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A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Removed Instance bchoco05

Formats ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)
0.95189588 p1 ( gdx sol )
(infeas: 9e-10)
0.95190303 p2 ( gdx sol )
(infeas: 2e-09)
Other points (infeas > 1e-08)  
Dual Bounds
0.96288154 (ANTIGONE)
0.98618300 (BARON)
0.99270487 (LINDO)
0.99823128 (SCIP)
1.00000000 (SHOT)
References Chang, YoungJung and Sahinidis, N V, Stabilizing controller design and the Belgian chocolate problem, 2009.
Source bcp5.gms from minlp.org model 57
Application Belgian chocolate problem
Added to library 24 Sep 2013
Removed from library 01 Mar 2022
Removed because Numerically difficult formulation (coefficient of order 1E-10 and 1E7)
Problem type MBNLP
#Variables 90
#Binary Variables 6
#Integer Variables 0
#Nonlinear Variables 45
#Nonlinear Binary Variables 1
#Nonlinear Integer Variables 0
Objective Sense max
Objective type linear
Objective curvature linear
#Nonzeros in Objective 1
#Nonlinear Nonzeros in Objective 0
#Constraints 103
#Linear Constraints 73
#Quadratic Constraints 7
#Polynomial Constraints 2
#Signomial Constraints 21
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions  
Constraints curvature indefinite
#Nonzeros in Jacobian 334
#Nonlinear Nonzeros in Jacobian 92
#Nonzeros in (Upper-Left) Hessian of Lagrangian 164
#Nonzeros in Diagonal of Hessian of Lagrangian 14
#Blocks in Hessian of Lagrangian 4
Minimal blocksize in Hessian of Lagrangian 7
Maximal blocksize in Hessian of Lagrangian 21
Average blocksize in Hessian of Lagrangian 11.25
#Semicontinuities 0
#Nonlinear Semicontinuities 0
#SOS type 1 0
#SOS type 2 0
Minimal coefficient 1.0000e-10
Maximal coefficient 1.0000e+07
Infeasibility of initial point 1e+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
*        104       72        8       24        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         91       85        6        0        0        0        0        0
*  FX      1
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        336      244       92        0
*
*  Solve m using MINLP maximizing 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,x46,x47,x48,x49,x50,x51,x52,x53
          ,x54,x55,x56,x57,x58,x59,x60,x61,x62,x63,x64,x65,x66,x67,x68,x69,x70
          ,x71,x72,x73,x74,x75,x76,x77,x78,x79,x80,x81,x82,x83,x84,b85,b86,b87
          ,b88,b89,b90,objvar;

Positive Variables  x8,x9,x10,x11,x12,x13,x28,x29,x30,x31,x32,x33;

Binary Variables  b85,b86,b87,b88,b89,b90;

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;


e1..  - x1 + objvar =E= 0;

e2..  - x8 + 0.001*b85 =L= 0;

e3..  - x9 + 0.001*b86 =L= 0;

e4..  - x10 + 0.001*b87 =L= 0;

e5..  - x11 + 0.001*b88 =L= 0;

e6..  - x12 + 0.001*b89 =L= 0;

e7..  - x13 + 0.001*b90 =L= 0;

e8..    x8 - 10*b85 =L= 0;

e9..    x9 - 10*b86 =L= 0;

e10..    x10 - 10*b87 =L= 0;

e11..    x11 - 10*b88 =L= 0;

e12..    x12 - 10*b89 =L= 0;

e13..    x13 - 10*b90 =L= 0;

e14..  - x28 + 0.001*b85 =L= 0;

e15..  - x29 + 0.001*b86 =L= 0;

e16..  - x30 + 0.001*b87 =L= 0;

e17..  - x31 + 0.001*b88 =L= 0;

e18..  - x32 + 0.001*b89 =L= 0;

e19..  - x33 + 0.001*b90 =L= 0;

e20..    x28 - 10*b85 =L= 0;

e21..    x29 - 10*b86 =L= 0;

e22..    x30 - 10*b87 =L= 0;

e23..    x31 - 10*b88 =L= 0;

e24..    x32 - 10*b89 =L= 0;

e25..    x33 - 10*b90 =L= 0;

e26..    b85 - b86 =G= 0;

e27..    b86 - b87 =G= 0;

e28..    b87 - b88 =G= 0;

e29..    b88 - b89 =G= 0;

e30..    b89 - b90 =G= 0;

e31..  - 10000000*x2 + 10000000*x8 + x14 =E= 0;

e32.. 2000000*x1*x2 - 1000000*x3 + 1000000*x9 + x15 =E= 0;

e33.. 200000*x1*x3 - 100000*x2 - 100000*x4 - 100000*x8 + 100000*x10 + x16 =E= 0
      ;

e34.. 20000*x1*x4 - 10000*x3 - 10000*x5 - 10000*x9 + 10000*x11 + x17 =E= 0;

e35.. 2000*x1*x5 - 1000*x4 - 1000*x6 - 1000*x10 + 1000*x12 + x18 =E= 0;

e36.. 200*x1*x6 - 100*x5 - 100*x7 - 100*x11 + 100*x13 + x19 =E= 0;

e37.. 20*x1*x7 - 10*x6 - 10*x12 + x20 =E= 0;

e38..  - x7 - x13 + x21 =E= 0;

e39..  - x2 + 1E-5*x3 - 1E-10*x4 + x22 =E= 0;

e40..  - x3 + 2E-5*x4 - 3E-10*x5 + x23 =E= 0;

e41..  - x4 + 3E-5*x5 - 6E-10*x6 + x24 =E= 0;

e42..  - x5 + 4E-5*x6 - 1E-9*x7 + x25 =E= 0;

e43..  - x6 + 5E-5*x7 + x26 =E= 0;

e44..  - x7 + x27 =E= 0;

e45..  - x8 + 1E-5*x9 - 1E-10*x10 + x28 =E= 0;

e46..  - x9 + 2E-5*x10 - 3E-10*x11 + x29 =E= 0;

e47..  - x10 + 3E-5*x11 - 6E-10*x12 + x30 =E= 0;

e48..  - x11 + 4E-5*x12 - 1E-9*x13 + x31 =E= 0;

e49..  - x12 + 5E-5*x13 + x32 =E= 0;

e50..  - x13 + x33 =E= 0;

e51..  - x14 + 1E-5*x15 - 1E-10*x16 + x34 =E= 0;

e52..  - x15 + 2E-5*x16 - 3E-10*x17 + x35 =E= 0;

e53..  - x16 + 3E-5*x17 - 6E-10*x18 + x36 =E= 0;

e54..  - x17 + 4E-5*x18 - 1E-9*x19 + x37 =E= 0;

e55..  - x18 + 5E-5*x19 - 1.5E-9*x20 + x38 =E= 0;

e56..  - x19 + 6E-5*x20 - 2.1E-9*x21 + x39 =E= 0;

e57..  - x20 + 7E-5*x21 + x40 =E= 0;

e58..  - x21 + x41 =E= 0;

e59..  - x27 + x42 =E= 0;

e60..  - x25 + x43 =E= 0;

e61..  - x23 + x44 =E= 0;

e62..  - x26 + x45 =E= 0;

e63..  - x24 + x46 =E= 0;

e64..  - x22 + x47 =E= 0;

e65.. x42/x45*x46 - x43 + x48 =E= 0;

e66.. x42/x45*x47 - x44 + x49 =E= 0;

e67.. x45/x48*x49 - x46 + x51 =E= 0;

e68.. x45/x48*x50 - x47 + x52 =E= 0;

e69.. x48/x51*x52 - x49 + x54 =E= 0;

e70.. x48/x51*x53 - x50 + x55 =E= 0;

e71..    x50 =E= 0;

e72..    x53 =E= 0;

e73..    x56 =E= 0;

e74..  - x41 + x57 =E= 0;

e75..  - x39 + x58 =E= 0;

e76..  - x37 + x59 =E= 0;

e77..  - x35 + x60 =E= 0;

e78..  - x40 + x61 =E= 0;

e79..  - x38 + x62 =E= 0;

e80..  - x36 + x63 =E= 0;

e81..  - x34 + x64 =E= 0;

e82.. x57/x61*x62 - x58 + x65 =E= 0;

e83.. x57/x61*x63 - x59 + x66 =E= 0;

e84.. x57/x61*x64 - x60 + x67 =E= 0;

e85.. x61/x65*x66 - x62 + x69 =E= 0;

e86.. x61/x65*x67 - x63 + x70 =E= 0;

e87.. x61/x65*x68 - x64 + x71 =E= 0;

e88.. x65/x69*x70 - x66 + x73 =E= 0;

e89.. x65/x69*x71 - x67 + x74 =E= 0;

e90.. x65/x69*x72 - x68 + x75 =E= 0;

e91.. x69/x73*x74 - x70 + x77 =E= 0;

e92.. x69/x73*x75 - x71 + x78 =E= 0;

e93.. x69/x73*x76 - x72 + x79 =E= 0;

e94.. x73/x77*x78 - x74 + x81 =E= 0;

e95.. x73/x77*x79 - x75 + x82 =E= 0;

e96.. x73/x77*x80 - x76 + x83 =E= 0;

e97..    x68 =E= 0;

e98..    x72 =E= 0;

e99..    x76 =E= 0;

e100..    x80 =E= 0;

e101..    x84 =E= 0;

e102.. x31*x32 - x30*x33 - 1E-5*b90 =G= 0;

e103.. x30*x31*x32 - x30*x30*x33 + x28*x32*x33 - x29*x32*x32 - 1E-5*b89 =G= 0;

e104.. x29*x30*x31*x32 - x30**2*x29*x33 - x29**2*x32**2 + 2*x28*x29*x32*x33 + 
       x28*x30*x31*x33 - x28**2*x33**2 - x31**2*x28*x32 + (x29*x30 - x28*x31)*(
       1 - b89) - 1E-5*b88 =G= 0;

* set non-default bounds
x1.lo = 0.95; x1.up = 1;
x2.lo = 0.001; x2.up = 10;
x3.lo = 0.001; x3.up = 10;
x4.lo = 0.001; x4.up = 10;
x5.lo = 0.001; x5.up = 10;
x6.lo = 0.001; x6.up = 10;
x7.lo = 0.001; x7.up = 10;
x14.lo = 0.001; x14.up = 10;
x15.lo = 0.001; x15.up = 10;
x16.lo = 0.001; x16.up = 10;
x17.lo = 0.001; x17.up = 10;
x18.lo = 0.001; x18.up = 10;
x19.lo = 0.001; x19.up = 10;
x20.lo = 0.001; x20.up = 10;
x21.lo = 0.001; x21.up = 10;
x22.lo = 0.001; x22.up = 10;
x23.lo = 0.001; x23.up = 10;
x24.lo = 0.001; x24.up = 10;
x25.lo = 0.001; x25.up = 10;
x26.lo = 0.001; x26.up = 10;
x27.lo = 0.001; x27.up = 10;
x34.lo = 0.001; x34.up = 10;
x35.lo = 0.001; x35.up = 10;
x36.lo = 0.001; x36.up = 10;
x37.lo = 0.001; x37.up = 10;
x38.lo = 0.001; x38.up = 10;
x39.lo = 0.001; x39.up = 10;
x40.lo = 0.001; x40.up = 10;
x41.lo = 0.001; x41.up = 10;
x42.lo = 1E-5; x42.up = 10;
x43.lo = 0.001; x43.up = 10;
x44.lo = 0.001; x44.up = 10;
x45.lo = 1E-5; x45.up = 10;
x46.lo = 0.001; x46.up = 10;
x47.lo = 0.001; x47.up = 10;
x48.lo = 1E-5; x48.up = 10;
x49.lo = -10; x49.up = 10;
x50.lo = -10; x50.up = 10;
x51.lo = 1E-5; x51.up = 10;
x52.lo = -10; x52.up = 10;
x53.lo = -10; x53.up = 10;
x54.lo = 1E-5; x54.up = 10;
x55.lo = -10; x55.up = 10;
x56.lo = -10; x56.up = 10;
x57.lo = 1E-5; x57.up = 10;
x58.lo = 0.001; x58.up = 10;
x59.lo = 0.001; x59.up = 10;
x60.lo = 0.001; x60.up = 10;
x61.lo = 1E-5; x61.up = 10;
x62.lo = 0.001; x62.up = 10;
x63.lo = 0.001; x63.up = 10;
x64.lo = 0.001; x64.up = 10;
x65.lo = 1E-5; x65.up = 10;
x66.lo = -10; x66.up = 10;
x67.lo = -10; x67.up = 10;
x68.lo = -10; x68.up = 10;
x69.lo = 1E-5; x69.up = 10;
x70.lo = -10; x70.up = 10;
x71.lo = -10; x71.up = 10;
x72.lo = -10; x72.up = 10;
x73.lo = 1E-5; x73.up = 10;
x74.lo = -10; x74.up = 10;
x75.lo = -10; x75.up = 10;
x76.lo = -10; x76.up = 10;
x77.lo = 1E-5; x77.up = 10;
x78.lo = -10; x78.up = 10;
x79.lo = -10; x79.up = 10;
x80.lo = -10; x80.up = 10;
x81.lo = 1E-5; x81.up = 10;
x82.lo = -10; x82.up = 10;
x83.lo = -10; x83.up = 10;
x84.lo = -10; x84.up = 10;
b85.fx = 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% maximizing objvar;


Last updated: 2022-10-14 Git hash: 2be6d7c0
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