MINLPLib
A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
Home // Instances // Documentation // Download // Statistics
Instance clay0203m
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ⓘ | 41573.25600000 (ALPHAECP) 41573.25800000 (ANTIGONE) 41573.26248000 (BARON) 41573.26200000 (BONMIN) 41573.15082000 (COUENNE) 41573.26235000 (CPLEX) 41573.25733000 (GUROBI) 41573.26223000 (LINDO) 41573.26250000 (SCIP) 41573.26191000 (SHOT) |
| Referencesⓘ | Sawaya, Nicolas W, Reformulations, relaxations and cutting planes for generalized disjunctive programming, PhD thesis, Carnegie Mellon University, 2006. |
| Sourceⓘ | CLay0203M.gms from CMU-IBM MINLP solver project page |
| Applicationⓘ | Layout |
| Added to libraryⓘ | 28 Sep 2013 |
| Problem typeⓘ | MBQCP |
| #Variablesⓘ | 30 |
| #Binary Variablesⓘ | 18 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 6 |
| #Nonlinear Binary Variablesⓘ | 0 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | linear |
| Objective curvatureⓘ | linear |
| #Nonzeros in Objectiveⓘ | 6 |
| #Nonlinear Nonzeros in Objectiveⓘ | 0 |
| #Constraintsⓘ | 54 |
| #Linear Constraintsⓘ | 30 |
| #Quadratic Constraintsⓘ | 24 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 0 |
| Operands in Gen. Nonlin. Functionsⓘ | |
| Constraints curvatureⓘ | convex |
| #Nonzeros in Jacobianⓘ | 162 |
| #Nonlinear Nonzeros in Jacobianⓘ | 48 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 6 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 6 |
| #Blocks in Hessian of Lagrangianⓘ | 6 |
| 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ⓘ | 7.4320e+03 |
| Infeasibility of initial pointⓘ | 2 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 55 7 12 36 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 31 13 18 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 169 121 48 0
*
* Solve m using MINLP minimizing objvar;
Variables x1,x2,x3,x4,x5,x6,b7,b8,b9,b10,b11,b12,b13,b14,b15,b16,b17,b18,b19
,b20,b21,b22,b23,b24,x25,x26,x27,x28,x29,x30,objvar;
Positive Variables x25,x26,x27,x28,x29,x30;
Binary Variables b7,b8,b9,b10,b11,b12,b13,b14,b15,b16,b17,b18,b19,b20,b21,b22
,b23,b24;
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.. - 300*x25 - 240*x26 - 100*x27 - 300*x28 - 240*x29 - 100*x30 + objvar
=E= 0;
e2.. - x1 + x2 + x25 =G= 0;
e3.. - x1 + x3 + x26 =G= 0;
e4.. - x2 + x3 + x27 =G= 0;
e5.. x1 - x2 + x25 =G= 0;
e6.. x1 - x3 + x26 =G= 0;
e7.. x2 - x3 + x27 =G= 0;
e8.. - x4 + x5 + x28 =G= 0;
e9.. - x4 + x6 + x29 =G= 0;
e10.. - x5 + x6 + x30 =G= 0;
e11.. x4 - x5 + x28 =G= 0;
e12.. x4 - x6 + x29 =G= 0;
e13.. x5 - x6 + x30 =G= 0;
e14.. x1 - x2 + 46*b7 =L= 40;
e15.. x1 - x3 + 46*b8 =L= 42;
e16.. x2 - x3 + 46*b9 =L= 41;
e17.. - x1 + x2 + 46*b10 =L= 40;
e18.. - x1 + x3 + 46*b11 =L= 42;
e19.. - x2 + x3 + 46*b12 =L= 41;
e20.. x4 - x5 + 81*b13 =L= 75.5;
e21.. x4 - x6 + 81*b14 =L= 76.5;
e22.. x5 - x6 + 81*b15 =L= 77;
e23.. - x4 + x5 + 81*b16 =L= 75.5;
e24.. - x4 + x6 + 81*b17 =L= 76.5;
e25.. - x5 + x6 + 81*b18 =L= 77;
e26.. b7 + b10 + b13 + b16 =E= 1;
e27.. b8 + b11 + b14 + b17 =E= 1;
e28.. b9 + b12 + b15 + b18 =E= 1;
e29.. sqr((-17.5) + x1) + sqr((-7) + x4) + 6814*b19 =L= 6850;
e30.. sqr((-18.5) + x2) + sqr((-7.5) + x5) + 6678*b20 =L= 6714;
e31.. sqr((-16.5) + x3) + sqr((-8.5) + x6) + 6958*b21 =L= 6994;
e32.. sqr((-52.5) + x1) + sqr((-77) + x4) + 6556*b22 =L= 6581;
e33.. sqr((-53.5) + x2) + sqr((-77.5) + x5) + 6697*b23 =L= 6722;
e34.. sqr((-51.5) + x3) + sqr((-78.5) + x6) + 6985*b24 =L= 7010;
e35.. sqr((-17.5) + x1) + sqr((-13) + x4) + 5950*b19 =L= 5986;
e36.. sqr((-18.5) + x2) + sqr((-12.5) + x5) + 5953*b20 =L= 5989;
e37.. sqr((-16.5) + x3) + sqr((-11.5) + x6) + 6517*b21 =L= 6553;
e38.. sqr((-52.5) + x1) + sqr((-83) + x4) + 7432*b22 =L= 7457;
e39.. sqr((-53.5) + x2) + sqr((-82.5) + x5) + 7432*b23 =L= 7457;
e40.. sqr((-51.5) + x3) + sqr((-81.5) + x6) + 7432*b24 =L= 7457;
e41.. sqr((-12.5) + x1) + sqr((-7) + x4) + 7189*b19 =L= 7225;
e42.. sqr((-11.5) + x2) + sqr((-7.5) + x5) + 7189*b20 =L= 7225;
e43.. sqr((-13.5) + x3) + sqr((-8.5) + x6) + 7189*b21 =L= 7225;
e44.. sqr((-47.5) + x1) + sqr((-77) + x4) + 6171*b22 =L= 6196;
e45.. sqr((-46.5) + x2) + sqr((-77.5) + x5) + 6172*b23 =L= 6197;
e46.. sqr((-48.5) + x3) + sqr((-78.5) + x6) + 6748*b24 =L= 6773;
e47.. sqr((-12.5) + x1) + sqr((-13) + x4) + 6325*b19 =L= 6361;
e48.. sqr((-11.5) + x2) + sqr((-12.5) + x5) + 6464*b20 =L= 6500;
e49.. sqr((-13.5) + x3) + sqr((-11.5) + x6) + 6748*b21 =L= 6784;
e50.. sqr((-47.5) + x1) + sqr((-83) + x4) + 7047*b22 =L= 7072;
e51.. sqr((-46.5) + x2) + sqr((-82.5) + x5) + 6907*b23 =L= 6932;
e52.. sqr((-48.5) + x3) + sqr((-81.5) + x6) + 7195*b24 =L= 7220;
e53.. b19 + b22 =E= 1;
e54.. b20 + b23 =E= 1;
e55.. b21 + b24 =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