MINLPLib
A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Instance ghg_1veh
| Formatsⓘ | ams gms mod nl osil py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | 7.78163488 (ANTIGONE) 7.78163401 (BARON) 7.78162290 (COUENNE) 7.78163384 (LINDO) 7.78162582 (SCIP) -26.23077338 (SHOT) |
| 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ⓘ | 29 |
| #Binary Variablesⓘ | 12 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 24 |
| #Nonlinear Binary Variablesⓘ | 10 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | signomial |
| Objective curvatureⓘ | indefinite |
| #Nonzeros in Objectiveⓘ | 22 |
| #Nonlinear Nonzeros in Objectiveⓘ | 20 |
| #Constraintsⓘ | 37 |
| #Linear Constraintsⓘ | 10 |
| #Quadratic Constraintsⓘ | 9 |
| #Polynomial Constraintsⓘ | 9 |
| #Signomial Constraintsⓘ | 2 |
| #General Nonlinear Constraintsⓘ | 7 |
| Operands in Gen. Nonlin. Functionsⓘ | div exp mul |
| Constraints curvatureⓘ | indefinite |
| #Nonzeros in Jacobianⓘ | 108 |
| #Nonlinear Nonzeros in Jacobianⓘ | 71 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 261 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 9 |
| #Blocks in Hessian of Lagrangianⓘ | 1 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 24 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 24 |
| Average blocksize in Hessian of Lagrangianⓘ | 24.0 |
| #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ⓘ | 2.931 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 38 18 9 11 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 30 18 12 0 0 0 0 0
* FX 1
*
* Nonzero counts
* Total const NL DLL
* 131 40 91 0
*
* Solve m using MINLP minimizing objvar;
Variables b1,b2,b3,b4,b5,b6,b7,b8,b9,b10,b11,b12,x13,x14,x15,x16,x17,x18,x19
,x20,x21,x22,x23,x24,x25,x26,x27,x28,x29,objvar;
Positive Variables x24,x25,x26,x27,x28,x29;
Binary Variables b1,b2,b3,b4,b5,b6,b7,b8,b9,b10,b11,b12;
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;
e1.. -21.6*x15*x16*x20 + x24 =E= 0;
e2.. -(0.007852585706*x13**3 + 0.154288922601*x14**3 + 0.352933730854*x15**3 -
0.004816150342*x13**2*x14 - 0.00547943134*x14**2*x13 - 0.02533808214*x13**
2*x15 + 0.00021201136*x15**2*x13 - 0.057118497613*x14**2*x15 -
0.042739509965*x15**2*x14 - 0.01583097252*x13*x14*x15 - 0.001028174658*x13
**2 - 0.805369774847*x14**2 - 0.655580550098*x15**2 + 0.057270405947*x13*
x14 + 0.07973036236*x13*x15 + 0.342091579946*x14*x15 - 0.191345333621*x13
+ 1.188971392024*x14 - 0.346682012779*x15) + x20 =E= 4.960068215723;
e3.. -(2.21406746341*x13**3 + 1.086659693552*x14**3 + 5.577874978662*x15**3 -
0.815241697738*x13**2*x14 + 0.509578110533*x14**2*x13 + 1.561758113326*x13
**2*x15 + 2.212321055022*x15**2*x13 - 0.612567680918*x14**2*x15 +
0.254008083604*x15**2*x14 - 0.159429747244*x13*x14*x15 - 8.905599398536*
x13**2 - 6.095001164559*x14**2 - 15.207539664993*x15**2 + 0.089172114876*
x13*x14 - 3.273526677614*x13*x15 + 2.498376358946*x14*x15 + 2.621894664006
*x13 + 9.284846067558*x14 + 5.837143728557*x15) + x21 =E= 57.679680208231;
e4.. -(1.456640469666*x13**3 - 5.495718264905*x14**3 - 28.456261951645*x15**3
+ 0.912917970314*x13**2*x14 - 0.88119920631*x14**2*x13 - 1.049763024383*
x13**2*x15 - 0.308107344863*x15**2*x13 + 2.043536297441*x14**2*x15 +
15.609611231641*x15**2*x14 + 0.336486837518*x13*x14*x15 - 4.634160849469*
x13**2 + 31.478262635483*x14**2 + 34.016843490037*x15**2 + 1.153148892739*
x13*x14 + 1.168601192983*x13*x15 - 32.056936006397*x14*x15 +
3.405095041238*x13 - 54.472915571467*x14 + 9.56987912824*x15) + x17
=E= 44.230616625681;
e5.. -(3.334445194766*x13**3 - 2.265666208775*x14**3 - 20.256566414583*x15**3
+ 0.413782262402*x13**2*x14 - 3.523622273943*x14**2*x13 - 0.285910055687*
x13**2*x15 - 10.110726634622*x15**2*x13 + 1.95072196814*x14**2*x15 +
10.308512463418*x15**2*x14 + 5.808426325827*x13*x14*x15 - 6.932398033967*
x13**2 + 15.80019426934*x14**2 + 39.197963873266*x15**2 + 7.900706395772*
x13*x14 + 6.58186092156*x13*x15 - 30.119438887106*x14*x15 - 6.733798415788
*x13 - 26.385308892431*x14 - 4.098268423019*x15) + x18 =E= 32.102172356117
;
e6.. -(-0.194075741585*x13**2 - 0.004843420334*x14**2 + 0.04736686635*x15**2 +
9.4029979e-5*x13*x14 + 0.011329651793*x13*x15 - 0.001017352942*x14*x15 +
0.382275988592*x13 + 0.019484588535*x14 - 0.077357069039*x15) + x19
=E= 0.140278656706;
e7.. x17 =L= 11;
e8.. x18 =L= 11;
e9.. x19 =G= 0.32;
e10.. exp(-0.029595*x24)*(33.7894914681534 + x24) + x26 =E= 33.7894914681534;
e11.. exp(-0.029595*x24) + x27 =E= 1;
e12.. -0.134723681728774*(0.010073140669*x13**2 + 0.011394190823*x14**2 +
0.052910213683*x15**2 + 0.000159410872*x13*x14 + 0.008036404292*x13*x15
- 0.003423392047*x14*x15 + 0.097124049148*x13 + 0.03829180344*x14 +
0.370440556286*x15) + x22 =E= 0.29587368369345;
e13.. -0.134723681728774*(0.46598008632*x13**2 - 0.00797004615*x14**2 -
0.01779288613*x15**2 - 0.01429434551*x13*x14 - 0.03832188467*x13*x15 +
0.00970510229*x14*x15 - 0.88981702163*x13 + 0.07730602595*x14 +
0.39988032723*x15) + x23 =E= 0.194162178290626;
e14.. -(2715.7894736842/x20 + 5187*x22 - 5187*x23)*x24/(4320*x15 - 5187*x23)
+ x25 =E= 0;
e15.. exp(-0.029595*x25)*(33.7894914681534 + x25) + x28 =E= 33.7894914681534;
e16.. exp(-0.029595*x25) + x29 =E= 1;
e17.. b1 + b2 + b3 =E= 1;
e18.. b1*x24 =L= 0;
e19.. b2*x24 =G= 0;
e20.. b2*(-200 + x24) =L= 0;
e21.. b3*(-200 + x24) =G= 0;
e22.. b4 + b5 + b6 =E= 1;
e23.. b8*b4*x25 =L= 0;
e24.. b8*b5*x25 =G= 0;
e25.. b8*b5*(-200 + x25) =L= 0;
e26.. b8*b6*(-200 + x25) =G= 0;
e27.. b7 + b8 + b9 =E= 1;
e28.. (-150000 + 124927.703875072*x15/x23)*b7 =L= 0;
e29.. (-150000 + 124927.703875072*x15/x23)*b8 =G= 0;
e30.. (150000 - 4320*x15/(0.0172/x20 + 0.03458*x22))*b8 =G= 0;
e31.. (150000 - 4320*x15/(0.0172/x20 + 0.03458*x22))*b9 =L= 0;
e32.. b7*(-1 + b4) =G= 0;
e33.. b9*(-1 + b4) =G= 0;
e34.. b2 + b4 + b8 =L= 2;
e35.. b3 + b4 + b8 =L= 2;
e36.. b3 + b5 + b8 =L= 2;
e37.. -(1.87912853526074 + (376.046780997472/x21 + 0.997312113279821*(
0.854659090909091/x20 - 11.34/x21)*x24)*b1 + (0.854659090909091*x26/x20
+ (376.046780997472 - 11.34*x26)/x21 + (0.854659090909091/x20 - 11.34/
x21)*x24*(0.997312113279821 - x27))*b2 + 28.341428570246*b3/x20 + (
0.573023666281862*b4*b8 + 0.573023666281862*b9)*x15 + b1*b5*b8*(0.6*(
0.03458*x23*x28 + (0.0181052631578947/x20 + 0.03458*x22 - 0.03458*x23)*
x24*x29) + 0.01728*x15*(33.1610917987189 - x28)) + b2*b5*b8*(0.6*((
0.0181052631578947/x20 + 0.03458*x22)*x26 + 0.03458*x23*(x28 - x26) + (
0.0181052631578947/x20 + 0.03458*x22 - 0.03458*x23)*x24*(x29 - x27)) +
0.01728*x15*(33.1610917987189 - x28)) + 0.6*(b1*b6*b8 + b1*b7)*((
0.0180565982614873/x20 + 0.0344870528772162*x22 - 0.0344870528772162*x23)
*x24 + 1.1467105543997*x23) + 0.6*(b2*b6*b8 + b2*b7)*((0.0181052631578947
/x20 + 0.03458*x22)*x26 + 0.03458*x23*(33.1610917987189 - x26) + (
0.0181052631578947/x20 + 0.03458*x22 - 0.03458*x23)*x24*(
0.997312113279821 - x27)) + 19.8966550792313*(b3*b6*b8 + b3*b7)*(
0.0181052631578947/x20 + 0.03458*x22))*b10 - 8.20275610163388*b11
- 14.6264770436496*b12 + objvar =E= 0;
e38.. b10 + b11 + b12 =E= 1;
* set non-default bounds
x13.lo = 0.526315789473684; x13.up = 1.05263157894737;
x14.lo = 0.961538461538462; x14.up = 2.11538461538462;
x15.lo = 0.2; x15.up = 1;
x16.fx = 0.8;
x17.lo = 6; x17.up = 13;
x18.lo = 6; x18.up = 13;
x19.lo = 0.26; x19.up = 0.35;
x20.lo = 4.9; x20.up = 5.5;
x21.lo = 55; x21.up = 63;
x22.lo = 0.296392099803303; x22.up = 0.404171045186323;
x23.lo = 0.134723681728774; x23.up = 0.229030258938916;
x24.up = 90;
x25.up = 200;
x26.up = 26;
x27.up = 1;
x28.up = 34.1;
x29.up = 1;
* set non-default levels
b2.l = 1;
b5.l = 1;
b8.l = 1;
b10.l = 1;
x13.l = 1;
x14.l = 1;
x15.l = 0.5;
x17.l = 13;
x18.l = 10.9460692020431;
x19.l = 0.3215334333865;
x20.l = 5.218428550001;
x21.l = 58.1078648496005;
x22.l = 0.344077403769737;
x23.l = 0.16888643257787;
x24.l = 45.0872226720086;
x25.l = 49.2705196815703;
x26.l = 13.01907481523;
x27.l = 0.736672389572227;
x28.l = 14.4644383631733;
x29.l = 0.767336256792154;
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