MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

Home // Instances // Documentation // Download // Statistics


Instance: batch0812_nc

Nonconvex variant of batch0812
Formats ams gms mod nl osil
Primal Bounds
2687026.78400000 p1 ( gdx sol )
(infeas: 9e-13)
Dual Bounds
2687024.52500000 (ANTIGONE)
2687026.77400000 (BARON)
2687025.95500000 (COUENNE)
2687026.78400000 (LINDO)
2687026.68200000 (SCIP)
References You, Fengqi and Grossmann, I E, Mixed-Integer Nonlinear Programming Models for the Optimal Design of Multi-product Batch Plant, 2009.
Source nonconvex2.gms from minlp.org model 48
Application Multi-Product Batch Plant Design
Added to library 24 Sep 2013
Problem type MBNLP
#Variables 76
#Binary Variables 36
#Integer Variables 0
#Nonlinear Variables 40
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 0
Objective Sense min
Objective type signomial
Objective curvature indefinite
#Nonzeros in Objective 24
#Nonlinear Nonzeros in Objective 24
#Constraints 205
#Linear Constraints 108
#Quadratic Constraints 96
#Polynomial Constraints 0
#Signomial Constraints 1
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions  
Constraints curvature indefinite
#Nonzeros in Jacobian 448
#Nonlinear Nonzeros in Jacobian 208
#Nonzeros in (Upper-Left) Hessian of Lagrangian 252
#Nonzeros in Diagonal of Hessian of Lagrangian 20
#Blocks in Hessian of Lagrangian 1
Minimal blocksize in Hessian of Lagrangian 40
Maximal blocksize in Hessian of Lagrangian 40
Average blocksize in Hessian of Lagrangian 40.0
#Semicontinuities 0
#Nonlinear Semicontinuities 0
#SOS type 1 0
#SOS type 2 0
Infeasibility of initial point 4.2e+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
*        206       13      192        1        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         77       41       36        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        473      241      232        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,b41,b42,b43,b44,b45,b46,b47,b48,b49,b50,b51,b52,b53
          ,b54,b55,b56,b57,b58,b59,b60,b61,b62,b63,b64,b65,b66,b67,b68,b69,b70
          ,b71,b72,b73,b74,b75,b76,objvar;

Binary Variables  b41,b42,b43,b44,b45,b46,b47,b48,b49,b50,b51,b52,b53,b54,b55
          ,b56,b57,b58,b59,b60,b61,b62,b63,b64,b65,b66,b67,b68,b69,b70,b71,b72
          ,b73,b74,b75,b76;

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,e151,e152,e153,e154,e155
          ,e156,e157,e158,e159,e160,e161,e162,e163,e164,e165,e166,e167,e168
          ,e169,e170,e171,e172,e173,e174,e175,e176,e177,e178,e179,e180,e181
          ,e182,e183,e184,e185,e186,e187,e188,e189,e190,e191,e192,e193,e194
          ,e195,e196,e197,e198,e199,e200,e201,e202,e203,e204,e205,e206;


e1.. -(250*x13**0.6*x1 + 550*x14**0.6*x2 + 250*x15**0.6*x3 + 1000*x16**0.6*x4
      + 300*x17**0.6*x5 + 800*x18**0.6*x6 + 200*x19**0.6*x7 + 1200*x20**0.6*x8
      + 250*x21**0.6*x9 + 250*x22**0.6*x10 + 450*x23**0.6*x11 + 700*x24**0.6*
     x12) + objvar =E= 0;

e2..    x13 - 7.9*x25 =G= 0;

e3..    x14 - 2*x25 =G= 0;

e4..    x15 - 5.2*x25 =G= 0;

e5..    x16 - 4.9*x25 =G= 0;

e6..    x17 - 6.1*x25 =G= 0;

e7..    x18 - 4.2*x25 =G= 0;

e8..    x19 - 2.8*x25 =G= 0;

e9..    x20 - 3.3*x25 =G= 0;

e10..    x21 - 4.1*x25 =G= 0;

e11..    x22 - 3.8*x25 =G= 0;

e12..    x23 - 2.8*x25 =G= 0;

e13..    x24 - 3.9*x25 =G= 0;

e14..    x13 - 0.7*x26 =G= 0;

e15..    x14 - 0.8*x26 =G= 0;

e16..    x15 - 0.9*x26 =G= 0;

e17..    x16 - 3.4*x26 =G= 0;

e18..    x17 - 2.1*x26 =G= 0;

e19..    x18 - 2.5*x26 =G= 0;

e20..    x19 - 3.3*x26 =G= 0;

e21..    x20 - 3*x26 =G= 0;

e22..    x21 - 2.7*x26 =G= 0;

e23..    x22 - 2.4*x26 =G= 0;

e24..    x23 - 2.2*x26 =G= 0;

e25..    x24 - 3.1*x26 =G= 0;

e26..    x13 - 0.7*x27 =G= 0;

e27..    x14 - 2.6*x27 =G= 0;

e28..    x15 - 1.6*x27 =G= 0;

e29..    x16 - 3.6*x27 =G= 0;

e30..    x17 - 3.2*x27 =G= 0;

e31..    x18 - 2.9*x27 =G= 0;

e32..    x19 - 2.6*x27 =G= 0;

e33..    x20 - 2.2*x27 =G= 0;

e34..    x21 - 4.6*x27 =G= 0;

e35..    x22 - 4.3*x27 =G= 0;

e36..    x23 - 4.2*x27 =G= 0;

e37..    x24 - 4.6*x27 =G= 0;

e38..    x13 - 4.7*x28 =G= 0;

e39..    x14 - 2.3*x28 =G= 0;

e40..    x15 - 1.6*x28 =G= 0;

e41..    x16 - 2.7*x28 =G= 0;

e42..    x17 - 1.2*x28 =G= 0;

e43..    x18 - 2.5*x28 =G= 0;

e44..    x19 - 1.5*x28 =G= 0;

e45..    x20 - 1.5*x28 =G= 0;

e46..    x21 - 1.3*x28 =G= 0;

e47..    x22 - 1.7*x28 =G= 0;

e48..    x23 - 1.5*x28 =G= 0;

e49..    x24 - 1.8*x28 =G= 0;

e50..    x13 - 1.2*x29 =G= 0;

e51..    x14 - 3.6*x29 =G= 0;

e52..    x15 - 2.4*x29 =G= 0;

e53..    x16 - 4.5*x29 =G= 0;

e54..    x17 - 1.6*x29 =G= 0;

e55..    x18 - 2.1*x29 =G= 0;

e56..    x19 - 2.4*x29 =G= 0;

e57..    x20 - 2.7*x29 =G= 0;

e58..    x21 - 2.8*x29 =G= 0;

e59..    x22 - 3.5*x29 =G= 0;

e60..    x23 - 3.5*x29 =G= 0;

e61..    x24 - 4.3*x29 =G= 0;

e62..    x13 - 0.7*x30 =G= 0;

e63..    x14 - 2.4*x30 =G= 0;

e64..    x15 - 3.1*x30 =G= 0;

e65..    x16 - 2.2*x30 =G= 0;

e66..    x17 - 3.7*x30 =G= 0;

e67..    x18 - 4.8*x30 =G= 0;

e68..    x19 - 4.5*x30 =G= 0;

e69..    x20 - 5.2*x30 =G= 0;

e70..    x21 - 6.4*x30 =G= 0;

e71..    x22 - 5.7*x30 =G= 0;

e72..    x23 - 6.4*x30 =G= 0;

e73..    x24 - 6.8*x30 =G= 0;

e74..    x13 - 2.3*x31 =G= 0;

e75..    x14 - 4.7*x31 =G= 0;

e76..    x15 - 5.2*x31 =G= 0;

e77..    x16 - 3.5*x31 =G= 0;

e78..    x17 - 2.9*x31 =G= 0;

e79..    x18 - 3.6*x31 =G= 0;

e80..    x19 - 3.3*x31 =G= 0;

e81..    x20 - 3.2*x31 =G= 0;

e82..    x21 - 4.1*x31 =G= 0;

e83..    x22 - 3.7*x31 =G= 0;

e84..    x23 - 3.4*x31 =G= 0;

e85..    x24 - 3.7*x31 =G= 0;

e86..    x13 - 0.4*x32 =G= 0;

e87..    x14 - 0.9*x32 =G= 0;

e88..    x15 - 1.1*x32 =G= 0;

e89..    x16 - 1.4*x32 =G= 0;

e90..    x17 - 1.6*x32 =G= 0;

e91..    x18 - 2.2*x32 =G= 0;

e92..    x19 - 2*x32 =G= 0;

e93..    x20 - 1.8*x32 =G= 0;

e94..    x21 - 1.8*x32 =G= 0;

e95..    x22 - 1.6*x32 =G= 0;

e96..    x23 - 1.8*x32 =G= 0;

e97..    x24 - 2*x32 =G= 0;

e98.. x1*x33 =G= 6.4;

e99.. x2*x33 =G= 4.7;

e100.. x3*x33 =G= 8.3;

e101.. x4*x33 =G= 3.9;

e102.. x5*x33 =G= 2.1;

e103.. x6*x33 =G= 1.2;

e104.. x7*x33 =G= 0.8;

e105.. x8*x33 =G= 2.2;

e106.. x9*x33 =G= 1.2;

e107.. x10*x33 =G= 2.5;

e108.. x11*x33 =G= 3.4;

e109.. x12*x33 =G= 3.8;

e110.. x1*x34 =G= 6.8;

e111.. x2*x34 =G= 6.4;

e112.. x3*x34 =G= 6.5;

e113.. x4*x34 =G= 4.4;

e114.. x5*x34 =G= 2.3;

e115.. x6*x34 =G= 3.2;

e116.. x7*x34 =G= 0.4;

e117.. x8*x34 =G= 0.2;

e118.. x9*x34 =G= 0.5;

e119.. x10*x34 =G= 3.3;

e120.. x11*x34 =G= 0.6;

e121.. x12*x34 =G= 1.2;

e122.. x1*x35 =G= 1;

e123.. x2*x35 =G= 6.3;

e124.. x3*x35 =G= 5.4;

e125.. x4*x35 =G= 11.9;

e126.. x5*x35 =G= 5.7;

e127.. x6*x35 =G= 6.2;

e128.. x7*x35 =G= 1.1;

e129.. x8*x35 =G= 0.6;

e130.. x9*x35 =G= 1.2;

e131.. x10*x35 =G= 4.3;

e132.. x11*x35 =G= 2.8;

e133.. x12*x35 =G= 5.2;

e134.. x1*x36 =G= 3.2;

e135.. x2*x36 =G= 3;

e136.. x3*x36 =G= 3.5;

e137.. x4*x36 =G= 3.3;

e138.. x5*x36 =G= 2.8;

e139.. x6*x36 =G= 3.4;

e140.. x7*x36 =G= 1.7;

e141.. x8*x36 =G= 0.9;

e142.. x9*x36 =G= 2.2;

e143.. x10*x36 =G= 2.15;

e144.. x11*x36 =G= 1.8;

e145.. x12*x36 =G= 2.5;

e146.. x1*x37 =G= 2.1;

e147.. x2*x37 =G= 2.5;

e148.. x3*x37 =G= 4.2;

e149.. x4*x37 =G= 3.6;

e150.. x5*x37 =G= 5.7;

e151.. x6*x37 =G= 2.2;

e152.. x7*x37 =G= 1.2;

e153.. x8*x37 =G= 0.6;

e154.. x9*x37 =G= 1.15;

e155.. x10*x37 =G= 3.1;

e156.. x11*x37 =G= 4.2;

e157.. x12*x37 =G= 1.6;

e158.. x1*x38 =G= 1.1;

e159.. x2*x38 =G= 0.8;

e160.. x3*x38 =G= 0.4;

e161.. x4*x38 =G= 1.1;

e162.. x5*x38 =G= 1.8;

e163.. x6*x38 =G= 2.5;

e164.. x7*x38 =G= 0.5;

e165.. x8*x38 =G= 1.3;

e166.. x9*x38 =G= 1.4;

e167.. x10*x38 =G= 4.25;

e168.. x11*x38 =G= 2.7;

e169.. x12*x38 =G= 0.9;

e170.. x1*x39 =G= 4.2;

e171.. x2*x39 =G= 4;

e172.. x3*x39 =G= 2.2;

e173.. x4*x39 =G= 0.5;

e174.. x5*x39 =G= 3.4;

e175.. x6*x39 =G= 2.2;

e176.. x7*x39 =G= 1.4;

e177.. x8*x39 =G= 0.9;

e178.. x9*x39 =G= 2.1;

e179.. x10*x39 =G= 4.4;

e180.. x11*x39 =G= 2.2;

e181.. x12*x39 =G= 3.2;

e182.. x1*x40 =G= 2.7;

e183.. x2*x40 =G= 4.3;

e184.. x3*x40 =G= 1.9;

e185.. x4*x40 =G= 2;

e186.. x5*x40 =G= 1.7;

e187.. x6*x40 =G= 0.7;

e188.. x7*x40 =G= 0.3;

e189.. x8*x40 =G= 0.2;

e190.. x9*x40 =G= 1.6;

e191.. x10*x40 =G= 3.5;

e192.. x11*x40 =G= 3.4;

e193.. x12*x40 =G= 2.1;

e194.. 485000*x33/x25 + 297000*x34/x26 + 320000*x35/x27 + 283000*x36/x28 + 
       363000*x37/x29 + 265000*x38/x30 + 288000*x39/x31 + 145000*x40/x32
        =L= 6000;

e195..    x1 - b41 - 2*b53 - 4*b65 =E= 1;

e196..    x2 - b42 - 2*b54 - 4*b66 =E= 1;

e197..    x3 - b43 - 2*b55 - 4*b67 =E= 1;

e198..    x4 - b44 - 2*b56 - 4*b68 =E= 1;

e199..    x5 - b45 - 2*b57 - 4*b69 =E= 1;

e200..    x6 - b46 - 2*b58 - 4*b70 =E= 1;

e201..    x7 - b47 - 2*b59 - 4*b71 =E= 1;

e202..    x8 - b48 - 2*b60 - 4*b72 =E= 1;

e203..    x9 - b49 - 2*b61 - 4*b73 =E= 1;

e204..    x10 - b50 - 2*b62 - 4*b74 =E= 1;

e205..    x11 - b51 - 2*b63 - 4*b75 =E= 1;

e206..    x12 - b52 - 2*b64 - 4*b76 =E= 1;

* set non-default bounds
x1.lo = 1; x1.up = 5;
x2.lo = 1; x2.up = 5;
x3.lo = 1; x3.up = 5;
x4.lo = 1; x4.up = 5;
x5.lo = 1; x5.up = 5;
x6.lo = 1; x6.up = 5;
x7.lo = 1; x7.up = 5;
x8.lo = 1; x8.up = 5;
x9.lo = 1; x9.up = 5;
x10.lo = 1; x10.up = 5;
x11.lo = 1; x11.up = 5;
x12.lo = 1; x12.up = 5;
x13.lo = 300; x13.up = 3000;
x14.lo = 300; x14.up = 3000;
x15.lo = 300; x15.up = 3000;
x16.lo = 300; x16.up = 3000;
x17.lo = 300; x17.up = 3000;
x18.lo = 300; x18.up = 3000;
x19.lo = 300; x19.up = 3000;
x20.lo = 300; x20.up = 3000;
x21.lo = 300; x21.up = 3000;
x22.lo = 300; x22.up = 3000;
x23.lo = 300; x23.up = 3000;
x24.lo = 300; x24.up = 3000;
x25.lo = 134.183333333333; x25.up = 379.746835443038;
x26.lo = 67.32; x26.up = 882.352941176471;
x27.lo = 126.933333333333; x27.up = 652.173913043478;
x28.lo = 33.0166666666667; x28.up = 638.297872340426;
x29.lo = 68.97; x29.up = 666.666666666667;
x30.lo = 37.5416666666667; x30.up = 441.176470588235;
x31.lo = 42.24; x31.up = 576.923076923077;
x32.lo = 20.7833333333333; x32.up = 1363.63636363636;
x33.lo = 1.66; x33.up = 8.3;
x34.lo = 1.36; x34.up = 6.8;
x35.lo = 2.38; x35.up = 11.9;
x36.lo = 0.7; x36.up = 3.5;
x37.lo = 1.14; x37.up = 5.7;
x38.lo = 0.85; x38.up = 4.25;
x39.lo = 0.88; x39.up = 4.4;
x40.lo = 0.86; x40.up = 4.3;

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: 2018-08-19 Git hash: 033934c0
Imprint / Privacy Policy