MINLPLib
A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Removed Instance clay0203h
Non overlapping rectangular units must be placed within the confines of certain designated areas such that the cost of connecting these units is minimized.
| Formatsⓘ | ams gms mod nl osil py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | 41573.30176000 (ALPHAECP) 9357.62980100 (ANTIGONE) 41573.30176000 (BARON) 41573.30176000 (BONMIN) 41573.30176000 (COUENNE) 41573.30176000 (LINDO) 41573.30174000 (SCIP) 40183.68648000 (SHOT) |
| Referencesⓘ | Sawaya, Nicolas W, Reformulations, relaxations and cutting planes for generalized disjunctive programming, PhD thesis, Carnegie Mellon University, 2006. |
| Sourceⓘ | CLay0203H.gms from CMU-IBM MINLP solver project page |
| Applicationⓘ | Layout |
| Added to libraryⓘ | 28 Sep 2013 |
| Removed from libraryⓘ | 16 Feb 2022 |
| Removed becauseⓘ | Superseded by clay0203hfsg |
| Problem typeⓘ | MBNLP |
| #Variablesⓘ | 90 |
| #Binary Variablesⓘ | 18 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 18 |
| #Nonlinear Binary Variablesⓘ | 6 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | linear |
| Objective curvatureⓘ | linear |
| #Nonzeros in Objectiveⓘ | 6 |
| #Nonlinear Nonzeros in Objectiveⓘ | 0 |
| #Constraintsⓘ | 132 |
| #Linear Constraintsⓘ | 108 |
| #Quadratic Constraintsⓘ | 0 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 24 |
| Operands in Gen. Nonlin. Functionsⓘ | div mul sqr |
| Constraints curvatureⓘ | convex |
| #Nonzeros in Jacobianⓘ | 360 |
| #Nonlinear Nonzeros in Jacobianⓘ | 72 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 42 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 18 |
| #Blocks in Hessian of Lagrangianⓘ | 6 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 3 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 3 |
| Average blocksize in Hessian of Lagrangianⓘ | 3.0 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 1.0000e-06 |
| Maximal coefficientⓘ | 6.8890e+03 |
| Infeasibility of initial pointⓘ | 12.5 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 133 25 12 96 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 91 73 18 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 367 295 72 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,x46,x47,x48,x49,x50,x51,x52,x53
,x54,x55,x56,x57,x58,x59,x60,x61,x62,x63,x64,x65,x66,b67,b68,b69,b70
,b71,b72,b73,b74,b75,b76,b77,b78,b79,b80,b81,b82,b83,b84,x85,x86,x87
,x88,x89,x90,objvar;
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,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,x85,x86,x87,x88,x89,x90;
Binary Variables b67,b68,b69,b70,b71,b72,b73,b74,b75,b76,b77,b78,b79,b80,b81
,b82,b83,b84;
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;
e1.. - 300*x85 - 240*x86 - 100*x87 - 300*x88 - 240*x89 - 100*x90 + objvar
=E= 0;
e2.. - x1 + x2 + x85 =G= 0;
e3.. - x1 + x3 + x86 =G= 0;
e4.. - x2 + x3 + x87 =G= 0;
e5.. x1 - x2 + x85 =G= 0;
e6.. x1 - x3 + x86 =G= 0;
e7.. x2 - x3 + x87 =G= 0;
e8.. - x4 + x5 + x88 =G= 0;
e9.. - x4 + x6 + x89 =G= 0;
e10.. - x5 + x6 + x90 =G= 0;
e11.. x4 - x5 + x88 =G= 0;
e12.. x4 - x6 + x89 =G= 0;
e13.. x5 - x6 + x90 =G= 0;
e14.. x1 - x7 - x9 - x11 - x13 =E= 0;
e15.. x1 - x8 - x10 - x12 - x14 =E= 0;
e16.. x2 - x15 - x17 - x19 - x21 =E= 0;
e17.. x2 - x16 - x18 - x20 - x22 =E= 0;
e18.. x3 - x23 - x25 - x27 - x29 =E= 0;
e19.. x3 - x24 - x26 - x28 - x30 =E= 0;
e20.. x4 - x31 - x33 - x35 - x37 =E= 0;
e21.. x4 - x32 - x34 - x36 - x38 =E= 0;
e22.. x5 - x39 - x41 - x43 - x45 =E= 0;
e23.. x5 - x40 - x42 - x44 - x46 =E= 0;
e24.. x6 - x47 - x49 - x51 - x53 =E= 0;
e25.. x6 - x48 - x50 - x52 - x54 =E= 0;
e26.. x7 - 52.5*b67 =L= 0;
e27.. x8 - 52.5*b68 =L= 0;
e28.. x9 - 52.5*b70 =L= 0;
e29.. x10 - 52.5*b71 =L= 0;
e30.. x11 - 52.5*b73 =L= 0;
e31.. x12 - 52.5*b74 =L= 0;
e32.. x13 - 52.5*b76 =L= 0;
e33.. x14 - 52.5*b77 =L= 0;
e34.. x15 - 52.5*b67 =L= 0;
e35.. x16 - 51.5*b69 =L= 0;
e36.. x17 - 52.5*b70 =L= 0;
e37.. x18 - 51.5*b72 =L= 0;
e38.. x19 - 52.5*b73 =L= 0;
e39.. x20 - 51.5*b75 =L= 0;
e40.. x21 - 52.5*b76 =L= 0;
e41.. x22 - 51.5*b78 =L= 0;
e42.. x23 - 52.5*b68 =L= 0;
e43.. x24 - 51.5*b69 =L= 0;
e44.. x25 - 52.5*b71 =L= 0;
e45.. x26 - 51.5*b72 =L= 0;
e46.. x27 - 52.5*b74 =L= 0;
e47.. x28 - 51.5*b75 =L= 0;
e48.. x29 - 52.5*b77 =L= 0;
e49.. x30 - 51.5*b78 =L= 0;
e50.. x31 - 82*b67 =L= 0;
e51.. x32 - 82*b68 =L= 0;
e52.. x33 - 82*b70 =L= 0;
e53.. x34 - 82*b71 =L= 0;
e54.. x35 - 82*b73 =L= 0;
e55.. x36 - 82*b74 =L= 0;
e56.. x37 - 82*b76 =L= 0;
e57.. x38 - 82*b77 =L= 0;
e58.. x39 - 82*b67 =L= 0;
e59.. x40 - 82.5*b69 =L= 0;
e60.. x41 - 82*b70 =L= 0;
e61.. x42 - 82.5*b72 =L= 0;
e62.. x43 - 82*b73 =L= 0;
e63.. x44 - 82.5*b75 =L= 0;
e64.. x45 - 82*b76 =L= 0;
e65.. x46 - 82.5*b78 =L= 0;
e66.. x47 - 82*b68 =L= 0;
e67.. x48 - 82.5*b69 =L= 0;
e68.. x49 - 82*b71 =L= 0;
e69.. x50 - 82.5*b72 =L= 0;
e70.. x51 - 82*b74 =L= 0;
e71.. x52 - 82.5*b75 =L= 0;
e72.. x53 - 82*b77 =L= 0;
e73.. x54 - 82.5*b78 =L= 0;
e74.. x7 - x15 + 6*b67 =L= 0;
e75.. x8 - x23 + 4*b68 =L= 0;
e76.. x16 - x24 + 5*b69 =L= 0;
e77.. - x9 + x17 + 6*b70 =L= 0;
e78.. - x10 + x25 + 4*b71 =L= 0;
e79.. - x18 + x26 + 5*b72 =L= 0;
e80.. x35 - x43 + 5.5*b73 =L= 0;
e81.. x36 - x51 + 4.5*b74 =L= 0;
e82.. x44 - x52 + 4*b75 =L= 0;
e83.. - x37 + x45 + 5.5*b76 =L= 0;
e84.. - x38 + x53 + 4.5*b77 =L= 0;
e85.. - x46 + x54 + 4*b78 =L= 0;
e86.. b67 + b70 + b73 + b76 =E= 1;
e87.. b68 + b71 + b74 + b77 =E= 1;
e88.. b69 + b72 + b75 + b78 =E= 1;
e89.. x1 - x55 - x58 =E= 0;
e90.. x2 - x56 - x59 =E= 0;
e91.. x3 - x57 - x60 =E= 0;
e92.. x4 - x61 - x64 =E= 0;
e93.. x5 - x62 - x65 =E= 0;
e94.. x6 - x63 - x66 =E= 0;
e95.. x55 - 18.5*b79 =L= 0;
e96.. x56 - 17.5*b80 =L= 0;
e97.. x57 - 19.5*b81 =L= 0;
e98.. x58 - 52.5*b82 =L= 0;
e99.. x59 - 51.5*b83 =L= 0;
e100.. x60 - 53.5*b84 =L= 0;
e101.. x61 - 13*b79 =L= 0;
e102.. x62 - 13.5*b80 =L= 0;
e103.. x63 - 14.5*b81 =L= 0;
e104.. x64 - 82*b82 =L= 0;
e105.. x65 - 82.5*b83 =L= 0;
e106.. x66 - 83.5*b84 =L= 0;
e107.. (sqr(x55/(1e-6 + b79)) - 35*x55/(1e-6 + b79) + 306.25*b79 + sqr(x61/(
1e-6 + b79)) - 14*x61/(1e-6 + b79) + 49*b79 - 36*b79)*(1e-6 + b79) =L= 0
;
e108.. (sqr(x56/(1e-6 + b80)) - 37*x56/(1e-6 + b80) + 342.25*b80 + sqr(x62/(
1e-6 + b80)) - 15*x62/(1e-6 + b80) + 56.25*b80 - 36*b80)*(1e-6 + b80)
=L= 0;
e109.. (sqr(x57/(1e-6 + b81)) - 33*x57/(1e-6 + b81) + 272.25*b81 + sqr(x63/(
1e-6 + b81)) - 17*x63/(1e-6 + b81) + 72.25*b81 - 36*b81)*(1e-6 + b81)
=L= 0;
e110.. (sqr(x58/(1e-6 + b82)) - 105*x58/(1e-6 + b82) + 2756.25*b82 + sqr(x64/(
1e-6 + b82)) - 154*x64/(1e-6 + b82) + 5929*b82 - 25*b82)*(1e-6 + b82)
=L= 0;
e111.. (sqr(x59/(1e-6 + b83)) - 107*x59/(1e-6 + b83) + 2862.25*b83 + sqr(x65/(
1e-6 + b83)) - 155*x65/(1e-6 + b83) + 6006.25*b83 - 25*b83)*(1e-6 + b83)
=L= 0;
e112.. (sqr(x60/(1e-6 + b84)) - 103*x60/(1e-6 + b84) + 2652.25*b84 + sqr(x66/(
1e-6 + b84)) - 157*x66/(1e-6 + b84) + 6162.25*b84 - 25*b84)*(1e-6 + b84)
=L= 0;
e113.. (sqr(x55/(1e-6 + b79)) - 35*x55/(1e-6 + b79) + 306.25*b79 + sqr(x61/(
1e-6 + b79)) - 26*x61/(1e-6 + b79) + 169*b79 - 36*b79)*(1e-6 + b79)
=L= 0;
e114.. (sqr(x56/(1e-6 + b80)) - 37*x56/(1e-6 + b80) + 342.25*b80 + sqr(x62/(
1e-6 + b80)) - 25*x62/(1e-6 + b80) + 156.25*b80 - 36*b80)*(1e-6 + b80)
=L= 0;
e115.. (sqr(x57/(1e-6 + b81)) - 33*x57/(1e-6 + b81) + 272.25*b81 + sqr(x63/(
1e-6 + b81)) - 23*x63/(1e-6 + b81) + 132.25*b81 - 36*b81)*(1e-6 + b81)
=L= 0;
e116.. (sqr(x58/(1e-6 + b82)) - 105*x58/(1e-6 + b82) + 2756.25*b82 + sqr(x64/(
1e-6 + b82)) - 166*x64/(1e-6 + b82) + 6889*b82 - 25*b82)*(1e-6 + b82)
=L= 0;
e117.. (sqr(x59/(1e-6 + b83)) - 107*x59/(1e-6 + b83) + 2862.25*b83 + sqr(x65/(
1e-6 + b83)) - 165*x65/(1e-6 + b83) + 6806.25*b83 - 25*b83)*(1e-6 + b83)
=L= 0;
e118.. (sqr(x60/(1e-6 + b84)) - 103*x60/(1e-6 + b84) + 2652.25*b84 + sqr(x66/(
1e-6 + b84)) - 163*x66/(1e-6 + b84) + 6642.25*b84 - 25*b84)*(1e-6 + b84)
=L= 0;
e119.. (sqr(x55/(1e-6 + b79)) - 25*x55/(1e-6 + b79) + 156.25*b79 + sqr(x61/(
1e-6 + b79)) - 14*x61/(1e-6 + b79) + 49*b79 - 36*b79)*(1e-6 + b79) =L= 0
;
e120.. (sqr(x56/(1e-6 + b80)) - 23*x56/(1e-6 + b80) + 132.25*b80 + sqr(x62/(
1e-6 + b80)) - 15*x62/(1e-6 + b80) + 56.25*b80 - 36*b80)*(1e-6 + b80)
=L= 0;
e121.. (sqr(x57/(1e-6 + b81)) - 27*x57/(1e-6 + b81) + 182.25*b81 + sqr(x63/(
1e-6 + b81)) - 17*x63/(1e-6 + b81) + 72.25*b81 - 36*b81)*(1e-6 + b81)
=L= 0;
e122.. (sqr(x58/(1e-6 + b82)) - 95*x58/(1e-6 + b82) + 2256.25*b82 + sqr(x64/(
1e-6 + b82)) - 154*x64/(1e-6 + b82) + 5929*b82 - 25*b82)*(1e-6 + b82)
=L= 0;
e123.. (sqr(x59/(1e-6 + b83)) - 93*x59/(1e-6 + b83) + 2162.25*b83 + sqr(x65/(
1e-6 + b83)) - 155*x65/(1e-6 + b83) + 6006.25*b83 - 25*b83)*(1e-6 + b83)
=L= 0;
e124.. (sqr(x60/(1e-6 + b84)) - 97*x60/(1e-6 + b84) + 2352.25*b84 + sqr(x66/(
1e-6 + b84)) - 157*x66/(1e-6 + b84) + 6162.25*b84 - 25*b84)*(1e-6 + b84)
=L= 0;
e125.. (sqr(x55/(1e-6 + b79)) - 25*x55/(1e-6 + b79) + 156.25*b79 + sqr(x61/(
1e-6 + b79)) - 26*x61/(1e-6 + b79) + 169*b79 - 36*b79)*(1e-6 + b79)
=L= 0;
e126.. (sqr(x56/(1e-6 + b80)) - 23*x56/(1e-6 + b80) + 132.25*b80 + sqr(x62/(
1e-6 + b80)) - 25*x62/(1e-6 + b80) + 156.25*b80 - 36*b80)*(1e-6 + b80)
=L= 0;
e127.. (sqr(x57/(1e-6 + b81)) - 27*x57/(1e-6 + b81) + 182.25*b81 + sqr(x63/(
1e-6 + b81)) - 23*x63/(1e-6 + b81) + 132.25*b81 - 36*b81)*(1e-6 + b81)
=L= 0;
e128.. (sqr(x58/(1e-6 + b82)) - 95*x58/(1e-6 + b82) + 2256.25*b82 + sqr(x64/(
1e-6 + b82)) - 166*x64/(1e-6 + b82) + 6889*b82 - 25*b82)*(1e-6 + b82)
=L= 0;
e129.. (sqr(x59/(1e-6 + b83)) - 93*x59/(1e-6 + b83) + 2162.25*b83 + sqr(x65/(
1e-6 + b83)) - 165*x65/(1e-6 + b83) + 6806.25*b83 - 25*b83)*(1e-6 + b83)
=L= 0;
e130.. (sqr(x60/(1e-6 + b84)) - 97*x60/(1e-6 + b84) + 2352.25*b84 + sqr(x66/(
1e-6 + b84)) - 163*x66/(1e-6 + b84) + 6642.25*b84 - 25*b84)*(1e-6 + b84)
=L= 0;
e131.. b79 + b82 =E= 1;
e132.. b80 + b83 =E= 1;
e133.. b81 + b84 =E= 1;
* set non-default bounds
x1.lo = 11.5; x1.up = 52.5;
x2.lo = 12.5; x2.up = 51.5;
x3.lo = 10.5; x3.up = 53.5;
x4.lo = 7; x4.up = 82;
x5.lo = 6.5; x5.up = 82.5;
x6.lo = 5.5; x6.up = 83.5;
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