MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance: gastrans

The problem of distributing gas through a network of pipelines is formulated as a cost minimization subject to nonlinear flow-pressure relations, material balances, and pressure bounds. The Belgian gas network is used as an example.
Formats ams gms mod nl osil pip
Primal Bounds
89.08584000 p1 ( gdx sol )
(infeas: 2e-11)
Dual Bounds
89.08584000 (ANTIGONE)
89.08584000 (BARON)
89.08584000 (COUENNE)
89.08584000 (LINDO)
89.08584000 (SCIP)
References de Wolf, Daniel and Smeers, Yves, The Gas Transmission Problem Solved by and Extension of the Simplex Algorithm, Management Science, 46:11, 2000, 1454-1465.
Source GAMS Model Library model gastrans, Wolf & Smeers formulation
Application Gas Transmission
Added to library 01 May 2001
Problem type MBNLP
#Variables 106
#Binary Variables 21
#Integer Variables 0
#Nonlinear Variables 45
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 0
Objective Sense min
Objective type linear
Objective curvature linear
#Nonzeros in Objective 5
#Nonlinear Nonzeros in Objective 0
#Constraints 149
#Linear Constraints 125
#Quadratic Constraints 3
#Polynomial Constraints 21
#Signomial Constraints 0
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions  
Constraints curvature indefinite
#Nonzeros in Jacobian 413
#Nonlinear Nonzeros in Jacobian 45
#Nonzeros in (Upper-Left) Hessian of Lagrangian 66
#Nonzeros in Diagonal of Hessian of Lagrangian 24
#Blocks in Hessian of Lagrangian 24
Minimal blocksize in Hessian of Lagrangian 1
Maximal blocksize in Hessian of Lagrangian 2
Average blocksize in Hessian of Lagrangian 1.875
#Semicontinuities 0
#Nonlinear Semicontinuities 0
#SOS type 1 0
#SOS type 2 0
Infeasibility of initial point 1.847e+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
*        150       63       45       42        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*        107       86       21        0        0        0        0        0
*  FX      5
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        419      374       45        0
*
*  Solve m using MINLP minimizing objvar;


Variables  x1,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,b46,b47,b48,b49,b50,b51,b52,b53
          ,b54,b55,b56,b57,b58,b59,b60,b61,b62,b63,b64,b65,b66,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,x97,x98,x99,x100,x101,x102,x103
          ,x104,x105,x106,objvar;

Positive Variables  x10,x11,x22,x67,x73,x76,x80,x87,x89,x90,x93,x96,x97,x98
          ,x100,x101,x103,x104,x105,x106;

Binary Variables  b46,b47,b48,b49,b50,b51,b52,b53,b54,b55,b56,b57,b58,b59,b60
          ,b61,b62,b63,b64,b65,b66;

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;


e1..  - 2.28*x73 - 2.28*x76 - 1.68*x80 - 1.68*x82 - 2.28*x85 + objvar =E= 0;

e2..  - x17 + x18 - x67 =E= 0;

e3..  - x6 + x7 - x68 =E= 0;

e4..  - x23 + x24 - x69 =E= 0;

e5..  - x10 - x11 + x12 + x13 - x70 =E= 0;

e6..  - x20 - x71 =E= 0;

e7..  - x3 - x4 + x5 - x72 =E= 0;

e8..  - x1 - x2 + x3 + x4 - x73 =E= 0;

e9..  - x7 + x8 - x74 =E= 0;

e10..  - x12 - x13 + x14 + x15 - x75 =E= 0;

e11..    x6 - x76 =E= 0;

e12..  - x19 + x20 - x77 =E= 0;

e13..  - x16 + x17 - x78 =E= 0;

e14..  - x24 - x79 =E= 0;

e15..  - x9 - x18 + x19 - x80 =E= 0;

e16..  - x22 + x23 - x81 =E= 0;

e17..    x10 + x11 - x82 =E= 0;

e18..  - x21 + x22 - x83 =E= 0;

e19..  - x14 - x15 + x16 + x21 - x84 =E= 0;

e20..    x1 + x2 - x85 =E= 0;

e21..  - x5 - x8 + x9 - x86 =E= 0;

e22.. sqr(x1)*x25 + 8.99076279639865*x93 - 8.99076279639865*x105 =E= 0;

e23.. sqr(x2)*x26 + 8.99076279639865*x93 - 8.99076279639865*x105 =E= 0;

e24.. sqr(x3)*x27 + 5.99384186426577*x92 - 5.99384186426577*x93 =E= 0;

e25.. sqr(x4)*x28 + 5.99384186426577*x92 - 5.99384186426577*x93 =E= 0;

e26.. sqr(x5)*x29 - 1.38319427636902*x92 + 1.38319427636902*x106 =E= 0;

e27.. sqr(x6)*x30 + 0.0993769948466698*x88 - 0.0993769948466698*x96 =E= 0;

e28.. sqr(x7)*x31 - 0.147352095807131*x88 + 0.147352095807131*x94 =E= 0;

e29.. sqr(x8)*x32 - 0.224905830442463*x94 + 0.224905830442463*x106 =E= 0;

e30.. sqr(x9)*x33 + 0.653873657919902*x100 - 0.653873657919902*x106 =E= 0;

e31.. sqr(x12)*x34 - 1.79815255927973*x90 + 1.79815255927973*x95 =E= 0;

e32.. sqr(x13)*x35 - 0.0265962529480588*x90 + 0.0265962529480588*x95 =E= 0;

e33.. sqr(x14)*x36 - 1.43852204742378*x95 + 1.43852204742378*x104 =E= 0;

e34.. sqr(x15)*x37 - 0.021277002358447*x95 + 0.021277002358447*x104 =E= 0;

e35.. sqr(x16)*x38 + 0.856263123466538*x98 - 0.856263123466538*x104 =E= 0;

e36.. sqr(x17)*x39 + 0.899076279639865*x87 - 0.899076279639865*x98 =E= 0;

e37.. sqr(x18)*x40 - 7.19261023711892*x87 + 7.19261023711892*x100 =E= 0;

e38.. sqr(x19)*x41 + 3.59630511855946*x97 - 3.59630511855946*x100 =E= 0;

e39.. sqr(x20)*x42 + 1.43852204742378*x91 - 1.43852204742378*x97 =E= 0;

e40.. sqr(x21)*x43 + 0.0509935163731392*x103 - 0.0509935163731392*x104 =E= 0;

e41.. sqr(x23)*x44 + 0.0016882734118691*x89 - 0.0016882734118691*x101 =E= 0;

e42.. sqr(x24)*x45 - 0.0275751323938619*x89 + 0.0275751323938619*x99 =E= 0;

e43.. -sqr(x10) + 7.19261023711892*x90 - 7.19261023711892*x102 =G= 0;

e44.. -sqr(x11) + 0.106385011792235*x90 - 0.106385011792235*x102 =G= 0;

e45.. -sqr(x22) + 0.00636349209089121*x101 - 0.00636349209089121*x103 =G= 0;

e46..    x25 - 2*b46 =E= -1;

e47..    x26 - 2*b47 =E= -1;

e48..    x27 - 2*b48 =E= -1;

e49..    x28 - 2*b49 =E= -1;

e50..    x29 - 2*b50 =E= -1;

e51..    x30 - 2*b51 =E= -1;

e52..    x31 - 2*b52 =E= -1;

e53..    x32 - 2*b53 =E= -1;

e54..    x33 - 2*b54 =E= -1;

e55..    x34 - 2*b55 =E= -1;

e56..    x35 - 2*b56 =E= -1;

e57..    x36 - 2*b57 =E= -1;

e58..    x37 - 2*b58 =E= -1;

e59..    x38 - 2*b59 =E= -1;

e60..    x39 - 2*b60 =E= -1;

e61..    x40 - 2*b61 =E= -1;

e62..    x41 - 2*b62 =E= -1;

e63..    x42 - 2*b63 =E= -1;

e64..    x43 - 2*b64 =E= -1;

e65..    x44 - 2*b65 =E= -1;

e66..    x45 - 2*b66 =E= -1;

e67..  - 5929*b46 - x93 + x105 =G= -5929;

e68..  - 5929*b47 - x93 + x105 =G= -5929;

e69..  - 6400*b48 - x92 + x93 =G= -6400;

e70..  - 6400*b49 - x92 + x93 =G= -6400;

e71..  - 5500*b50 + x92 - x106 =G= -5500;

e72..  - 6400*b51 - x88 + x96 =G= -6400;

e73..  - 5500*b52 + x88 - x94 =G= -5500;

e74..  - 5500*b53 + x94 - x106 =G= -5500;

e75..  - 4382.44*b54 - x100 + x106 =G= -4382.44;

e76..  - 4382.44*b55 + x90 - x95 =G= -4382.44;

e77..  - 4382.44*b56 + x90 - x95 =G= -4382.44;

e78..  - 3482.44*b57 + x95 - x104 =G= -3482.44;

e79..  - 3482.44*b58 + x95 - x104 =G= -3482.44;

e80..  - 4382.44*b59 - x98 + x104 =G= -4382.44;

e81..  - 4382.44*b60 - x87 + x98 =G= -4382.44;

e82..  - 4382.44*b61 + x87 - x100 =G= -4382.44;

e83..  - 4382.44*b62 - x97 + x100 =G= -4382.44;

e84..  - 4382.44*b63 - x91 + x97 =G= -4382.44;

e85..  - 4382.44*b64 - x103 + x104 =G= -4382.44;

e86..  - 4382.44*b65 - x89 + x101 =G= -4382.44;

e87..  - 4382.44*b66 + x89 - x99 =G= -4382.44;

e88..  - 5929*b46 - x93 + x105 =L= 0;

e89..  - 5929*b47 - x93 + x105 =L= 0;

e90..  - 5029*b48 - x92 + x93 =L= 0;

e91..  - 5029*b49 - x92 + x93 =L= 0;

e92..  - 6400*b50 + x92 - x106 =L= 0;

e93..  - 5029*b51 - x88 + x96 =L= 0;

e94..  - 5500*b52 + x88 - x94 =L= 0;

e95..  - 6400*b53 + x94 - x106 =L= 0;

e96..  - 6400*b54 - x100 + x106 =L= 0;

e97..  - 3482.44*b55 + x90 - x95 =L= 0;

e98..  - 3482.44*b56 + x90 - x95 =L= 0;

e99..  - 4382.44*b57 + x95 - x104 =L= 0;

e100..  - 4382.44*b58 + x95 - x104 =L= 0;

e101..  - 4382.44*b59 - x98 + x104 =L= 0;

e102..  - 4382.44*b60 - x87 + x98 =L= 0;

e103..  - 4382.44*b61 + x87 - x100 =L= 0;

e104..  - 4382.44*b62 - x97 + x100 =L= 0;

e105..  - 1882.44*b63 - x91 + x97 =L= 0;

e106..  - 4382.44*b64 - x103 + x104 =L= 0;

e107..  - 3969*b65 - x89 + x101 =L= 0;

e108..  - 3757.44*b66 + x89 - x99 =L= 0;

e109..    x1 - 230.881425454383*b46 =G= -230.881425454383;

e110..    x2 - 230.881425454383*b47 =G= -230.881425454383;

e111..    x3 - 195.858591670881*b48 =G= -195.858591670881;

e112..    x4 - 195.858591670881*b49 =G= -195.858591670881;

e113..    x5 - 87.2213765084548*b50 =G= -87.2213765084548;

e114..    x6 - 25.2192935471771*b51 =G= -25.2192935471771;

e115..    x7 - 28.4681669051455*b52 =G= -28.4681669051455;

e116..    x8 - 35.1707558553061*b53 =G= -35.1707558553061;

e117..    x9 - 53.5309450076729*b54 =G= -53.5309450076729;

e118..    x12 - 88.7710296317997*b55 =G= -88.7710296317997;

e119..    x13 - 10.7961327691767*b56 =G= -10.7961327691767;

e120..    x14 - 70.7782927092091*b57 =G= -70.7782927092091;

e121..    x15 - 8.6078966125965*b58 =G= -8.6078966125965;

e122..    x16 - 61.2578302162646*b59 =G= -61.2578302162646;

e123..    x17 - 62.7705970255575*b60 =G= -62.7705970255575;

e124..    x18 - 177.542059263599*b61 =G= -177.542059263599;

e125..    x19 - 125.541194051115*b62 =G= -125.541194051115;

e126..    x20 - 79.3992226757409*b63 =G= -79.3992226757409;

e127..    x21 - 14.9491145521834*b64 =G= -14.9491145521834;

e128..    x23 - 2.72006561154535*b65 =G= -2.72006561154535;

e129..    x24 - 10.9930142912741*b66 =G= -10.9930142912741;

e130..    x1 - 230.881425454383*b46 =L= 0;

e131..    x2 - 230.881425454383*b47 =L= 0;

e132..    x3 - 173.61748395652*b48 =L= 0;

e133..    x4 - 173.61748395652*b49 =L= 0;

e134..    x5 - 94.0874240733678*b50 =L= 0;

e135..    x6 - 22.3554670513479*b51 =L= 0;

e136..    x7 - 28.4681669051455*b52 =L= 0;

e137..    x8 - 37.939390016601*b53 =L= 0;

e138..    x9 - 64.6899637554959*b54 =L= 0;

e139..    x12 - 79.1325369145847*b55 =L= 0;

e140..    x13 - 9.62392098452798*b56 =L= 0;

e141..    x14 - 79.3992226757409*b57 =L= 0;

e142..    x15 - 9.65635470639685*b58 =L= 0;

e143..    x16 - 61.2578302162646*b59 =L= 0;

e144..    x17 - 62.7705970255575*b60 =L= 0;

e145..    x18 - 177.542059263599*b61 =L= 0;

e146..    x19 - 125.541194051115*b62 =L= 0;

e147..    x20 - 52.0377886055166*b63 =L= 0;

e148..    x21 - 14.9491145521834*b64 =L= 0;

e149..    x23 - 2.58858207745253*b65 =L= 0;

e150..    x24 - 10.1789933422708*b66 =L= 0;

* set non-default bounds
x67.up = 1.2;
x68.up = -4.034;
x69.up = -0.222;
x70.fx = 0;
x71.up = -15.616;
x72.up = -3.918;
x73.up = 8.4;
x74.up = -5.256;
x75.up = -6.385;
x76.up = 4.8;
x77.up = -6.848;
x78.up = -2.12;
x79.up = -1.919;
x80.up = 0.96;
x81.fx = 0;
x82.lo = 20.344; x82.up = 22.012;
x83.fx = 0;
x84.fx = 0;
x85.lo = 8.87; x85.up = 11.594;
x86.fx = 0;
x87.up = 4382.44;
x88.lo = 900; x88.up = 6400;
x89.up = 4382.44;
x90.up = 4382.44;
x91.lo = 2500; x91.up = 4382.44;
x92.lo = 900; x92.up = 6400;
x93.up = 5929;
x94.lo = 900; x94.up = 6400;
x95.lo = 900; x95.up = 4382.44;
x96.up = 5929;
x97.up = 4382.44;
x98.up = 4382.44;
x99.lo = 625; x99.up = 4382.44;
x100.up = 4382.44;
x101.up = 3969;
x102.lo = 2500; x102.up = 4382.44;
x103.up = 4382.44;
x104.up = 4382.44;
x105.up = 5929;
x106.up = 6400;

* set non-default levels
x1.l = 5.45594117499038;
x2.l = 3.49005882500962;
x3.l = 8.46373378118172;
x4.l = 8.88226621881828;
x5.l = 13.428;
x6.l = 4.8;
x7.l = 0.766;
x8.l = -4.49;
x9.l = 8.938;
x10.l = 22.012;
x12.l = 18.1380867287228;
x13.l = 3.87391327127718;
x14.l = 12.1798336524591;
x15.l = 3.44716634754093;
x16.l = 13.486;
x17.l = 11.366;
x18.l = 12.566;
x19.l = 22.464;
x20.l = 15.616;
x21.l = 2.141;
x22.l = 2.141;
x23.l = 2.141;
x24.l = 1.919;
x27.l = -75.3049979497412;
x28.l = -68.3754533453309;
x29.l = 6.90403568495296;
x32.l = 10.0403890555214;
x34.l = 19.0338757369553;
x35.l = 6.17166731394037;
x36.l = 8.7272279190673;
x37.l = 1.6114349200345;
x42.l = -14.7474499350948;
x44.l = 1.46180871006652;
x45.l = -4.68001962388774;
x85.l = 8.946;
x96.l = 900;
objvar.l = 89.0858399999993;

* 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;
e13.m = 1;
e14.m = 1;
e15.m = 1;
e16.m = 1;
e17.m = 1;
e18.m = 1;
e19.m = 1;
e20.m = 1;
e21.m = 1;
e22.m = 1;
e23.m = 1;
e24.m = 1;
e25.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;
x1.m = 1;
x11.m = 1;
x12.m = 1;
x14.m = 1;
x28.m = 1;
x30.m = 1;
x67.m = 1;
x68.m = 1;
x69.m = 1;
x70.m = 1;
x71.m = 1;
x72.m = 1;
x73.m = 1;
x74.m = 1;
x75.m = 1;
x76.m = 1;
x77.m = 1;
x78.m = 1;
x79.m = 1;
x80.m = 1;
x81.m = 1;
x82.m = 1;
x83.m = 1;
x84.m = 1;
x86.m = 1;
x87.m = 1;
x88.m = 1;
x89.m = 1;
x90.m = 1;
x91.m = 1;
x92.m = 1;
x93.m = 1;
x94.m = 1;
x95.m = 1;
x97.m = 1;
x98.m = 1;
x99.m = 1;
x100.m = 1;
x101.m = 1;
x102.m = 1;
x103.m = 1;
x104.m = 1;
x105.m = 1;
x106.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: 2018-09-14 Git hash: ac5a5314
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