MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance: ghg_2veh

Formats ams gms mod nl osil
Primal Bounds
7.77090454 p1 ( gdx sol )
(infeas: 1e-13)
Dual Bounds
0.00000000 (ANTIGONE)
7.27958135 (BARON)
6.24967114 (COUENNE)
7.09617548 (LINDO)
7.43354565 (SCIP)
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 57
#Binary Variables 18
#Integer Variables 0
#Nonlinear Variables 49
#Nonlinear Binary Variables 18
#Nonlinear Integer Variables 0
Objective Sense min
Objective type linear
Objective curvature linear
#Nonzeros in Objective 2
#Nonlinear Nonzeros in Objective 0
#Constraints 62
#Linear Constraints 14
#Quadratic Constraints 24
#Polynomial Constraints 10
#Signomial Constraints 0
#General Nonlinear Constraints 14
Operands in Gen. Nonlin. Functions mul div exp
Constraints curvature indefinite
#Nonzeros in Jacobian 212
#Nonlinear Nonzeros in Jacobian 154
#Nonzeros in (Upper-Left) Hessian of Lagrangian 493
#Nonzeros in Diagonal of Hessian of Lagrangian 17
#Blocks in Hessian of Lagrangian 1
Minimal blocksize in Hessian of Lagrangian 49
Maximal blocksize in Hessian of Lagrangian 49
Average blocksize in Hessian of Lagrangian 49.0
#Semicontinuities 0
#Nonlinear Semicontinuities 0
#SOS type 1 0
#SOS type 2 0
Infeasibility of initial point 52.6
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
*         63       37       12       14        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         58       40       18        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        215       61      154        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,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,objvar;

Positive Variables  x22,x26,x29,x30,x33,x34,x35,x36,x40,x44,x47,x48,x51,x52
          ,x53,x54,x55,x56,x57;

Binary Variables  b1,b2,b3,b4,b5,b6,b7,b8,b9,b10,b11,b12,b13,b14,b15,b16,b17
          ,b18;

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;


e1.. -21.6*x21*x22*x27 + x26 =E= 0;

e2.. -(0.007852585706*x19**3 + 0.154288922601*x20**3 + 0.352933730854*x21**3 - 
     0.004816150342*x19**2*x20 - 0.00547943134*x20**2*x19 - 0.02533808214*x19**
     2*x21 + 0.00021201136*x21**2*x19 - 0.057118497613*x20**2*x21 - 
     0.042739509965*x21**2*x20 - 0.01583097252*x19*x20*x21 - 0.001028174658*x19
     **2 - 0.805369774847*x20**2 - 0.655580550098*x21**2 + 0.057270405947*x19*
     x20 + 0.07973036236*x19*x21 + 0.342091579946*x20*x21 - 0.191345333621*x19
      + 1.188971392024*x20 - 0.346682012779*x21) + x27 =E= 4.960068215723;

e3.. -(2.21406746341*x19**3 + 1.086659693552*x20**3 + 5.577874978662*x21**3 - 
     0.815241697738*x19**2*x20 + 0.509578110533*x20**2*x19 + 1.561758113326*x19
     **2*x21 + 2.212321055022*x21**2*x19 - 0.612567680918*x20**2*x21 + 
     0.254008083604*x21**2*x20 - 0.159429747244*x19*x20*x21 - 8.905599398536*
     x19**2 - 6.095001164559*x20**2 - 15.207539664993*x21**2 + 0.089172114876*
     x19*x20 - 3.273526677614*x19*x21 + 2.498376358946*x20*x21 + 2.621894664006
     *x19 + 9.284846067558*x20 + 5.837143728557*x21) + x28 =E= 57.679680208231;

e4.. -(1.456640469666*x19**3 - 5.495718264905*x20**3 - 28.456261951645*x21**3
      + 0.912917970314*x19**2*x20 - 0.88119920631*x20**2*x19 - 1.049763024383*
     x19**2*x21 - 0.308107344863*x21**2*x19 + 2.043536297441*x20**2*x21 + 
     15.609611231641*x21**2*x20 + 0.336486837518*x19*x20*x21 - 4.634160849469*
     x19**2 + 31.478262635483*x20**2 + 34.016843490037*x21**2 + 1.153148892739*
     x19*x20 + 1.168601192983*x19*x21 - 32.056936006397*x20*x21 + 
     3.405095041238*x19 - 54.472915571467*x20 + 9.56987912824*x21) + x23
      =E= 44.230616625681;

e5.. -(3.334445194766*x19**3 - 2.265666208775*x20**3 - 20.256566414583*x21**3
      + 0.413782262402*x19**2*x20 - 3.523622273943*x20**2*x19 - 0.285910055687*
     x19**2*x21 - 10.110726634622*x21**2*x19 + 1.95072196814*x20**2*x21 + 
     10.308512463418*x21**2*x20 + 5.808426325827*x19*x20*x21 - 6.932398033967*
     x19**2 + 15.80019426934*x20**2 + 39.197963873266*x21**2 + 7.900706395772*
     x19*x20 + 6.58186092156*x19*x21 - 30.119438887106*x20*x21 - 6.733798415788
     *x19 - 26.385308892431*x20 - 4.098268423019*x21) + x24 =E= 32.102172356117
     ;

e6.. -(-0.194075741585*x19**2 - 0.004843420334*x20**2 + 0.04736686635*x21**2 + 
     9.4029979e-5*x19*x20 + 0.011329651793*x19*x21 - 0.001017352942*x20*x21 + 
     0.382275988592*x19 + 0.019484588535*x20 - 0.077357069039*x21) + x25
      =E= 0.140278656706;

e7..    x23 =L= 11;

e8..    x24 =L= 11;

e9..    x25 =G= 0.32;

e10.. -21.6*x39*x40*x45 + x44 =E= 0;

e11.. -(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) + x45 =E= 4.960068215723;

e12.. -(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) + x46
       =E= 57.679680208231;

e13.. -(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;

e14.. -(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;

e15.. -(-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;

e16..    x41 =L= 11;

e17..    x42 =L= 11;

e18..    x43 =G= 0.32;

e19.. exp(-0.029595*x26)*(33.7894914681534 + x26) + x33 =E= 33.7894914681534;

e20.. exp(-0.029595*x26) + x34 =E= 1;

e21.. -0.134723681728774*(0.010073140669*x19**2 + 0.011394190823*x20**2 + 
      0.052910213683*x21**2 + 0.000159410872*x19*x20 + 0.008036404292*x19*x21
       - 0.003423392047*x20*x21 + 0.097124049148*x19 + 0.03829180344*x20 + 
      0.370440556286*x21) + x31 =E= 0.29587368369345;

e22.. -0.134723681728774*(0.46598008632*x19**2 - 0.00797004615*x20**2 - 
      0.01779288613*x21**2 - 0.01429434551*x19*x20 - 0.03832188467*x19*x21 + 
      0.00970510229*x20*x21 - 0.88981702163*x19 + 0.07730602595*x20 + 
      0.39988032723*x21) + x32 =E= 0.194162178290626;

e23.. -(2715.7894736842/x27 + 5187*x31 - 5187*x32)*x26/(4320*x21 - 5187*x32)
       + x30 =E= 0;

e24.. exp(-0.029595*x30)*(33.7894914681534 + x30) + x35 =E= 33.7894914681534;

e25.. exp(-0.029595*x30) + x36 =E= 1;

e26.. exp(-0.029595*x44)*(33.7894914681534 + x44) + x51 =E= 33.7894914681534;

e27.. exp(-0.029595*x44) + x52 =E= 1;

e28.. -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) + x49 =E= 0.29587368369345;

e29.. -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) + x50 =E= 0.194162178290626;

e30.. -(2715.7894736842/x45 + 5187*x49 - 5187*x50)*x44/(4320*x39 - 5187*x50)
       + x48 =E= 0;

e31.. exp(-0.029595*x48)*(33.7894914681534 + x48) + x53 =E= 33.7894914681534;

e32.. exp(-0.029595*x48) + x54 =E= 1;

e33..    b1 + b2 + b3 =E= 1;

e34.. b1*x26 =L= 0;

e35.. b2*x26 =G= 0;

e36.. b2*(x26 - x55) =L= 0;

e37.. b3*(x26 - x55) =G= 0;

e38..    b4 + b5 + b6 =E= 1;

e39.. b4*x30 =L= 0;

e40.. b5*x30 =G= 0;

e41.. b5*(x30 - x55) =L= 0;

e42.. b6*(x30 - x55) =G= 0;

e43..    b3 + b5 =L= 1;

e44.. b4*(-1 + b1) =G= 0;

e45..    b7 + b8 + b9 =E= 1;

e46.. b7*(x44 - x55) =L= 0;

e47.. b8*(x44 - x55) =G= 0;

e48.. b8*(-200 + x44) =L= 0;

e49.. b9*(-200 + x44) =G= 0;

e50..    b10 + b11 + b12 =E= 1;

e51.. b10*(x48 - x55) =L= 0;

e52.. b11*(x48 - x55) =G= 0;

e53.. b11*(-200 + x48) =L= 0;

e54.. b12*(-200 + x48) =G= 0;

e55..    b9 + b11 =L= 1;

e56.. b10*(-1 + b7) =G= 0;

e57.. -(0.412152560083595*b15*x56 + 0.247360857459789*b14*x56 + ((11.34*x56/x28
       + (0.854659090909091/x27 - 11.34/x28)*x26*x57)*b1 + 0.0566666666666667*
      x56 + (0.854659090909091*x33/x27 + (11.34*x56 - 11.34*x33)/x28 + (
      0.854659090909091/x27 - 11.34/x28)*x26*(x57 - x34))*b2 + 
      0.854659090909091*x56/x27*b3 + 0.01728*b4*x21*x56 + b1*b5*(0.6*(0.03458*
      x32*x35 + (0.0181052631578947/x27 + 0.03458*x31 - 0.03458*x32)*x26*x36)
       + 0.01728*x21*(x56 - x35)) + b2*b5*(0.6*((0.0181052631578947/x27 + 
      0.03458*x31)*x33 + 0.03458*x32*(x35 - x33) + (0.0181052631578947/x27 + 
      0.03458*x31 - 0.03458*x32)*x26*(x36 - x34)) + 0.01728*x21*(x56 - x35)) + 
      0.6*b1*b6*(0.03458*x32*x56 + (0.0181052631578947/x27 + 0.03458*x31 - 
      0.03458*x32)*x26*x57) + 0.6*b2*b6*((0.0181052631578947/x27 + 0.03458*x31)
      *x33 + 0.03458*x32*(x56 - x33) + (0.0181052631578947/x27 + 0.03458*x31 - 
      0.03458*x32)*x26*(x57 - x34)) + 0.6*b3*b6*(0.0181052631578947/x27 + 
      0.03458*x31)*x56)*b13) + x29 =E= 0;

e58..    b13 + b14 + b15 =E= 1;

e59.. -(b18*(13.6674288800091 - 0.412152560083595*x56) + b17*(8.20275610163388
       - 0.247360857459789*x56) + (1.87912853526074 + ((376.046780997472 - 
      11.34*x56)/x46 + (0.854659090909091/x45 - 11.34/x46)*x44*(
      0.997312113279821 - x57))*b7 - 0.0566666666666667*x56 + ((
      0.854659090909091*x51 - 0.854659090909091*x56)/x45 + (376.046780997472 - 
      11.34*x51)/x46 + (0.854659090909091/x45 - 11.34/x46)*x44*(
      0.997312113279821 - x52))*b8 + (28.341428570246 - 0.854659090909091*x56)/
      x45*b9 + 0.01728*b10*x39*(33.1610917987189 - x56) + b7*b11*(0.6*(0.03458*
      x50*(x53 - x56) + (0.0181052631578947/x45 + 0.03458*x49 - 0.03458*x50)*
      x44*(x54 - x57)) + 0.01728*x39*(33.1610917987189 - x53)) + b8*b11*(0.6*((
      0.0181052631578947/x45 + 0.03458*x49)*(x51 - x56) + 0.03458*x50*(x53 - 
      x51) + (0.0181052631578947/x45 + 0.03458*x49 - 0.03458*x50)*x44*(x54 - 
      x52)) + 0.01728*x39*(33.1610917987189 - x53)) + 0.6*b7*b12*(0.03458*x50*(
      33.1610917987189 - x56) + (0.0181052631578947/x45 + 0.03458*x49 - 0.03458
      *x50)*x44*(0.997312113279821 - x57)) + 0.6*b8*b12*((0.0181052631578947/
      x45 + 0.03458*x49)*(x51 - x56) + 0.03458*x50*(33.1610917987189 - x51) + (
      0.0181052631578947/x45 + 0.03458*x49 - 0.03458*x50)*x44*(
      0.997312113279821 - x52)) + 0.6*b9*b12*(0.0181052631578947/x45 + 0.03458*
      x49)*(33.1610917987189 - x56))*b16) + x47 =E= 0;

e60..    b16 + b17 + b18 =E= 1;

e61..  - x29 - x47 + objvar =E= 0;

e62.. exp(-0.029595*x55)*(33.7894914681534 + x55) + x56 =E= 33.7894914681534;

e63.. exp(-0.029595*x55) + x57 =E= 1;

* set non-default bounds
x19.lo = 0.526315789473684; x19.up = 1.05263157894737;
x20.lo = 0.961538461538462; x20.up = 2.11538461538462;
x21.lo = 0.2; x21.up = 1;
x22.up = 0.8;
x23.lo = 6; x23.up = 13;
x24.lo = 6; x24.up = 13;
x25.lo = 0.26; x25.up = 0.35;
x26.up = 90;
x27.lo = 4.9; x27.up = 5.5;
x28.lo = 55; x28.up = 63;
x30.up = 200;
x31.lo = 0.296392099803303; x31.up = 0.404171045186323;
x32.lo = 0.134723681728774; x32.up = 0.229030258938916;
x33.up = 26;
x34.up = 1;
x35.up = 34.1;
x36.up = 1;
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.up = 90;
x45.lo = 4.9; x45.up = 5.5;
x46.lo = 55; x46.up = 63;
x48.up = 200;
x49.lo = 0.296392099803303; x49.up = 0.404171045186323;
x50.lo = 0.134723681728774; x50.up = 0.229030258938916;
x51.up = 26;
x52.up = 1;
x53.up = 34.1;
x54.up = 1;
x55.up = 200;
x56.up = 34.1;
x57.up = 1;

* set non-default levels
b2.l = 1;
b5.l = 1;
b7.l = 1;
b11.l = 1;
b13.l = 1;
b16.l = 1;
x19.l = 1;
x20.l = 1;
x21.l = 0.3;
x22.l = 0.8;
x23.l = 13;
x24.l = 10.6604143883993;
x25.l = 0.3273636888081;
x26.l = 27.4760701692312;
x27.l = 5.30016785671899;
x28.l = 58.4294759668997;
x30.l = 82.6048888012009;
x31.l = 0.332831162843986;
x32.l = 0.159266373947579;
x33.l = 6.62084546202556;
x34.l = 0.556542937336767;
x35.l = 23.6919439882642;
x36.l = 0.913247121927004;
x37.l = 0.8;
x39.l = 0.4;
x40.l = 0.8;
x41.l = 13;
x42.l = 12.0499480711157;
x43.l = 0.31546674627608;
x44.l = 36.408786197323;
x45.l = 5.26747485493678;
x46.l = 59.9333303564984;
x48.l = 58.2740173254705;
x49.l = 0.334395741702399;
x50.l = 0.165538447790303;
x51.l = 9.8912291834487;
x52.l = 0.659560560750654;
x53.l = 17.380013231931;
x54.l = 0.821759148100612;
x55.l = 30;
x56.l = 7.53758887227811;
x57.l = 0.588460387570554;

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: 2018-09-14 Git hash: ac5a5314
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