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)
-1.28796692 p1 ( gdx sol )
(infeas: 2e-15)
Other points (infeas > 1e-08)  
Dual Bounds
-1.28796692 (ANTIGONE)
-2.12194828 (BARON)
-100.00000000 (LINDO)
-100.00000000 (SCIP)
-100.00000000 (SHOT)
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 of Objective Gradient and Jacobian
Sparsity Hessian of Lagrangian Sparsity of 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: 2022-08-11 Git hash: f176bd52
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