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Instance clay0204m
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ⓘ | 6545.00000000 (ALPHAECP) 6545.00000000 (ANTIGONE) 6545.00000000 (BARON) 6545.00000000 (BONMIN) 6545.00000000 (COUENNE) 6544.99998800 (CPLEX) 6545.00000000 (GUROBI) 6545.00000000 (LINDO) 6545.00000000 (SCIP) 6544.99997700 (SHOT) |
| Referencesⓘ | Sawaya, Nicolas W, Reformulations, relaxations and cutting planes for generalized disjunctive programming, PhD thesis, Carnegie Mellon University, 2006. |
| Sourceⓘ | CLay0204M.gms from CMU-IBM MINLP solver project page |
| Applicationⓘ | Layout |
| Added to libraryⓘ | 28 Sep 2013 |
| Problem typeⓘ | MBQCP |
| #Variablesⓘ | 52 |
| #Binary Variablesⓘ | 32 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 8 |
| #Nonlinear Binary Variablesⓘ | 0 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | linear |
| Objective curvatureⓘ | linear |
| #Nonzeros in Objectiveⓘ | 12 |
| #Nonlinear Nonzeros in Objectiveⓘ | 0 |
| #Constraintsⓘ | 90 |
| #Linear Constraintsⓘ | 58 |
| #Quadratic Constraintsⓘ | 32 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 0 |
| Operands in Gen. Nonlin. Functionsⓘ | |
| Constraints curvatureⓘ | convex |
| #Nonzeros in Jacobianⓘ | 272 |
| #Nonlinear Nonzeros in Jacobianⓘ | 64 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 8 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 8 |
| #Blocks in Hessian of Lagrangianⓘ | 8 |
| 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ⓘ | 2.5 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 91 11 24 56 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 53 21 32 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 285 221 64 0
*
* Solve m using MINLP minimizing objvar;
Variables x1,x2,x3,x4,x5,x6,x7,x8,b9,b10,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,x41,x42,x43,x44,x45,x46,x47,x48,x49,x50,x51,x52
,objvar;
Positive Variables x41,x42,x43,x44,x45,x46,x47,x48,x49,x50,x51,x52;
Binary Variables b9,b10,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;
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;
e1.. - 300*x41 - 240*x42 - 210*x43 - 100*x44 - 150*x45 - 120*x46 - 300*x47
- 240*x48 - 210*x49 - 100*x50 - 150*x51 - 120*x52 + objvar =E= 0;
e2.. - x1 + x2 + x41 =G= 0;
e3.. - x1 + x3 + x42 =G= 0;
e4.. - x1 + x4 + x43 =G= 0;
e5.. - x2 + x3 + x44 =G= 0;
e6.. - x2 + x4 + x45 =G= 0;
e7.. - x3 + x4 + x46 =G= 0;
e8.. x1 - x2 + x41 =G= 0;
e9.. x1 - x3 + x42 =G= 0;
e10.. x1 - x4 + x43 =G= 0;
e11.. x2 - x3 + x44 =G= 0;
e12.. x2 - x4 + x45 =G= 0;
e13.. x3 - x4 + x46 =G= 0;
e14.. - x5 + x6 + x47 =G= 0;
e15.. - x5 + x7 + x48 =G= 0;
e16.. - x5 + x8 + x49 =G= 0;
e17.. - x6 + x7 + x50 =G= 0;
e18.. - x6 + x8 + x51 =G= 0;
e19.. - x7 + x8 + x52 =G= 0;
e20.. x5 - x6 + x47 =G= 0;
e21.. x5 - x7 + x48 =G= 0;
e22.. x5 - x8 + x49 =G= 0;
e23.. x6 - x7 + x50 =G= 0;
e24.. x6 - x8 + x51 =G= 0;
e25.. x7 - x8 + x52 =G= 0;
e26.. x1 - x2 + 51*b9 =L= 45;
e27.. x1 - x3 + 51*b10 =L= 47;
e28.. x1 - x4 + 51*b11 =L= 47.5;
e29.. x2 - x3 + 51*b12 =L= 46;
e30.. x2 - x4 + 51*b13 =L= 46.5;
e31.. x3 - x4 + 51*b14 =L= 48.5;
e32.. - x1 + x2 + 51*b15 =L= 45;
e33.. - x1 + x3 + 51*b16 =L= 47;
e34.. - x1 + x4 + 51*b17 =L= 47.5;
e35.. - x2 + x3 + 51*b18 =L= 46;
e36.. - x2 + x4 + 51*b19 =L= 46.5;
e37.. - x3 + x4 + 51*b20 =L= 48.5;
e38.. x5 - x6 + 86*b21 =L= 80.5;
e39.. x5 - x7 + 86*b22 =L= 81.5;
e40.. x5 - x8 + 86*b23 =L= 81.5;
e41.. x6 - x7 + 86*b24 =L= 82;
e42.. x6 - x8 + 86*b25 =L= 82;
e43.. x7 - x8 + 86*b26 =L= 83;
e44.. - x5 + x6 + 86*b27 =L= 80.5;
e45.. - x5 + x7 + 86*b28 =L= 81.5;
e46.. - x5 + x8 + 86*b29 =L= 81.5;
e47.. - x6 + x7 + 86*b30 =L= 82;
e48.. - x6 + x8 + 86*b31 =L= 82;
e49.. - x7 + x8 + 86*b32 =L= 83;
e50.. b9 + b15 + b21 + b27 =E= 1;
e51.. b10 + b16 + b22 + b28 =E= 1;
e52.. b11 + b17 + b23 + b29 =E= 1;
e53.. b12 + b18 + b24 + b30 =E= 1;
e54.. b13 + b19 + b25 + b31 =E= 1;
e55.. b14 + b20 + b26 + b32 =E= 1;
e56.. sqr((-17.5) + x1) + sqr((-7) + x5) + 7964*b33 =L= 8000;
e57.. sqr((-18.5) + x2) + sqr((-7.5) + x6) + 7808*b34 =L= 7844;
e58.. sqr((-16.5) + x3) + sqr((-8.5) + x7) + 8128*b35 =L= 8164;
e59.. sqr((-16) + x4) + sqr((-8.5) + x8) + 8213*b36 =L= 8249;
e60.. sqr((-52.5) + x1) + sqr((-77) + x5) + 6481*b37 =L= 6581;
e61.. sqr((-53.5) + x2) + sqr((-77.5) + x6) + 6622*b38 =L= 6722;
e62.. sqr((-51.5) + x3) + sqr((-78.5) + x7) + 6951.25*b39 =L= 7051.25;
e63.. sqr((-51) + x4) + sqr((-78.5) + x8) + 6910*b40 =L= 7010;
e64.. sqr((-17.5) + x1) + sqr((-13) + x5) + 7040*b33 =L= 7076;
e65.. sqr((-18.5) + x2) + sqr((-12.5) + x6) + 7033*b34 =L= 7069;
e66.. sqr((-16.5) + x3) + sqr((-11.5) + x7) + 7657*b35 =L= 7693;
e67.. sqr((-16) + x4) + sqr((-11.5) + x8) + 7742*b36 =L= 7778;
e68.. sqr((-52.5) + x1) + sqr((-83) + x5) + 7357*b37 =L= 7457;
e69.. sqr((-53.5) + x2) + sqr((-82.5) + x6) + 7357*b38 =L= 7457;
e70.. sqr((-51.5) + x3) + sqr((-81.5) + x7) + 7398.25*b39 =L= 7498.25;
e71.. sqr((-51) + x4) + sqr((-81.5) + x8) + 7357*b40 =L= 7457;
e72.. sqr((-12.5) + x1) + sqr((-7) + x5) + 8389*b33 =L= 8425;
e73.. sqr((-11.5) + x2) + sqr((-7.5) + x6) + 8389*b34 =L= 8425;
e74.. sqr((-13.5) + x3) + sqr((-8.5) + x7) + 8389*b35 =L= 8425;
e75.. sqr((-14) + x4) + sqr((-8.5) + x8) + 8389*b36 =L= 8425;
e76.. sqr((-47.5) + x1) + sqr((-77) + x5) + 6096*b37 =L= 6196;
e77.. sqr((-46.5) + x2) + sqr((-77.5) + x6) + 6097*b38 =L= 6197;
e78.. sqr((-48.5) + x3) + sqr((-78.5) + x7) + 6711.25*b39 =L= 6811.25;
e79.. sqr((-49) + x4) + sqr((-78.5) + x8) + 6750*b40 =L= 6850;
e80.. sqr((-12.5) + x1) + sqr((-13) + x5) + 7465*b33 =L= 7501;
e81.. sqr((-11.5) + x2) + sqr((-12.5) + x6) + 7614*b34 =L= 7650;
e82.. sqr((-13.5) + x3) + sqr((-11.5) + x7) + 7918*b35 =L= 7954;
e83.. sqr((-14) + x4) + sqr((-11.5) + x8) + 7918*b36 =L= 7954;
e84.. sqr((-47.5) + x1) + sqr((-83) + x5) + 6972*b37 =L= 7072;
e85.. sqr((-46.5) + x2) + sqr((-82.5) + x6) + 6832*b38 =L= 6932;
e86.. sqr((-48.5) + x3) + sqr((-81.5) + x7) + 7158.25*b39 =L= 7258.25;
e87.. sqr((-49) + x4) + sqr((-81.5) + x8) + 7197*b40 =L= 7297;
e88.. b33 + b37 =E= 1;
e89.. b34 + b38 =E= 1;
e90.. b35 + b39 =E= 1;
e91.. b36 + b40 =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 = 7; x5.up = 87;
x6.lo = 6.5; x6.up = 87.5;
x7.lo = 5.5; x7.up = 88.5;
x8.lo = 5.5; x8.up = 88.5;
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