;
i39.up = 15;
i40.up = 15;
i41.up = 15;
i42.up = 15;
i43.up = 15;
i44.up = 15;
i45.up = 172;
i46.up = 330;
i47.up = 232;
i48.up = 60;
i49.up = 30;
i50.up = 15;
i51.up = 225;
i52.up = 60;
x61.lo = 50; x61.up = 1000;
x62.lo = 100; x62.up = 2000;
x63.lo = 2; x63.up = 200;
x64.lo = 1; x64.up = 135;
x65.lo = 0.001; x65.up = 1;
x66.lo = 0.001; x66.up = 1;
x67.lo = 0.001; x67.up = 1;
x68.lo = 0.001; x68.up = 1;
x69.lo = -1; x69.up = 1.3;
x70.lo = 1; x70.up = 32.2;
x71.lo = 10; x71.up = 110;
x72.lo = 18.4; x72.up = 100;
x73.up = 5300;
x74.lo = 0.48; x74.up = 2500;
x75.lo = 0.001; x75.up = 1;
x76.lo = 1.4; x76.up = 14;
x77.lo = 0.001; x77.up = 1;
x78.lo = 1.4; x78.up = 14;
x79.lo = -5.4; x79.up = 6100;
x80.lo = -16000;
x81.lo = -1; x81.up = 10;
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