MINLPLib
A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Instance wastepaper5
Layout-Optimization of Screening Systems in Recovered Paper Production- 5 Screens
| Formatsⓘ | ams gms mod nl osil py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | 0.00005278 (ANTIGONE) 0.00002365 (BARON) 0.00000000 (COUENNE) 0.00081924 (GUROBI) 0.00000000 (LINDO) 0.00000000 (SCIP) 0.00000000 (SHOT) 0.00000000 (XPRESS) |
| Referencesⓘ | Fügenschuh, Armin, Hayn, Christine, and Michaels, Dennis, Mixed-integer linear methods for layout-optimization of screening systems in recovered paper production, Optimization and Engineering, 15, 2014, 533-573. |
| Applicationⓘ | Waste paper treatment |
| Added to libraryⓘ | 03 Jun 2015 |
| Problem typeⓘ | MBNLP |
| #Variablesⓘ | 104 |
| #Binary Variablesⓘ | 65 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 95 |
| #Nonlinear Binary Variablesⓘ | 60 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | linear |
| Objective curvatureⓘ | linear |
| #Nonzeros in Objectiveⓘ | 1 |
| #Nonlinear Nonzeros in Objectiveⓘ | 0 |
| #Constraintsⓘ | 46 |
| #Linear Constraintsⓘ | 22 |
| #Quadratic Constraintsⓘ | 14 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 10 |
| #General Nonlinear Constraintsⓘ | 0 |
| Operands in Gen. Nonlin. Functionsⓘ | |
| Constraints curvatureⓘ | indefinite |
| #Nonzeros in Jacobianⓘ | 390 |
| #Nonlinear Nonzeros in Jacobianⓘ | 260 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 265 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 5 |
| #Blocks in Hessian of Lagrangianⓘ | 15 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 3 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 8 |
| Average blocksize in Hessian of Lagrangianⓘ | 6.333333 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 6.0000e-02 |
| Maximal coefficientⓘ | 1.0000e+00 |
| Infeasibility of initial pointⓘ | 1 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 47 46 0 1 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 105 40 65 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 392 132 260 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,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,b77,b78,b79,b80,b81,b82,b83,b84,b85,b86
,b87,b88,b89,b90,b91,b92,b93,b94,b95,b96,b97,b98,b99,b100,b101,b102
,b103,b104,b105;
Positive Variables 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;
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,b77,b78,b79,b80,b81,b82,b83,b84,b85,b86,b87,b88,b89
,b90,b91,b92,b93,b94,b95,b96,b97,b98,b99,b100,b101,b102,b103,b104
,b105;
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;
e1.. objvar - x25 =E= 0;
e2.. x7 =L= 0.0675;
e3.. x9 - x10 + x11 =E= 0;
e4.. x12 - x13 + x14 =E= 0;
e5.. x15 - x16 + x17 =E= 0;
e6.. x18 - x19 + x20 =E= 0;
e7.. x21 - x22 + x23 =E= 0;
e8.. x26 - x27 + x28 =E= 0;
e9.. x29 - x30 + x31 =E= 0;
e10.. x32 - x33 + x34 =E= 0;
e11.. x35 - x36 + x37 =E= 0;
e12.. x38 - x39 + x40 =E= 0;
e13.. x2**0.29*x10 - x11 =E= 0;
e14.. x3**0.13*x13 - x14 =E= 0;
e15.. x4**0.06*x16 - x17 =E= 0;
e16.. x5**0.15*x19 - x20 =E= 0;
e17.. x6**0.2*x22 - x23 =E= 0;
e18.. x2**0.74*x27 - x28 =E= 0;
e19.. x3**0.79*x30 - x31 =E= 0;
e20.. x4**0.71*x33 - x34 =E= 0;
e21.. x5**0.8*x36 - x37 =E= 0;
e22.. x6**0.7*x39 - x40 =E= 0;
e23.. b41*x9 + b46*x11 + b51*x12 + b56*x14 + b61*x15 + b66*x17 + b71*x18 + b76*
x20 + b81*x21 + b86*x23 - x10 + 0.675*b91 =E= 0;
e24.. b42*x9 + b47*x11 + b52*x12 + b57*x14 + b62*x15 + b67*x17 + b72*x18 + b77*
x20 + b82*x21 + b87*x23 - x13 + 0.675*b92 =E= 0;
e25.. b43*x9 + b48*x11 + b53*x12 + b58*x14 + b63*x15 + b68*x17 + b73*x18 + b78*
x20 + b83*x21 + b88*x23 - x16 + 0.675*b93 =E= 0;
e26.. b44*x9 + b49*x11 + b54*x12 + b59*x14 + b64*x15 + b69*x17 + b74*x18 + b79*
x20 + b84*x21 + b89*x23 - x19 + 0.675*b94 =E= 0;
e27.. b45*x9 + b50*x11 + b55*x12 + b60*x14 + b65*x15 + b70*x17 + b75*x18 + b80*
x20 + b85*x21 + b90*x23 - x22 + 0.675*b95 =E= 0;
e28.. b41*x26 + b46*x28 + b51*x29 + b56*x31 + b61*x32 + b66*x34 + b71*x35 + b76
*x37 + b81*x38 + b86*x40 - x27 + 0.649*b91 =E= 0;
e29.. b42*x26 + b47*x28 + b52*x29 + b57*x31 + b62*x32 + b67*x34 + b72*x35 + b77
*x37 + b82*x38 + b87*x40 - x30 + 0.649*b92 =E= 0;
e30.. b43*x26 + b48*x28 + b53*x29 + b58*x31 + b63*x32 + b68*x34 + b73*x35 + b78
*x37 + b83*x38 + b88*x40 - x33 + 0.649*b93 =E= 0;
e31.. b44*x26 + b49*x28 + b54*x29 + b59*x31 + b64*x32 + b69*x34 + b74*x35 + b79
*x37 + b84*x38 + b89*x40 - x36 + 0.649*b94 =E= 0;
e32.. b45*x26 + b50*x28 + b55*x29 + b60*x31 + b65*x32 + b70*x34 + b75*x35 + b80
*x37 + b85*x38 + b90*x40 - x39 + 0.649*b95 =E= 0;
e33.. b96*x9 + b97*x12 + b98*x15 + b99*x18 + b100*x21 - x7 =E= 0;
e34.. b96*x26 + b97*x29 + b98*x32 + b99*x35 + b100*x38 - x24 =E= 0;
e35.. b101*x11 + b102*x14 + b103*x17 + b104*x20 + b105*x23 - x8 =E= 0;
e36.. b101*x28 + b102*x31 + b103*x34 + b104*x37 + b105*x40 - x25 =E= 0;
e37.. b41 + b42 + b43 + b44 + b45 + b96 =E= 1;
e38.. b51 + b52 + b53 + b54 + b55 + b97 =E= 1;
e39.. b61 + b62 + b63 + b64 + b65 + b98 =E= 1;
e40.. b71 + b72 + b73 + b74 + b75 + b99 =E= 1;
e41.. b81 + b82 + b83 + b84 + b85 + b100 =E= 1;
e42.. b46 + b47 + b48 + b49 + b50 + b101 =E= 1;
e43.. b56 + b57 + b58 + b59 + b60 + b102 =E= 1;
e44.. b66 + b67 + b68 + b69 + b70 + b103 =E= 1;
e45.. b76 + b77 + b78 + b79 + b80 + b104 =E= 1;
e46.. b86 + b87 + b88 + b89 + b90 + b105 =E= 1;
e47.. b91 + b92 + b93 + b94 + b95 =E= 1;
* set non-default bounds
x2.lo = 0.1; x2.up = 0.9;
x3.lo = 0.1; x3.up = 0.9;
x4.lo = 0.1; x4.up = 0.9;
x5.lo = 0.1; x5.up = 0.9;
x6.lo = 0.1; x6.up = 0.9;
x7.up = 10;
x8.up = 10;
x9.up = 10;
x10.up = 10;
x11.up = 10;
x12.up = 10;
x13.up = 10;
x14.up = 10;
x15.up = 10;
x16.up = 10;
x17.up = 10;
x18.up = 10;
x19.up = 10;
x20.up = 10;
x21.up = 10;
x22.up = 10;
x23.up = 10;
x24.up = 10;
x25.up = 10;
x26.up = 10;
x27.up = 10;
x28.up = 10;
x29.up = 10;
x30.up = 10;
x31.up = 10;
x32.up = 10;
x33.up = 10;
x34.up = 10;
x35.up = 10;
x36.up = 10;
x37.up = 10;
x38.up = 10;
x39.up = 10;
x40.up = 10;
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: 2025-08-07 Git hash: e62cedfc