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Instance clay0305m
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 lp mod nl osil pip py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | 8092.50000000 (ALPHAECP) 8092.50000000 (ANTIGONE) 8092.50000000 (BARON) 8092.50000000 (BONMIN) 8092.50000000 (COUENNE) 8092.49999800 (CPLEX) 8092.50000000 (GUROBI) 8092.50000000 (LINDO) 8092.50000000 (SCIP) 8092.49999700 (SHOT) |
| Referencesⓘ | Sawaya, Nicolas W, Reformulations, relaxations and cutting planes for generalized disjunctive programming, PhD thesis, Carnegie Mellon University, 2006. |
| Sourceⓘ | CLay0305M.gms from CMU-IBM MINLP solver project page |
| Applicationⓘ | Layout |
| Added to libraryⓘ | 28 Sep 2013 |
| Problem typeⓘ | MBQCP |
| #Variablesⓘ | 85 |
| #Binary Variablesⓘ | 55 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 10 |
| #Nonlinear Binary Variablesⓘ | 0 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | linear |
| Objective curvatureⓘ | linear |
| #Nonzeros in Objectiveⓘ | 20 |
| #Nonlinear Nonzeros in Objectiveⓘ | 0 |
| #Constraintsⓘ | 155 |
| #Linear Constraintsⓘ | 95 |
| #Quadratic Constraintsⓘ | 60 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 0 |
| Operands in Gen. Nonlin. Functionsⓘ | |
| Constraints curvatureⓘ | convex |
| #Nonzeros in Jacobianⓘ | 475 |
| #Nonlinear Nonzeros in Jacobianⓘ | 120 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 10 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 10 |
| #Blocks in Hessian of Lagrangianⓘ | 10 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 1 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 1 |
| Average blocksize in Hessian of Lagrangianⓘ | 1.0 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 1.0000e+00 |
| Maximal coefficientⓘ | 8.3890e+03 |
| Infeasibility of initial pointⓘ | 3.5 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 156 16 40 100 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 86 31 55 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 496 376 120 0
*
* Solve m using MINLP minimizing objvar;
Variables x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,b11,b12,b13,b14,b15,b16,b17,b18,b19
,b20,b21,b22,b23,b24,b25,b26,b27,b28,b29,b30,b31,b32,b33,b34,b35,b36
,b37,b38,b39,b40,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,x66,x67,x68,x69,x70
,x71,x72,x73,x74,x75,x76,x77,x78,x79,x80,x81,x82,x83,x84,x85,objvar;
Positive Variables x66,x67,x68,x69,x70,x71,x72,x73,x74,x75,x76,x77,x78,x79
,x80,x81,x82,x83,x84,x85;
Binary Variables b11,b12,b13,b14,b15,b16,b17,b18,b19,b20,b21,b22,b23,b24,b25
,b26,b27,b28,b29,b30,b31,b32,b33,b34,b35,b36,b37,b38,b39,b40,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;
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,e134,e135,e136,e137,e138,e139,e140,e141,e142
,e143,e144,e145,e146,e147,e148,e149,e150,e151,e152,e153,e154,e155
,e156;
e1.. - 300*x66 - 240*x67 - 210*x68 - 50*x69 - 100*x70 - 150*x71 - 30*x72
- 120*x73 - 25*x74 - 60*x75 - 300*x76 - 240*x77 - 210*x78 - 50*x79
- 100*x80 - 150*x81 - 30*x82 - 120*x83 - 25*x84 - 60*x85 + objvar =E= 0;
e2.. - x1 + x2 + x66 =G= 0;
e3.. - x1 + x3 + x67 =G= 0;
e4.. - x1 + x4 + x68 =G= 0;
e5.. - x1 + x5 + x69 =G= 0;
e6.. - x2 + x3 + x70 =G= 0;
e7.. - x2 + x4 + x71 =G= 0;
e8.. - x2 + x5 + x72 =G= 0;
e9.. - x3 + x4 + x73 =G= 0;
e10.. - x3 + x5 + x74 =G= 0;
e11.. - x4 + x5 + x75 =G= 0;
e12.. x1 - x2 + x66 =G= 0;
e13.. x1 - x3 + x67 =G= 0;
e14.. x1 - x4 + x68 =G= 0;
e15.. x1 - x5 + x69 =G= 0;
e16.. x2 - x3 + x70 =G= 0;
e17.. x2 - x4 + x71 =G= 0;
e18.. x2 - x5 + x72 =G= 0;
e19.. x3 - x4 + x73 =G= 0;
e20.. x3 - x5 + x74 =G= 0;
e21.. x4 - x5 + x75 =G= 0;
e22.. - x6 + x7 + x76 =G= 0;
e23.. - x6 + x8 + x77 =G= 0;
e24.. - x6 + x9 + x78 =G= 0;
e25.. - x6 + x10 + x79 =G= 0;
e26.. - x7 + x8 + x80 =G= 0;
e27.. - x7 + x9 + x81 =G= 0;
e28.. - x7 + x10 + x82 =G= 0;
e29.. - x8 + x9 + x83 =G= 0;
e30.. - x8 + x10 + x84 =G= 0;
e31.. - x9 + x10 + x85 =G= 0;
e32.. x6 - x7 + x76 =G= 0;
e33.. x6 - x8 + x77 =G= 0;
e34.. x6 - x9 + x78 =G= 0;
e35.. x6 - x10 + x79 =G= 0;
e36.. x7 - x8 + x80 =G= 0;
e37.. x7 - x9 + x81 =G= 0;
e38.. x7 - x10 + x82 =G= 0;
e39.. x8 - x9 + x83 =G= 0;
e40.. x8 - x10 + x84 =G= 0;
e41.. x9 - x10 + x85 =G= 0;
e42.. x1 - x2 + 51*b11 =L= 45;
e43.. x1 - x3 + 51*b12 =L= 47;
e44.. x1 - x4 + 51*b13 =L= 47.5;
e45.. x1 - x5 + 51*b14 =L= 44;
e46.. x2 - x3 + 51*b15 =L= 46;
e47.. x2 - x4 + 51*b16 =L= 46.5;
e48.. x2 - x5 + 51*b17 =L= 43;
e49.. x3 - x4 + 51*b18 =L= 48.5;
e50.. x3 - x5 + 51*b19 =L= 45;
e51.. x4 - x5 + 51*b20 =L= 45.5;
e52.. - x1 + x2 + 51*b21 =L= 45;
e53.. - x1 + x3 + 51*b22 =L= 47;
e54.. - x1 + x4 + 51*b23 =L= 47.5;
e55.. - x1 + x5 + 51*b24 =L= 44;
e56.. - x2 + x3 + 51*b25 =L= 46;
e57.. - x2 + x4 + 51*b26 =L= 46.5;
e58.. - x2 + x5 + 51*b27 =L= 43;
e59.. - x3 + x4 + 51*b28 =L= 48.5;
e60.. - x3 + x5 + 51*b29 =L= 45;
e61.. - x4 + x5 + 51*b30 =L= 45.5;
e62.. x6 - x7 + 86*b31 =L= 80.5;
e63.. x6 - x8 + 86*b32 =L= 81.5;
e64.. x6 - x9 + 86*b33 =L= 81.5;
e65.. x6 - x10 + 86*b34 =L= 79.5;
e66.. x7 - x8 + 86*b35 =L= 82;
e67.. x7 - x9 + 86*b36 =L= 82;
e68.. x7 - x10 + 86*b37 =L= 80;
e69.. x8 - x9 + 86*b38 =L= 83;
e70.. x8 - x10 + 86*b39 =L= 81;
e71.. x9 - x10 + 86*b40 =L= 81;
e72.. - x6 + x7 + 86*b41 =L= 80.5;
e73.. - x6 + x8 + 86*b42 =L= 81.5;
e74.. - x6 + x9 + 86*b43 =L= 81.5;
e75.. - x6 + x10 + 86*b44 =L= 79.5;
e76.. - x7 + x8 + 86*b45 =L= 82;
e77.. - x7 + x9 + 86*b46 =L= 82;
e78.. - x7 + x10 + 86*b47 =L= 80;
e79.. - x8 + x9 + 86*b48 =L= 83;
e80.. - x8 + x10 + 86*b49 =L= 81;
e81.. - x9 + x10 + 86*b50 =L= 81;
e82.. b11 + b21 + b31 + b41 =E= 1;
e83.. b12 + b22 + b32 + b42 =E= 1;
e84.. b13 + b23 + b33 + b43 =E= 1;
e85.. b14 + b24 + b34 + b44 =E= 1;
e86.. b15 + b25 + b35 + b45 =E= 1;
e87.. b16 + b26 + b36 + b46 =E= 1;
e88.. b17 + b27 + b37 + b47 =E= 1;
e89.. b18 + b28 + b38 + b48 =E= 1;
e90.. b19 + b29 + b39 + b49 =E= 1;
e91.. b20 + b30 + b40 + b50 =E= 1;
e92.. sqr((-17.5) + x1) + sqr((-7) + x6) + 7964*b51 =L= 8000;
e93.. sqr((-18.5) + x2) + sqr((-7.5) + x7) + 7808*b52 =L= 7844;
e94.. sqr((-16.5) + x3) + sqr((-8.5) + x8) + 8128*b53 =L= 8164;
e95.. sqr((-16) + x4) + sqr((-8.5) + x9) + 8213*b54 =L= 8249;
e96.. sqr((-19.5) + x5) + sqr((-6.5) + x10) + 7660*b55 =L= 7696;
e97.. sqr((-52.5) + x1) + sqr((-77) + x6) + 6481*b56 =L= 6581;
e98.. sqr((-53.5) + x2) + sqr((-77.5) + x7) + 6622*b57 =L= 6722;
e99.. sqr((-51.5) + x3) + sqr((-78.5) + x8) + 6910*b58 =L= 7010;
e100.. sqr((-51) + x4) + sqr((-78.5) + x9) + 6910*b59 =L= 7010;
e101.. sqr((-54.5) + x5) + sqr((-76.5) + x10) + 6342*b60 =L= 6442;
e102.. sqr((-32.5) + x1) + sqr((-47) + x6) + 2209*b61 =L= 2225;
e103.. sqr((-33.5) + x2) + sqr((-47.5) + x7) + 2194*b62 =L= 2210;
e104.. sqr((-31.5) + x3) + sqr((-48.5) + x8) + 2562*b63 =L= 2578;
e105.. sqr((-31) + x4) + sqr((-48.5) + x9) + 2617*b64 =L= 2633;
e106.. sqr((-34.5) + x5) + sqr((-46.5) + x10) + 2025*b65 =L= 2041;
e107.. sqr((-17.5) + x1) + sqr((-13) + x6) + 7040*b51 =L= 7076;
e108.. sqr((-18.5) + x2) + sqr((-12.5) + x7) + 7033*b52 =L= 7069;
e109.. sqr((-16.5) + x3) + sqr((-11.5) + x8) + 7657*b53 =L= 7693;
e110.. sqr((-16) + x4) + sqr((-11.5) + x9) + 7742*b54 =L= 7778;
e111.. sqr((-19.5) + x5) + sqr((-13.5) + x10) + 6589*b55 =L= 6625;
e112.. sqr((-52.5) + x1) + sqr((-83) + x6) + 7357*b56 =L= 7457;
e113.. sqr((-53.5) + x2) + sqr((-82.5) + x7) + 7357*b57 =L= 7457;
e114.. sqr((-51.5) + x3) + sqr((-81.5) + x8) + 7357*b58 =L= 7457;
e115.. sqr((-51) + x4) + sqr((-81.5) + x9) + 7357*b59 =L= 7457;
e116.. sqr((-54.5) + x5) + sqr((-83.5) + x10) + 7357*b60 =L= 7457;
e117.. sqr((-32.5) + x1) + sqr((-53) + x6) + 2725*b61 =L= 2741;
e118.. sqr((-33.5) + x2) + sqr((-52.5) + x7) + 2629*b62 =L= 2645;
e119.. sqr((-31.5) + x3) + sqr((-51.5) + x8) + 2829*b63 =L= 2845;
e120.. sqr((-31) + x4) + sqr((-51.5) + x9) + 2884*b64 =L= 2900;
e121.. sqr((-34.5) + x5) + sqr((-53.5) + x10) + 2541*b65 =L= 2557;
e122.. sqr((-12.5) + x1) + sqr((-7) + x6) + 8389*b51 =L= 8425;
e123.. sqr((-11.5) + x2) + sqr((-7.5) + x7) + 8389*b52 =L= 8425;
e124.. sqr((-13.5) + x3) + sqr((-8.5) + x8) + 8389*b53 =L= 8425;
e125.. sqr((-14) + x4) + sqr((-8.5) + x9) + 8389*b54 =L= 8425;
e126.. sqr((-10.5) + x5) + sqr((-6.5) + x10) + 8389*b55 =L= 8425;
e127.. sqr((-47.5) + x1) + sqr((-77) + x6) + 6096*b56 =L= 6196;
e128.. sqr((-46.5) + x2) + sqr((-77.5) + x7) + 6097*b57 =L= 6197;
e129.. sqr((-48.5) + x3) + sqr((-78.5) + x8) + 6673*b58 =L= 6773;
e130.. sqr((-49) + x4) + sqr((-78.5) + x9) + 6750*b59 =L= 6850;
e131.. sqr((-45.5) + x5) + sqr((-76.5) + x10) + 5685*b60 =L= 5785;
e132.. sqr((-27.5) + x1) + sqr((-47) + x6) + 2484*b61 =L= 2500;
e133.. sqr((-26.5) + x2) + sqr((-47.5) + x7) + 2565*b62 =L= 2581;
e134.. sqr((-28.5) + x3) + sqr((-48.5) + x8) + 2733*b63 =L= 2749;
e135.. sqr((-29) + x4) + sqr((-48.5) + x9) + 2733*b64 =L= 2749;
e136.. sqr((-25.5) + x5) + sqr((-46.5) + x10) + 2484*b65 =L= 2500;
e137.. sqr((-12.5) + x1) + sqr((-13) + x6) + 7465*b51 =L= 7501;
e138.. sqr((-11.5) + x2) + sqr((-12.5) + x7) + 7614*b52 =L= 7650;
e139.. sqr((-13.5) + x3) + sqr((-11.5) + x8) + 7918*b53 =L= 7954;
e140.. sqr((-14) + x4) + sqr((-11.5) + x9) + 7918*b54 =L= 7954;
e141.. sqr((-10.5) + x5) + sqr((-13.5) + x10) + 7318*b55 =L= 7354;
e142.. sqr((-47.5) + x1) + sqr((-83) + x6) + 6972*b56 =L= 7072;
e143.. sqr((-46.5) + x2) + sqr((-82.5) + x7) + 6832*b57 =L= 6932;
e144.. sqr((-48.5) + x3) + sqr((-81.5) + x8) + 7120*b58 =L= 7220;
e145.. sqr((-49) + x4) + sqr((-81.5) + x9) + 7197*b59 =L= 7297;
e146.. sqr((-45.5) + x5) + sqr((-83.5) + x10) + 6700*b60 =L= 6800;
e147.. sqr((-27.5) + x1) + sqr((-53) + x6) + 3000*b61 =L= 3016;
e148.. sqr((-26.5) + x2) + sqr((-52.5) + x7) + 3000*b62 =L= 3016;
e149.. sqr((-28.5) + x3) + sqr((-51.5) + x8) + 3000*b63 =L= 3016;
e150.. sqr((-29) + x4) + sqr((-51.5) + x9) + 3000*b64 =L= 3016;
e151.. sqr((-25.5) + x5) + sqr((-53.5) + x10) + 3000*b65 =L= 3016;
e152.. b51 + b56 + b61 =E= 1;
e153.. b52 + b57 + b62 =E= 1;
e154.. b53 + b58 + b63 =E= 1;
e155.. b54 + b59 + b64 =E= 1;
e156.. b55 + b60 + b65 =E= 1;
* set non-default bounds
x1.lo = 11.5; x1.up = 57.5;
x2.lo = 12.5; x2.up = 56.5;
x3.lo = 10.5; x3.up = 58.5;
x4.lo = 10; x4.up = 59;
x5.lo = 13.5; x5.up = 55.5;
x6.lo = 7; x6.up = 87;
x7.lo = 6.5; x7.up = 87.5;
x8.lo = 5.5; x8.up = 88.5;
x9.lo = 5.5; x9.up = 88.5;
x10.lo = 7.5; x10.up = 86.5;
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