MINLPLib
A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Instance nous1
| Formatsⓘ | ams gms lp mod nl osil pip py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | 1.56707200 (ANTIGONE) 1.56707200 (BARON) 1.32726524 (COUENNE) 1.56707200 (GUROBI) 1.56707180 (LINDO) 1.56707194 (SCIP) -0.94614200 (SHOT) |
| Referencesⓘ | Aggarwal, Avanish and Floudas, C A, Synthesis of General Distillation Sequences - Nonsharp Separations, Computers and Chemical Engineering, 14:6, 1990, 631-653. |
| Sourceⓘ | MINOPT Model Library model nous1.dat |
| Applicationⓘ | Synthesis of General Distillation Sequences |
| Added to libraryⓘ | 01 May 2001 |
| Problem typeⓘ | MBQCQP |
| #Variablesⓘ | 50 |
| #Binary Variablesⓘ | 2 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 42 |
| #Nonlinear Binary Variablesⓘ | 0 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | quadratic |
| Objective curvatureⓘ | indefinite |
| #Nonzeros in Objectiveⓘ | 12 |
| #Nonlinear Nonzeros in Objectiveⓘ | 10 |
| #Constraintsⓘ | 43 |
| #Linear Constraintsⓘ | 15 |
| #Quadratic Constraintsⓘ | 28 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 0 |
| Operands in Gen. Nonlin. Functionsⓘ | |
| Constraints curvatureⓘ | indefinite |
| #Nonzeros in Jacobianⓘ | 184 |
| #Nonlinear Nonzeros in Jacobianⓘ | 112 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 112 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 0 |
| #Blocks in Hessian of Lagrangianⓘ | 6 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 6 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 8 |
| Average blocksize in Hessian of Lagrangianⓘ | 7.0 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 5.7190e-04 |
| Maximal coefficientⓘ | 3.0000e+02 |
| Infeasibility of initial pointⓘ | 0.2857 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 44 42 0 2 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 51 49 2 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 197 75 122 0
*
* Solve m using MINLP minimizing objvar;
Variables objvar,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,x17,x18
,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,b50,b51;
Positive Variables x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,x17
,x18,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;
Binary Variables b50,b51;
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;
e1.. -((-0.0139904 - 0.0005719*x28 + 0.0042656*x29 + 0.0093514*x46 + 0.0077308*
x47)*x4 + (-0.0661588 + 0.0016371*x31 + 0.0288996*x32 + 0.0338147*x48 +
0.0373349*x49)*x5) + objvar - 0.23947*b50 - 0.75835*b51 =E= 0;
e2.. x2 + x3 + x20 + x21 =E= 300;
e3.. x6 - x12 - x13 =E= 0;
e4.. x7 - x11 - x14 - x15 =E= 0;
e5.. x8 - x10 - x16 - x17 =E= 0;
e6.. x9 - x18 - x19 =E= 0;
e7.. -x10*x40 - 0.333333333333333*x2 + x22 =E= 0;
e8.. -x10*x41 - 0.333333333333333*x2 + x23 =E= 0;
e9.. -x10*x42 - 0.333333333333333*x2 + x24 =E= 0;
e10.. -x11*x37 - 0.333333333333333*x3 + x25 =E= 0;
e11.. -x11*x38 - 0.333333333333333*x3 + x26 =E= 0;
e12.. -x11*x39 - 0.333333333333333*x3 + x27 =E= 0;
e13.. -(x6*x34 + x7*x37) + x22 =E= 0;
e14.. -(x6*x35 + x7*x38) + x23 =E= 0;
e15.. -(x6*x36 + x7*x39) + x24 =E= 0;
e16.. -(x8*x40 + x9*x43) + x25 =E= 0;
e17.. -(x8*x41 + x9*x44) + x26 =E= 0;
e18.. -(x8*x42 + x9*x45) + x27 =E= 0;
e19.. x22*x46 - x6*x34 =E= 0;
e20.. x23*x47 - x7*x38 =E= 0;
e21.. x26*x48 - x8*x41 =E= 0;
e22.. x27*x49 - x9*x45 =E= 0;
e23.. x12*x34 + x14*x37 + x16*x40 + x18*x43 + 0.333333333333333*x20 =E= 30;
e24.. x12*x35 + x14*x38 + x16*x41 + x18*x44 + 0.333333333333333*x20 =E= 50;
e25.. x12*x36 + x14*x39 + x16*x42 + x18*x45 + 0.333333333333333*x20 =E= 30;
e26.. x13*x34 + x15*x37 + x17*x40 + x19*x43 + 0.333333333333333*x21 =E= 70;
e27.. x13*x35 + x15*x38 + x17*x41 + x19*x44 + 0.333333333333333*x21 =E= 50;
e28.. x13*x36 + x15*x39 + x17*x42 + x19*x45 + 0.333333333333333*x21 =E= 70;
e29.. x4*x28 - x22 =E= 0;
e30.. x4*x29 - x23 =E= 0;
e31.. x4*x30 - x24 =E= 0;
e32.. x5*x31 - x25 =E= 0;
e33.. x5*x32 - x26 =E= 0;
e34.. x5*x33 - x27 =E= 0;
e35.. x34 + x35 + x36 =E= 1;
e36.. x37 + x38 + x39 =E= 1;
e37.. x40 + x41 + x42 =E= 1;
e38.. x43 + x44 + x45 =E= 1;
e39.. x28 + x29 + x30 =E= 1;
e40.. x31 + x32 + x33 =E= 1;
e41.. x36 =E= 0;
e42.. x43 =E= 0;
e43.. x4 - 300*b50 =L= 0;
e44.. x5 - 300*b51 =L= 0;
* set non-default bounds
x2.up = 300;
x3.up = 300;
x4.up = 300;
x5.up = 300;
x6.up = 300;
x7.up = 300;
x8.up = 300;
x9.up = 300;
x10.up = 300;
x11.up = 300;
x12.up = 300;
x13.up = 300;
x14.up = 300;
x15.up = 300;
x16.up = 300;
x17.up = 300;
x18.up = 300;
x19.up = 300;
x22.up = 100;
x23.up = 100;
x24.up = 100;
x25.up = 100;
x26.up = 100;
x27.up = 100;
x28.up = 1;
x29.up = 1;
x30.up = 1;
x31.up = 1;
x32.up = 1;
x33.up = 1;
x34.up = 1;
x35.up = 1;
x36.up = 1;
x37.up = 1;
x38.up = 1;
x39.up = 1;
x40.up = 1;
x41.up = 1;
x42.up = 1;
x43.up = 1;
x44.up = 1;
x45.up = 1;
x46.lo = 0.85; x46.up = 1;
x47.lo = 0.85; x47.up = 1;
x48.lo = 0.85; x48.up = 1;
x49.lo = 0.85; x49.up = 1;
* set non-default levels
objvar.l = 0.831536761904758;
x3.l = 85.7142857142855;
x4.l = 57.1428571428572;
x5.l = 85.7142857142855;
x6.l = 24.2857142857143;
x7.l = 32.8571428571428;
x8.l = 57.142857142857;
x9.l = 28.5714285714285;
x10.l = 57.1428571428572;
x13.l = 24.2857142857143;
x14.l = 32.8571428571428;
x19.l = 28.5714285714285;
x20.l = 77.1428571428574;
x21.l = 137.142857142857;
x22.l = 28.5714285714286;
x23.l = 24.2857142857143;
x24.l = 4.28571428571429;
x25.l = 28.5714285714285;
x26.l = 28.5714285714285;
x27.l = 28.5714285714285;
x28.l = 0.5;
x29.l = 0.425;
x30.l = 0.075;
x31.l = 0.333333333333333;
x32.l = 0.333333333333333;
x33.l = 0.333333333333333;
x34.l = 1;
x37.l = 0.130434782608696;
x38.l = 0.739130434782609;
x39.l = 0.130434782608694;
x40.l = 0.5;
x41.l = 0.425;
x42.l = 0.075;
x44.l = 0.150000000000001;
x45.l = 0.85;
x47.l = 1;
b50.l = 0.190476190476191;
b51.l = 0.285714285714285;
* set non-default marginals
e1.m = 1;
e2.m = 1;
e3.m = 1;
e4.m = 1;
e5.m = 1;
e6.m = 1;
e7.m = 1;
e8.m = 1;
e9.m = 1;
e10.m = 1;
e11.m = 1;
e12.m = 1;
e14.m = 1;
e15.m = 1;
e16.m = 1;
e18.m = 1;
e19.m = 1;
e20.m = 1;
e21.m = 1;
e22.m = 1;
e23.m = 1;
e24.m = 1;
e26.m = 1;
e27.m = 1;
e28.m = 1;
e29.m = 1;
e30.m = 1;
e31.m = 1;
e32.m = 1;
e33.m = 1;
e34.m = 1;
e35.m = 1;
e36.m = 1;
e37.m = 1;
e38.m = 1;
e39.m = 1;
e40.m = 1;
e41.m = 1;
e42.m = 1;
e43.m = 1;
e44.m = 1;
x2.m = 1;
x11.m = 1;
x12.m = 1;
x15.m = 1;
x17.m = 1;
x18.m = 1;
x34.m = 1;
x46.m = 1;
x48.m = 1;
x49.m = 1;
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: 2024-04-02 Git hash: 1dd5fb9b