MINLPLib
A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Instance clay0203hfsg
Non overlapping rectangular units must be placed within the confines of certain designated areas such that the cost of connecting these units is minimized. Equivalent perspective reformulation of clay0203.
| Formatsⓘ | ams gms mod nl osil py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | 41573.26107000 (ALPHAECP) 9002.69454300 (ANTIGONE) 41573.26246000 (BARON) 41573.26252000 (BONMIN) 41573.26173000 (COUENNE) 41573.26252000 (LINDO) 41573.26248000 (SCIP) 41573.23614000 (SHOT) |
| Referencesⓘ | Sawaya, Nicolas W, Reformulations, relaxations and cutting planes for generalized disjunctive programming, PhD thesis, Carnegie Mellon University, 2006. Kevin C. Furman, Nicolas W. Sawaya, Ignacio E. Grossmann, A computationally useful algebraic representation of nonlinear disjunctive convex sets using the perspective function, Tech. Rep., 2019. |
| Applicationⓘ | Layout |
| Added to libraryⓘ | 25 Sep 2019 |
| 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-03 |
| 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/(0.001 + 0.999*b79)) - 35*x55/(0.001 + 0.999*b79) + sqr(x61/(
0.001 + 0.999*b79)) - 14*x61/(0.001 + 0.999*b79))*(0.001 + 0.999*b79) +
306.25*b79 + 49*b79 - 36*b79 =L= 0;
e108.. (sqr(x56/(0.001 + 0.999*b80)) - 37*x56/(0.001 + 0.999*b80) + sqr(x62/(
0.001 + 0.999*b80)) - 15*x62/(0.001 + 0.999*b80))*(0.001 + 0.999*b80) +
342.25*b80 + 56.25*b80 - 36*b80 =L= 0;
e109.. (sqr(x57/(0.001 + 0.999*b81)) - 33*x57/(0.001 + 0.999*b81) + sqr(x63/(
0.001 + 0.999*b81)) - 17*x63/(0.001 + 0.999*b81))*(0.001 + 0.999*b81) +
272.25*b81 + 72.25*b81 - 36*b81 =L= 0;
e110.. (sqr(x58/(0.001 + 0.999*b82)) - 105*x58/(0.001 + 0.999*b82) + sqr(x64/(
0.001 + 0.999*b82)) - 154*x64/(0.001 + 0.999*b82))*(0.001 + 0.999*b82)
+ 2756.25*b82 + 5929*b82 - 25*b82 =L= 0;
e111.. (sqr(x59/(0.001 + 0.999*b83)) - 107*x59/(0.001 + 0.999*b83) + sqr(x65/(
0.001 + 0.999*b83)) - 155*x65/(0.001 + 0.999*b83))*(0.001 + 0.999*b83)
+ 2862.25*b83 + 6006.25*b83 - 25*b83 =L= 0;
e112.. (sqr(x60/(0.001 + 0.999*b84)) - 103*x60/(0.001 + 0.999*b84) + sqr(x66/(
0.001 + 0.999*b84)) - 157*x66/(0.001 + 0.999*b84))*(0.001 + 0.999*b84)
+ 2652.25*b84 + 6162.25*b84 - 25*b84 =L= 0;
e113.. (sqr(x55/(0.001 + 0.999*b79)) - 35*x55/(0.001 + 0.999*b79) + sqr(x61/(
0.001 + 0.999*b79)) - 26*x61/(0.001 + 0.999*b79))*(0.001 + 0.999*b79) +
306.25*b79 + 169*b79 - 36*b79 =L= 0;
e114.. (sqr(x56/(0.001 + 0.999*b80)) - 37*x56/(0.001 + 0.999*b80) + sqr(x62/(
0.001 + 0.999*b80)) - 25*x62/(0.001 + 0.999*b80))*(0.001 + 0.999*b80) +
342.25*b80 + 156.25*b80 - 36*b80 =L= 0;
e115.. (sqr(x57/(0.001 + 0.999*b81)) - 33*x57/(0.001 + 0.999*b81) + sqr(x63/(
0.001 + 0.999*b81)) - 23*x63/(0.001 + 0.999*b81))*(0.001 + 0.999*b81) +
272.25*b81 + 132.25*b81 - 36*b81 =L= 0;
e116.. (sqr(x58/(0.001 + 0.999*b82)) - 105*x58/(0.001 + 0.999*b82) + sqr(x64/(
0.001 + 0.999*b82)) - 166*x64/(0.001 + 0.999*b82))*(0.001 + 0.999*b82)
+ 2756.25*b82 + 6889*b82 - 25*b82 =L= 0;
e117.. (sqr(x59/(0.001 + 0.999*b83)) - 107*x59/(0.001 + 0.999*b83) + sqr(x65/(
0.001 + 0.999*b83)) - 165*x65/(0.001 + 0.999*b83))*(0.001 + 0.999*b83)
+ 2862.25*b83 + 6806.25*b83 - 25*b83 =L= 0;
e118.. (sqr(x60/(0.001 + 0.999*b84)) - 103*x60/(0.001 + 0.999*b84) + sqr(x66/(
0.001 + 0.999*b84)) - 163*x66/(0.001 + 0.999*b84))*(0.001 + 0.999*b84)
+ 2652.25*b84 + 6642.25*b84 - 25*b84 =L= 0;
e119.. (sqr(x55/(0.001 + 0.999*b79)) - 25*x55/(0.001 + 0.999*b79) + sqr(x61/(
0.001 + 0.999*b79)) - 14*x61/(0.001 + 0.999*b79))*(0.001 + 0.999*b79) +
156.25*b79 + 49*b79 - 36*b79 =L= 0;
e120.. (sqr(x56/(0.001 + 0.999*b80)) - 23*x56/(0.001 + 0.999*b80) + sqr(x62/(
0.001 + 0.999*b80)) - 15*x62/(0.001 + 0.999*b80))*(0.001 + 0.999*b80) +
132.25*b80 + 56.25*b80 - 36*b80 =L= 0;
e121.. (sqr(x57/(0.001 + 0.999*b81)) - 27*x57/(0.001 + 0.999*b81) + sqr(x63/(
0.001 + 0.999*b81)) - 17*x63/(0.001 + 0.999*b81))*(0.001 + 0.999*b81) +
182.25*b81 + 72.25*b81 - 36*b81 =L= 0;
e122.. (sqr(x58/(0.001 + 0.999*b82)) - 95*x58/(0.001 + 0.999*b82) + sqr(x64/(
0.001 + 0.999*b82)) - 154*x64/(0.001 + 0.999*b82))*(0.001 + 0.999*b82)
+ 2256.25*b82 + 5929*b82 - 25*b82 =L= 0;
e123.. (sqr(x59/(0.001 + 0.999*b83)) - 93*x59/(0.001 + 0.999*b83) + sqr(x65/(
0.001 + 0.999*b83)) - 155*x65/(0.001 + 0.999*b83))*(0.001 + 0.999*b83)
+ 2162.25*b83 + 6006.25*b83 - 25*b83 =L= 0;
e124.. (sqr(x60/(0.001 + 0.999*b84)) - 97*x60/(0.001 + 0.999*b84) + sqr(x66/(
0.001 + 0.999*b84)) - 157*x66/(0.001 + 0.999*b84))*(0.001 + 0.999*b84)
+ 2352.25*b84 + 6162.25*b84 - 25*b84 =L= 0;
e125.. (sqr(x55/(0.001 + 0.999*b79)) - 25*x55/(0.001 + 0.999*b79) + sqr(x61/(
0.001 + 0.999*b79)) - 26*x61/(0.001 + 0.999*b79))*(0.001 + 0.999*b79) +
156.25*b79 + 169*b79 - 36*b79 =L= 0;
e126.. (sqr(x56/(0.001 + 0.999*b80)) - 23*x56/(0.001 + 0.999*b80) + sqr(x62/(
0.001 + 0.999*b80)) - 25*x62/(0.001 + 0.999*b80))*(0.001 + 0.999*b80) +
132.25*b80 + 156.25*b80 - 36*b80 =L= 0;
e127.. (sqr(x57/(0.001 + 0.999*b81)) - 27*x57/(0.001 + 0.999*b81) + sqr(x63/(
0.001 + 0.999*b81)) - 23*x63/(0.001 + 0.999*b81))*(0.001 + 0.999*b81) +
182.25*b81 + 132.25*b81 - 36*b81 =L= 0;
e128.. (sqr(x58/(0.001 + 0.999*b82)) - 95*x58/(0.001 + 0.999*b82) + sqr(x64/(
0.001 + 0.999*b82)) - 166*x64/(0.001 + 0.999*b82))*(0.001 + 0.999*b82)
+ 2256.25*b82 + 6889*b82 - 25*b82 =L= 0;
e129.. (sqr(x59/(0.001 + 0.999*b83)) - 93*x59/(0.001 + 0.999*b83) + sqr(x65/(
0.001 + 0.999*b83)) - 165*x65/(0.001 + 0.999*b83))*(0.001 + 0.999*b83)
+ 2162.25*b83 + 6806.25*b83 - 25*b83 =L= 0;
e130.. (sqr(x60/(0.001 + 0.999*b84)) - 97*x60/(0.001 + 0.999*b84) + sqr(x66/(
0.001 + 0.999*b84)) - 163*x66/(0.001 + 0.999*b84))*(0.001 + 0.999*b84)
+ 2352.25*b84 + 6642.25*b84 - 25*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: 2024-12-17 Git hash: 8eaceb91