MINLPLib
A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Instance ghg_3veh
| Formatsⓘ | ams gms mod nl osil py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | 7.75432450 (ANTIGONE) 7.75432450 (BARON) 3.43964174 (COUENNE) 6.39178216 (GUROBI) 5.08793521 (LINDO) 5.87607353 (SCIP) 0.00000000 (SHOT) 4.13834258 (XPRESS) |
| Referencesⓘ | Shiau, Ching-Shin N and Michalek, Jeremy J, Global Optimization of Plug-In Hybrid Vehicle Design and Allocation to Minimize Life Cycle Greenhouse Gas Emissions, ASME Journal of Mechanical Design, 133:8, 2011, 084502. |
| Applicationⓘ | Optimal vehicle allocation for minimizing greenhouse gas emissions |
| Added to libraryⓘ | 29 Aug 2011 |
| Problem typeⓘ | MBNLP |
| #Variablesⓘ | 96 |
| #Binary Variablesⓘ | 36 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 84 |
| #Nonlinear Binary Variablesⓘ | 36 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | linear |
| Objective curvatureⓘ | linear |
| #Nonzeros in Objectiveⓘ | 3 |
| #Nonlinear Nonzeros in Objectiveⓘ | 0 |
| #Constraintsⓘ | 119 |
| #Linear Constraintsⓘ | 31 |
| #Quadratic Constraintsⓘ | 27 |
| #Polynomial Constraintsⓘ | 27 |
| #Signomial Constraintsⓘ | 9 |
| #General Nonlinear Constraintsⓘ | 25 |
| Operands in Gen. Nonlin. Functionsⓘ | div exp mul |
| Constraints curvatureⓘ | indefinite |
| #Nonzeros in Jacobianⓘ | 427 |
| #Nonlinear Nonzeros in Jacobianⓘ | 307 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 1049 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 29 |
| #Blocks in Hessian of Lagrangianⓘ | 1 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 84 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 84 |
| Average blocksize in Hessian of Lagrangianⓘ | 84.0 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 9.4030e-05 |
| Maximal coefficientⓘ | 1.5000e+05 |
| Infeasibility of initial pointⓘ | 57.07 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 120 59 27 34 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 97 61 36 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 431 124 307 0
*
* Solve m using MINLP minimizing objvar;
Variables b1,b2,b3,b4,b5,b6,b7,b8,b9,b10,b11,b12,b13,b14,b15,b16,b17,b18,b19
,b20,b21,b22,b23,b24,b25,b26,b27,b28,b29,b30,b31,b32,b33,b34,b35,b36
,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,objvar;
Positive Variables x40,x46,x49,x50,x51,x52,x53,x54,x58,x64,x67,x68,x69,x70
,x71,x72,x76,x82,x85,x86,x87,x88,x89,x90,x91,x92,x93,x94,x95,x96;
Binary Variables b1,b2,b3,b4,b5,b6,b7,b8,b9,b10,b11,b12,b13,b14,b15,b16,b17
,b18,b19,b20,b21,b22,b23,b24,b25,b26,b27,b28,b29,b30,b31,b32,b33,b34
,b35,b36;
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;
e1.. -21.6*x39*x40*x44 + x49 =E= 0;
e2.. -(0.007852585706*x37**3 + 0.154288922601*x38**3 + 0.352933730854*x39**3 -
0.004816150342*x37**2*x38 - 0.00547943134*x38**2*x37 - 0.02533808214*x37**
2*x39 + 0.00021201136*x39**2*x37 - 0.057118497613*x38**2*x39 -
0.042739509965*x39**2*x38 - 0.01583097252*x37*x38*x39 - 0.001028174658*x37
**2 - 0.805369774847*x38**2 - 0.655580550098*x39**2 + 0.057270405947*x37*
x38 + 0.07973036236*x37*x39 + 0.342091579946*x38*x39 - 0.191345333621*x37
+ 1.188971392024*x38 - 0.346682012779*x39) + x44 =E= 4.960068215723;
e3.. -(2.21406746341*x37**3 + 1.086659693552*x38**3 + 5.577874978662*x39**3 -
0.815241697738*x37**2*x38 + 0.509578110533*x38**2*x37 + 1.561758113326*x37
**2*x39 + 2.212321055022*x39**2*x37 - 0.612567680918*x38**2*x39 +
0.254008083604*x39**2*x38 - 0.159429747244*x37*x38*x39 - 8.905599398536*
x37**2 - 6.095001164559*x38**2 - 15.207539664993*x39**2 + 0.089172114876*
x37*x38 - 3.273526677614*x37*x39 + 2.498376358946*x38*x39 + 2.621894664006
*x37 + 9.284846067558*x38 + 5.837143728557*x39) + x45 =E= 57.679680208231;
e4.. -(1.456640469666*x37**3 - 5.495718264905*x38**3 - 28.456261951645*x39**3
+ 0.912917970314*x37**2*x38 - 0.88119920631*x38**2*x37 - 1.049763024383*
x37**2*x39 - 0.308107344863*x39**2*x37 + 2.043536297441*x38**2*x39 +
15.609611231641*x39**2*x38 + 0.336486837518*x37*x38*x39 - 4.634160849469*
x37**2 + 31.478262635483*x38**2 + 34.016843490037*x39**2 + 1.153148892739*
x37*x38 + 1.168601192983*x37*x39 - 32.056936006397*x38*x39 +
3.405095041238*x37 - 54.472915571467*x38 + 9.56987912824*x39) + x41
=E= 44.230616625681;
e5.. -(3.334445194766*x37**3 - 2.265666208775*x38**3 - 20.256566414583*x39**3
+ 0.413782262402*x37**2*x38 - 3.523622273943*x38**2*x37 - 0.285910055687*
x37**2*x39 - 10.110726634622*x39**2*x37 + 1.95072196814*x38**2*x39 +
10.308512463418*x39**2*x38 + 5.808426325827*x37*x38*x39 - 6.932398033967*
x37**2 + 15.80019426934*x38**2 + 39.197963873266*x39**2 + 7.900706395772*
x37*x38 + 6.58186092156*x37*x39 - 30.119438887106*x38*x39 - 6.733798415788
*x37 - 26.385308892431*x38 - 4.098268423019*x39) + x42 =E= 32.102172356117
;
e6.. -(-0.194075741585*x37**2 - 0.004843420334*x38**2 + 0.04736686635*x39**2 +
9.4029979e-5*x37*x38 + 0.011329651793*x37*x39 - 0.001017352942*x38*x39 +
0.382275988592*x37 + 0.019484588535*x38 - 0.077357069039*x39) + x43
=E= 0.140278656706;
e7.. x41 =L= 11.0001;
e8.. x42 =L= 11.0001;
e9.. x43 =G= 0.3199;
e10.. -21.6*x57*x58*x62 + x67 =E= 0;
e11.. -(0.007852585706*x55**3 + 0.154288922601*x56**3 + 0.352933730854*x57**3
- 0.004816150342*x55**2*x56 - 0.00547943134*x56**2*x55 - 0.02533808214*
x55**2*x57 + 0.00021201136*x57**2*x55 - 0.057118497613*x56**2*x57 -
0.042739509965*x57**2*x56 - 0.01583097252*x55*x56*x57 - 0.001028174658*
x55**2 - 0.805369774847*x56**2 - 0.655580550098*x57**2 + 0.057270405947*
x55*x56 + 0.07973036236*x55*x57 + 0.342091579946*x56*x57 - 0.191345333621
*x55 + 1.188971392024*x56 - 0.346682012779*x57) + x62 =E= 4.960068215723;
e12.. -(2.21406746341*x55**3 + 1.086659693552*x56**3 + 5.577874978662*x57**3 -
0.815241697738*x55**2*x56 + 0.509578110533*x56**2*x55 + 1.561758113326*
x55**2*x57 + 2.212321055022*x57**2*x55 - 0.612567680918*x56**2*x57 +
0.254008083604*x57**2*x56 - 0.159429747244*x55*x56*x57 - 8.905599398536*
x55**2 - 6.095001164559*x56**2 - 15.207539664993*x57**2 + 0.089172114876*
x55*x56 - 3.273526677614*x55*x57 + 2.498376358946*x56*x57 +
2.621894664006*x55 + 9.284846067558*x56 + 5.837143728557*x57) + x63
=E= 57.679680208231;
e13.. -(1.456640469666*x55**3 - 5.495718264905*x56**3 - 28.456261951645*x57**3
+ 0.912917970314*x55**2*x56 - 0.88119920631*x56**2*x55 - 1.049763024383*
x55**2*x57 - 0.308107344863*x57**2*x55 + 2.043536297441*x56**2*x57 +
15.609611231641*x57**2*x56 + 0.336486837518*x55*x56*x57 - 4.634160849469*
x55**2 + 31.478262635483*x56**2 + 34.016843490037*x57**2 + 1.153148892739
*x55*x56 + 1.168601192983*x55*x57 - 32.056936006397*x56*x57 +
3.405095041238*x55 - 54.472915571467*x56 + 9.56987912824*x57) + x59
=E= 44.230616625681;
e14.. -(3.334445194766*x55**3 - 2.265666208775*x56**3 - 20.256566414583*x57**3
+ 0.413782262402*x55**2*x56 - 3.523622273943*x56**2*x55 - 0.285910055687
*x55**2*x57 - 10.110726634622*x57**2*x55 + 1.95072196814*x56**2*x57 +
10.308512463418*x57**2*x56 + 5.808426325827*x55*x56*x57 - 6.932398033967*
x55**2 + 15.80019426934*x56**2 + 39.197963873266*x57**2 + 7.900706395772*
x55*x56 + 6.58186092156*x55*x57 - 30.119438887106*x56*x57 -
6.733798415788*x55 - 26.385308892431*x56 - 4.098268423019*x57) + x60
=E= 32.102172356117;
e15.. -(-0.194075741585*x55**2 - 0.004843420334*x56**2 + 0.04736686635*x57**2
+ 9.4029979e-5*x55*x56 + 0.011329651793*x55*x57 - 0.001017352942*x56*x57
+ 0.382275988592*x55 + 0.019484588535*x56 - 0.077357069039*x57) + x61
=E= 0.140278656706;
e16.. x59 =L= 11.0001;
e17.. x60 =L= 11.0001;
e18.. x61 =G= 0.3199;
e19.. -21.6*x75*x76*x80 + x85 =E= 0;
e20.. -(0.007852585706*x73**3 + 0.154288922601*x74**3 + 0.352933730854*x75**3
- 0.004816150342*x73**2*x74 - 0.00547943134*x74**2*x73 - 0.02533808214*
x73**2*x75 + 0.00021201136*x75**2*x73 - 0.057118497613*x74**2*x75 -
0.042739509965*x75**2*x74 - 0.01583097252*x73*x74*x75 - 0.001028174658*
x73**2 - 0.805369774847*x74**2 - 0.655580550098*x75**2 + 0.057270405947*
x73*x74 + 0.07973036236*x73*x75 + 0.342091579946*x74*x75 - 0.191345333621
*x73 + 1.188971392024*x74 - 0.346682012779*x75) + x80 =E= 4.960068215723;
e21.. -(2.21406746341*x73**3 + 1.086659693552*x74**3 + 5.577874978662*x75**3 -
0.815241697738*x73**2*x74 + 0.509578110533*x74**2*x73 + 1.561758113326*
x73**2*x75 + 2.212321055022*x75**2*x73 - 0.612567680918*x74**2*x75 +
0.254008083604*x75**2*x74 - 0.159429747244*x73*x74*x75 - 8.905599398536*
x73**2 - 6.095001164559*x74**2 - 15.207539664993*x75**2 + 0.089172114876*
x73*x74 - 3.273526677614*x73*x75 + 2.498376358946*x74*x75 +
2.621894664006*x73 + 9.284846067558*x74 + 5.837143728557*x75) + x81
=E= 57.679680208231;
e22.. -(1.456640469666*x73**3 - 5.495718264905*x74**3 - 28.456261951645*x75**3
+ 0.912917970314*x73**2*x74 - 0.88119920631*x74**2*x73 - 1.049763024383*
x73**2*x75 - 0.308107344863*x75**2*x73 + 2.043536297441*x74**2*x75 +
15.609611231641*x75**2*x74 + 0.336486837518*x73*x74*x75 - 4.634160849469*
x73**2 + 31.478262635483*x74**2 + 34.016843490037*x75**2 + 1.153148892739
*x73*x74 + 1.168601192983*x73*x75 - 32.056936006397*x74*x75 +
3.405095041238*x73 - 54.472915571467*x74 + 9.56987912824*x75) + x77
=E= 44.230616625681;
e23.. -(3.334445194766*x73**3 - 2.265666208775*x74**3 - 20.256566414583*x75**3
+ 0.413782262402*x73**2*x74 - 3.523622273943*x74**2*x73 - 0.285910055687
*x73**2*x75 - 10.110726634622*x75**2*x73 + 1.95072196814*x74**2*x75 +
10.308512463418*x75**2*x74 + 5.808426325827*x73*x74*x75 - 6.932398033967*
x73**2 + 15.80019426934*x74**2 + 39.197963873266*x75**2 + 7.900706395772*
x73*x74 + 6.58186092156*x73*x75 - 30.119438887106*x74*x75 -
6.733798415788*x73 - 26.385308892431*x74 - 4.098268423019*x75) + x78
=E= 32.102172356117;
e24.. -(-0.194075741585*x73**2 - 0.004843420334*x74**2 + 0.04736686635*x75**2
+ 9.4029979e-5*x73*x74 + 0.011329651793*x73*x75 - 0.001017352942*x74*x75
+ 0.382275988592*x73 + 0.019484588535*x74 - 0.077357069039*x75) + x79
=E= 0.140278656706;
e25.. x77 =L= 11.0001;
e26.. x78 =L= 11.0001;
e27.. x79 =G= 0.3199;
e28.. exp(-0.029595*x49)*(33.7894914681534 + x49) + x51 =E= 33.7894914681534;
e29.. exp(-0.029595*x49) + x52 =E= 1;
e30.. -0.134723681728774*(0.010073140669*x37**2 + 0.011394190823*x38**2 +
0.052910213683*x39**2 + 0.000159410872*x37*x38 + 0.008036404292*x37*x39
- 0.003423392047*x38*x39 + 0.097124049148*x37 + 0.03829180344*x38 +
0.370440556286*x39) + x47 =E= 0.29587368369345;
e31.. -0.134723681728774*(0.46598008632*x37**2 - 0.00797004615*x38**2 -
0.01779288613*x39**2 - 0.01429434551*x37*x38 - 0.03832188467*x37*x39 +
0.00970510229*x38*x39 - 0.88981702163*x37 + 0.07730602595*x38 +
0.39988032723*x39) + x48 =E= 0.194162178290626;
e32.. -(2715.7894736842/x44 + 5187*x47 - 5187*x48)*x49/(4320*x39 - 5187*x48)
+ x50 =E= 0;
e33.. exp(-0.029595*x50)*(33.7894914681534 + x50) + x53 =E= 33.7894914681534;
e34.. exp(-0.029595*x50) + x54 =E= 1;
e35.. exp(-0.029595*x67)*(33.7894914681534 + x67) + x69 =E= 33.7894914681534;
e36.. exp(-0.029595*x67) + x70 =E= 1;
e37.. -0.134723681728774*(0.010073140669*x55**2 + 0.011394190823*x56**2 +
0.052910213683*x57**2 + 0.000159410872*x55*x56 + 0.008036404292*x55*x57
- 0.003423392047*x56*x57 + 0.097124049148*x55 + 0.03829180344*x56 +
0.370440556286*x57) + x65 =E= 0.29587368369345;
e38.. -0.134723681728774*(0.46598008632*x55**2 - 0.00797004615*x56**2 -
0.01779288613*x57**2 - 0.01429434551*x55*x56 - 0.03832188467*x55*x57 +
0.00970510229*x56*x57 - 0.88981702163*x55 + 0.07730602595*x56 +
0.39988032723*x57) + x66 =E= 0.194162178290626;
e39.. -(2715.7894736842/x62 + 5187*x65 - 5187*x66)*x67/(4320*x57 - 5187*x66)
+ x68 =E= 0;
e40.. exp(-0.029595*x68)*(33.7894914681534 + x68) + x71 =E= 33.7894914681534;
e41.. exp(-0.029595*x68) + x72 =E= 1;
e42.. exp(-0.029595*x85)*(33.7894914681534 + x85) + x87 =E= 33.7894914681534;
e43.. exp(-0.029595*x85) + x88 =E= 1;
e44.. -0.134723681728774*(0.010073140669*x73**2 + 0.011394190823*x74**2 +
0.052910213683*x75**2 + 0.000159410872*x73*x74 + 0.008036404292*x73*x75
- 0.003423392047*x74*x75 + 0.097124049148*x73 + 0.03829180344*x74 +
0.370440556286*x75) + x83 =E= 0.29587368369345;
e45.. -0.134723681728774*(0.46598008632*x73**2 - 0.00797004615*x74**2 -
0.01779288613*x75**2 - 0.01429434551*x73*x74 - 0.03832188467*x73*x75 +
0.00970510229*x74*x75 - 0.88981702163*x73 + 0.07730602595*x74 +
0.39988032723*x75) + x84 =E= 0.194162178290626;
e46.. -(2715.7894736842/x80 + 5187*x83 - 5187*x84)*x85/(4320*x75 - 5187*x84)
+ x86 =E= 0;
e47.. exp(-0.029595*x86)*(33.7894914681534 + x86) + x89 =E= 33.7894914681534;
e48.. exp(-0.029595*x86) + x90 =E= 1;
e49.. b1 + b2 + b3 =E= 1;
e50.. b1*x49 =L= 0;
e51.. b2*x49 =G= 0;
e52.. b2*(x49 - x91) =L= 0;
e53.. b3*(x49 - x91) =G= 0;
e54.. b4 + b5 + b6 =E= 1;
e55.. b8*b4*x50 =L= 0;
e56.. b8*b5*x50 =G= 0;
e57.. b8*b5*(x50 - x91) =L= 0;
e58.. b8*b6*(x50 - x91) =G= 0;
e59.. b7 + b8 + b9 =E= 1;
e60.. (-150000 + 124927.703875072*x39/x48)*b7 =L= 0;
e61.. (-150000 + 124927.703875072*x39/x48)*b8 =G= 0;
e62.. (150000 - 4320*x39/(0.0181052631578947/x44 + 0.03458*x47))*b8 =G= 0;
e63.. (150000 - 4320*x39/(0.0181052631578947/x44 + 0.03458*x47))*b9 =L= 0;
e64.. b10 + b11 + b12 =E= 1;
e65.. b10*(x67 - x91) =L= 0;
e66.. b11*(x67 - x91) =G= 0;
e67.. b11*(x67 - x92) =L= 0;
e68.. b12*(x67 - x92) =G= 0;
e69.. b13 + b14 + b15 =E= 1;
e70.. b17*b13*(x68 - x91) =L= 0;
e71.. b17*b14*(x68 - x91) =G= 0;
e72.. b17*b14*(x68 - x92) =L= 0;
e73.. b17*b15*(x68 - x92) =G= 0;
e74.. b16 + b17 + b18 =E= 1;
e75.. (-150000 + 124927.703875072*x57/x66)*b16 =L= 0;
e76.. (-150000 + 124927.703875072*x57/x66)*b17 =G= 0;
e77.. (150000 - 4320*x57/(0.0181052631578947/x62 + 0.03458*x65))*b17 =G= 0;
e78.. (150000 - 4320*x57/(0.0181052631578947/x62 + 0.03458*x65))*b18 =L= 0;
e79.. b19 + b20 + b21 =E= 1;
e80.. b19*(x85 - x92) =L= 0;
e81.. b20*(x85 - x92) =G= 0;
e82.. b20*(-200 + x85) =L= 0;
e83.. b21*(-200 + x85) =G= 0;
e84.. b22 + b23 + b24 =E= 1;
e85.. b26*b22*(x86 - x92) =L= 0;
e86.. b26*b23*(x86 - x92) =G= 0;
e87.. b26*b23*(-200 + x86) =L= 0;
e88.. b26*b24*(-200 + x86) =G= 0;
e89.. b25 + b26 + b27 =E= 1;
e90.. (-150000 + 124927.703875072*x75/x84)*b25 =L= 0;
e91.. (-150000 + 124927.703875072*x75/x84)*b26 =G= 0;
e92.. (150000 - 4320*x75/(0.0181052631578947/x80 + 0.03458*x83))*b26 =G= 0;
e93.. (150000 - 4320*x75/(0.0181052631578947/x80 + 0.03458*x83))*b27 =L= 0;
e94.. b7*(-1 + b4) =G= 0;
e95.. b9*(-1 + b4) =G= 0;
e96.. b2 + b4 + b8 =L= 2;
e97.. b3 + b4 + b8 =L= 2;
e98.. b3 + b5 + b8 =L= 2;
e99.. b16*(-1 + b13) =G= 0;
e100.. b18*(-1 + b13) =G= 0;
e101.. b10 + b13 + b17 =L= 2;
e102.. b12 + b13 + b17 =L= 2;
e103.. b12 + b14 + b17 =L= 2;
e104.. b25*(-1 + b22) =G= 0;
e105.. b27*(-1 + b22) =G= 0;
e106.. b19 + b22 + b26 =L= 2;
e107.. b21 + b22 + b26 =L= 2;
e108.. b21 + b23 + b26 =L= 2;
e109.. -(0.441073446327684*b30*x93 + 0.247360857459789*b29*x93 + ((11.34*x93/
x45 + (0.854659090909091/x44 - 11.34/x45)*x49*x94)*b1 +
0.0566666666666667*x93 + (0.854659090909091*x51/x44 + (11.34*x93 - 11.34
*x51)/x45 + (0.854659090909091/x44 - 11.34/x45)*x49*(x94 - x52))*b2 +
0.854659090909091*x93/x44*b3 + (0.01728*b4*b8 + 0.01728*b9)*x39*x93 + b1
*b5*b8*(0.6*(0.03458*x48*x53 + (0.0181052631578947/x44 + 0.03458*x47 -
0.03458*x48)*x49*x54) + 0.01728*x39*(x93 - x53)) + b2*b5*b8*(0.6*((
0.0181052631578947/x44 + 0.03458*x47)*x51 + 0.03458*x48*(x53 - x51) + (
0.0181052631578947/x44 + 0.03458*x47 - 0.03458*x48)*x49*(x54 - x52)) +
0.01728*x39*(x93 - x53)) + 0.6*(b1*b6*b8 + b1*b7)*(0.03458*x48*x93 + (
0.0181052631578947/x44 + 0.03458*x47 - 0.03458*x48)*x49*x94) + 0.6*(b2*
b6*b8 + b2*b7)*((0.0181052631578947/x44 + 0.03458*x47)*x51 + 0.03458*x48
*(x93 - x51) + (0.0181052631578947/x44 + 0.03458*x47 - 0.03458*x48)*x49*
(x94 - x52)) + 0.6*(b3*b6*b8 + b3*b7)*(0.0181052631578947/x44 + 0.03458*
x47)*x93)*b28) + x46 =E= 0;
e110.. b28 + b29 + b30 =E= 1;
e111.. -(b33*(0.441073446327684*x95 - 0.441073446327684*x93) + b32*(
0.247360857459789*x95 - 0.247360857459789*x93) + (((11.34*x95 - 11.34*
x93)/x63 + (0.854659090909091/x62 - 11.34/x63)*x67*(x96 - x94))*b10 -
0.0566666666666667*x93 + 0.0566666666666667*x95 + ((0.854659090909091*
x69 - 0.854659090909091*x93)/x62 + (11.34*x95 - 11.34*x69)/x63 + (
0.854659090909091/x62 - 11.34/x63)*x67*(x96 - x70))*b11 + (
0.854659090909091*x95 - 0.854659090909091*x93)/x62*b12 + (0.01728*b13*
b17 + 0.01728*b18)*x57*(x95 - x93) + b10*b14*b17*(0.6*(0.03458*x66*(x71
- x93) + (0.0181052631578947/x62 + 0.03458*x65 - 0.03458*x66)*x67*(x72
- x94)) + 0.01728*x57*(x95 - x71)) + b11*b14*b17*(0.6*((
0.0181052631578947/x62 + 0.03458*x65)*(x69 - x93) + 0.03458*x66*(x71 -
x69) + (0.0181052631578947/x62 + 0.03458*x65 - 0.03458*x66)*x67*(x72 -
x70)) + 0.01728*x57*(x95 - x71)) + 0.6*(b10*b15*b17 + b10*b16)*(0.03458*
x66*(x95 - x93) + (0.0181052631578947/x62 + 0.03458*x65 - 0.03458*x66)*
x67*(x96 - x94)) + 0.6*(b11*b15*b17 + b11*b16)*((0.0181052631578947/x62
+ 0.03458*x65)*(x69 - x93) + 0.03458*x66*(x95 - x69) + (
0.0181052631578947/x62 + 0.03458*x65 - 0.03458*x66)*x67*(x96 - x70)) +
0.6*(b12*b15*b17 + b12*b16)*(0.0181052631578947/x62 + 0.03458*x65)*(x95
- x93))*b31) + x64 =E= 0;
e112.. b31 + b32 + b33 =E= 1;
e113.. -(b36*(14.6264770436496 - 0.441073446327684*x95) + b35*(8.20275610163388
- 0.247360857459789*x95) + (1.87912853526074 + ((376.046780997472 -
11.34*x95)/x81 + (0.854659090909091/x80 - 11.34/x81)*x85*(
0.997312113279821 - x96))*b19 - 0.0566666666666667*x95 + ((
0.854659090909091*x87 - 0.854659090909091*x95)/x80 + (376.046780997472
- 11.34*x87)/x81 + (0.854659090909091/x80 - 11.34/x81)*x85*(
0.997312113279821 - x88))*b20 + (28.341428570246 - 0.854659090909091*x95
)/x80*b21 + (0.01728*b22*b26 + 0.01728*b27)*x75*(33.1610917987189 - x95)
+ b19*b23*b26*(0.6*(0.03458*x84*(x89 - x95) + (0.0181052631578947/x80
+ 0.03458*x83 - 0.03458*x84)*x85*(x90 - x96)) + 0.01728*x75*(
33.1610917987189 - x89)) + b20*b23*b26*(0.6*((0.0181052631578947/x80 +
0.03458*x83)*(x87 - x95) + 0.03458*x84*(x89 - x87) + (0.0181052631578947
/x80 + 0.03458*x83 - 0.03458*x84)*x85*(x90 - x88)) + 0.01728*x75*(
33.1610917987189 - x89)) + 0.6*(b19*b24*b26 + b19*b25)*(0.03458*x84*(
33.1610917987189 - x95) + (0.0181052631578947/x80 + 0.03458*x83 -
0.03458*x84)*x85*(0.997312113279821 - x96)) + 0.6*(b20*b24*b26 + b20*b25
)*((0.0181052631578947/x80 + 0.03458*x83)*(x87 - x95) + 0.03458*x84*(
33.1610917987189 - x87) + (0.0181052631578947/x80 + 0.03458*x83 -
0.03458*x84)*x85*(0.997312113279821 - x88)) + 0.6*(b21*b24*b26 + b21*b25
)*(0.0181052631578947/x80 + 0.03458*x83)*(33.1610917987189 - x95))*b34)
+ x82 =E= 0;
e114.. b34 + b35 + b36 =E= 1;
e115.. exp(-0.029595*x91)*(33.7894914681534 + x91) + x93 =E= 33.7894914681534;
e116.. exp(-0.029595*x91) + x94 =E= 1;
e117.. exp(-0.029595*x92)*(33.7894914681534 + x92) + x95 =E= 33.7894914681534;
e118.. exp(-0.029595*x92) + x96 =E= 1;
e119.. x91 - x92 =L= 0;
e120.. - x46 - x64 - x82 + objvar =E= 0;
* set non-default bounds
x37.lo = 0.526315789473684; x37.up = 1.05263157894737;
x38.lo = 0.961538461538462; x38.up = 2.11538461538462;
x39.lo = 0.2; x39.up = 1;
x40.up = 0.8;
x41.lo = 6; x41.up = 13;
x42.lo = 6; x42.up = 13;
x43.lo = 0.26; x43.up = 0.35;
x44.lo = 4.9; x44.up = 5.5;
x45.lo = 55; x45.up = 63;
x47.lo = 0.296392099803303; x47.up = 0.404171045186323;
x48.lo = 0.134723681728774; x48.up = 0.229030258938916;
x49.up = 90;
x50.up = 200;
x51.up = 26;
x52.up = 1;
x53.up = 34.1;
x54.up = 1;
x55.lo = 0.526315789473684; x55.up = 1.05263157894737;
x56.lo = 0.961538461538462; x56.up = 2.11538461538462;
x57.lo = 0.2; x57.up = 1;
x58.up = 0.8;
x59.lo = 6; x59.up = 13;
x60.lo = 6; x60.up = 13;
x61.lo = 0.26; x61.up = 0.35;
x62.lo = 4.9; x62.up = 5.5;
x63.lo = 55; x63.up = 63;
x65.lo = 0.296392099803303; x65.up = 0.404171045186323;
x66.lo = 0.134723681728774; x66.up = 0.229030258938916;
x67.up = 90;
x68.up = 200;
x69.up = 26;
x70.up = 1;
x71.up = 34.1;
x72.up = 1;
x73.lo = 0.526315789473684; x73.up = 1.05263157894737;
x74.lo = 0.961538461538462; x74.up = 2.11538461538462;
x75.lo = 0.2; x75.up = 1;
x76.up = 0.8;
x77.lo = 6; x77.up = 13;
x78.lo = 6; x78.up = 13;
x79.lo = 0.26; x79.up = 0.35;
x80.lo = 4.9; x80.up = 5.5;
x81.lo = 55; x81.up = 63;
x83.lo = 0.296392099803303; x83.up = 0.404171045186323;
x84.lo = 0.134723681728774; x84.up = 0.229030258938916;
x85.up = 90;
x86.up = 200;
x87.up = 26;
x88.up = 1;
x89.up = 34.1;
x90.up = 1;
x91.up = 200;
x92.up = 200;
x93.up = 34.1;
x94.up = 1;
x95.up = 34.1;
x96.up = 1;
* set non-default levels
b2.l = 1;
b5.l = 1;
b8.l = 1;
b11.l = 1;
b14.l = 1;
b17.l = 1;
b20.l = 1;
b23.l = 1;
b26.l = 1;
b28.l = 1;
b31.l = 1;
b34.l = 1;
x37.l = 0.7;
x38.l = 1.3;
x39.l = 0.3;
x40.l = 0.8;
x41.l = 11.4287823650327;
x42.l = 10.3327145787012;
x43.l = 0.31304324384463;
x44.l = 5.34913143281842;
x45.l = 61.0970665725108;
x47.l = 0.33067952966495;
x48.l = 0.166352389404373;
x49.l = 27.7298973477307;
x50.l = 87.0746186204636;
x51.l = 6.71245303562714;
x52.l = 0.559861712645379;
x53.l = 24.6033726611686;
x54.l = 0.92399630626288;
x55.l = 0.8;
x56.l = 1.3;
x57.l = 0.4;
x58.l = 0.8;
x59.l = 11.425274117861;
x60.l = 9.49828897985979;
x61.l = 0.31886568491872;
x62.l = 5.30393747252268;
x63.l = 60.2374262842503;
x65.l = 0.337743204592998;
x66.l = 0.16835247462338;
x67.l = 36.6608158100768;
x68.l = 59.6460698604874;
x69.l = 9.98365557805552;
x70.l = 0.662090389526887;
x71.l = 17.7981634326254;
x72.l = 0.828851801090147;
x73.l = 0.9;
x74.l = 1.4;
x75.l = 0.5;
x76.l = 0.8;
x77.l = 10.8939370647334;
x78.l = 8.76253617561773;
x79.l = 0.3225788719383;
x80.l = 5.25028725476321;
x81.l = 59.1691778526634;
x83.l = 0.345907462122186;
x84.l = 0.172100567341578;
x85.l = 45.3624818811541;
x86.l = 50.7848330046186;
x87.l = 13.1156941888876;
x88.l = 0.738808820494851;
x89.l = 14.9745070751508;
x90.l = 0.777533140107315;
x91.l = 30;
x92.l = 36;
x93.l = 7.53758887227811;
x94.l = 0.588460387570554;
x95.l = 9.74121218769467;
x96.l = 0.655416900531042;
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