MINLPLib
A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Instance wastepaper6
Layout-Optimization of Screening Systems in Recovered Paper Production - 6 Screens
| Formatsⓘ | ams gms mod nl osil py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | 0.00000000 (ANTIGONE) 0.00000000 (BARON) 0.00000000 (COUENNE) 0.00000000 (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ⓘ | 136 |
| #Binary Variablesⓘ | 90 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 126 |
| #Nonlinear Binary Variablesⓘ | 84 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | linear |
| Objective curvatureⓘ | linear |
| #Nonzeros in Objectiveⓘ | 1 |
| #Nonlinear Nonzeros in Objectiveⓘ | 0 |
| #Constraintsⓘ | 54 |
| #Linear Constraintsⓘ | 26 |
| #Quadratic Constraintsⓘ | 16 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 12 |
| #General Nonlinear Constraintsⓘ | 0 |
| Operands in Gen. Nonlin. Functionsⓘ | |
| Constraints curvatureⓘ | indefinite |
| #Nonzeros in Jacobianⓘ | 527 |
| #Nonlinear Nonzeros in Jacobianⓘ | 360 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 366 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 6 |
| #Blocks in Hessian of Lagrangianⓘ | 18 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 3 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 9 |
| Average blocksize in Hessian of Lagrangianⓘ | 7.0 |
| #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
* 55 54 0 1 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 137 47 90 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 529 169 360 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,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,b106,b107,b108,b109,b110,b111,b112,b113,b114,b115
,b116,b117,b118,b119,b120,b121,b122,b123,b124,b125,b126,b127,b128
,b129,b130,b131,b132,b133,b134,b135,b136,b137;
Positive Variables 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;
Binary Variables 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,b106,b107,b108,b109,b110
,b111,b112,b113,b114,b115,b116,b117,b118,b119,b120,b121,b122,b123
,b124,b125,b126,b127,b128,b129,b130,b131,b132,b133,b134,b135,b136
,b137;
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;
e1.. objvar - x29 =E= 0;
e2.. x8 =L= 0.0675;
e3.. x10 - x11 + x12 =E= 0;
e4.. x13 - x14 + x15 =E= 0;
e5.. x16 - x17 + x18 =E= 0;
e6.. x19 - x20 + x21 =E= 0;
e7.. x22 - x23 + x24 =E= 0;
e8.. x25 - x26 + x27 =E= 0;
e9.. x30 - x31 + x32 =E= 0;
e10.. x33 - x34 + x35 =E= 0;
e11.. x36 - x37 + x38 =E= 0;
e12.. x39 - x40 + x41 =E= 0;
e13.. x42 - x43 + x44 =E= 0;
e14.. x45 - x46 + x47 =E= 0;
e15.. x2**0.29*x11 - x12 =E= 0;
e16.. x3**0.13*x14 - x15 =E= 0;
e17.. x4**0.06*x17 - x18 =E= 0;
e18.. x5**0.15*x20 - x21 =E= 0;
e19.. x6**0.2*x23 - x24 =E= 0;
e20.. x7**0.17*x26 - x27 =E= 0;
e21.. x2**0.74*x31 - x32 =E= 0;
e22.. x3**0.79*x34 - x35 =E= 0;
e23.. x4**0.71*x37 - x38 =E= 0;
e24.. x5**0.8*x40 - x41 =E= 0;
e25.. x6**0.7*x43 - x44 =E= 0;
e26.. x7**0.85*x46 - x47 =E= 0;
e27.. b48*x10 + b54*x12 + b60*x13 + b66*x15 + b72*x16 + b78*x18 + b84*x19 + b90
*x21 + b96*x22 + b102*x24 + b108*x25 + b114*x27 - x11 + 0.675*b120 =E= 0;
e28.. b49*x10 + b55*x12 + b61*x13 + b67*x15 + b73*x16 + b79*x18 + b85*x19 + b91
*x21 + b97*x22 + b103*x24 + b109*x25 + b115*x27 - x14 + 0.675*b121 =E= 0;
e29.. b50*x10 + b56*x12 + b62*x13 + b68*x15 + b74*x16 + b80*x18 + b86*x19 + b92
*x21 + b98*x22 + b104*x24 + b110*x25 + b116*x27 - x17 + 0.675*b122 =E= 0;
e30.. b51*x10 + b57*x12 + b63*x13 + b69*x15 + b75*x16 + b81*x18 + b87*x19 + b93
*x21 + b99*x22 + b105*x24 + b111*x25 + b117*x27 - x20 + 0.675*b123 =E= 0;
e31.. b52*x10 + b58*x12 + b64*x13 + b70*x15 + b76*x16 + b82*x18 + b88*x19 + b94
*x21 + b100*x22 + b106*x24 + b112*x25 + b118*x27 - x23 + 0.675*b124 =E= 0
;
e32.. b53*x10 + b59*x12 + b65*x13 + b71*x15 + b77*x16 + b83*x18 + b89*x19 + b95
*x21 + b101*x22 + b107*x24 + b113*x25 + b119*x27 - x26 + 0.675*b125 =E= 0
;
e33.. b48*x30 + b54*x32 + b60*x33 + b66*x35 + b72*x36 + b78*x38 + b84*x39 + b90
*x41 + b96*x42 + b102*x44 + b108*x45 + b114*x47 - x31 + 0.649*b120 =E= 0;
e34.. b49*x30 + b55*x32 + b61*x33 + b67*x35 + b73*x36 + b79*x38 + b85*x39 + b91
*x41 + b97*x42 + b103*x44 + b109*x45 + b115*x47 - x34 + 0.649*b121 =E= 0;
e35.. b50*x30 + b56*x32 + b62*x33 + b68*x35 + b74*x36 + b80*x38 + b86*x39 + b92
*x41 + b98*x42 + b104*x44 + b110*x45 + b116*x47 - x37 + 0.649*b122 =E= 0;
e36.. b51*x30 + b57*x32 + b63*x33 + b69*x35 + b75*x36 + b81*x38 + b87*x39 + b93
*x41 + b99*x42 + b105*x44 + b111*x45 + b117*x47 - x40 + 0.649*b123 =E= 0;
e37.. b52*x30 + b58*x32 + b64*x33 + b70*x35 + b76*x36 + b82*x38 + b88*x39 + b94
*x41 + b100*x42 + b106*x44 + b112*x45 + b118*x47 - x43 + 0.649*b124 =E= 0
;
e38.. b53*x30 + b59*x32 + b65*x33 + b71*x35 + b77*x36 + b83*x38 + b89*x39 + b95
*x41 + b101*x42 + b107*x44 + b113*x45 + b119*x47 - x46 + 0.649*b125 =E= 0
;
e39.. b126*x10 + b127*x13 + b128*x16 + b129*x19 + b130*x22 + b131*x25 - x8
=E= 0;
e40.. b126*x30 + b127*x33 + b128*x36 + b129*x39 + b130*x42 + b131*x45 - x28
=E= 0;
e41.. b132*x12 + b133*x15 + b134*x18 + b135*x21 + b136*x24 + b137*x27 - x9
=E= 0;
e42.. b132*x32 + b133*x35 + b134*x38 + b135*x41 + b136*x44 + b137*x47 - x29
=E= 0;
e43.. b48 + b49 + b50 + b51 + b52 + b53 + b126 =E= 1;
e44.. b60 + b61 + b62 + b63 + b64 + b65 + b127 =E= 1;
e45.. b72 + b73 + b74 + b75 + b76 + b77 + b128 =E= 1;
e46.. b84 + b85 + b86 + b87 + b88 + b89 + b129 =E= 1;
e47.. b96 + b97 + b98 + b99 + b100 + b101 + b130 =E= 1;
e48.. b108 + b109 + b110 + b111 + b112 + b113 + b131 =E= 1;
e49.. b54 + b55 + b56 + b57 + b58 + b59 + b132 =E= 1;
e50.. b66 + b67 + b68 + b69 + b70 + b71 + b133 =E= 1;
e51.. b78 + b79 + b80 + b81 + b82 + b83 + b134 =E= 1;
e52.. b90 + b91 + b92 + b93 + b94 + b95 + b135 =E= 1;
e53.. b102 + b103 + b104 + b105 + b106 + b107 + b136 =E= 1;
e54.. b114 + b115 + b116 + b117 + b118 + b119 + b137 =E= 1;
e55.. b120 + b121 + b122 + b123 + b124 + b125 =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.lo = 0.1; x7.up = 0.9;
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;
x41.up = 10;
x42.up = 10;
x43.up = 10;
x44.up = 10;
x45.up = 10;
x46.up = 10;
x47.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