MINLPLib
A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Instance transswitch0009r
Optimal Transmission Switching problem modeled using quadratic functions (rectangular coordinates)
| Formatsⓘ | ams gms mod nl osil pip py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | 2545.09965900 (ANTIGONE) 5051.35418900 (BARON) 5183.48288300 (COUENNE) 5296.65059300 (GUROBI) 4624.68080100 (LINDO) 5296.68414100 (SCIP) 1188.75000000 (SHOT) 1188.75020600 (XPRESS) |
| Referencesⓘ | Hijazi, H L, Coffrin, C, and Van Hentenryck, P, Convex Quadratic Relaxations of Nonlinear Programs in Power Systems, Tech. Rep. 2013-09, Optimization Online, 2013. |
| Applicationⓘ | Electricity Networks |
| Added to libraryⓘ | 11 Mar 2014 |
| Problem typeⓘ | MBNLP |
| #Variablesⓘ | 69 |
| #Binary Variablesⓘ | 9 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 66 |
| #Nonlinear Binary Variablesⓘ | 9 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | quadratic |
| Objective curvatureⓘ | convex |
| #Nonzeros in Objectiveⓘ | 3 |
| #Nonlinear Nonzeros in Objectiveⓘ | 3 |
| #Constraintsⓘ | 103 |
| #Linear Constraintsⓘ | 31 |
| #Quadratic Constraintsⓘ | 36 |
| #Polynomial Constraintsⓘ | 36 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 0 |
| Operands in Gen. Nonlin. Functionsⓘ | |
| Constraints curvatureⓘ | indefinite |
| #Nonzeros in Jacobianⓘ | 343 |
| #Nonlinear Nonzeros in Jacobianⓘ | 252 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 201 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 57 |
| #Blocks in Hessian of Lagrangianⓘ | 40 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 1 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 27 |
| Average blocksize in Hessian of Lagrangianⓘ | 1.65 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 1.0000e+00 |
| Maximal coefficientⓘ | 1.2250e+03 |
| Infeasibility of initial pointⓘ | 1.25 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 104 56 15 33 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 70 61 9 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 347 92 255 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,b55,b56,b57,b58,b59,b60,b61,b62,b63,x64,x65,x66,x67,x68,x69
,objvar;
Binary Variables b55,b56,b57,b58,b59,b60,b61,b62,b63;
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;
e1.. 1100*sqr(x64) + 500*x64 + 850*sqr(x65) + 120*x65 + 1225*sqr(x66) + 100*x66
- objvar =E= -1085;
e2.. -17.0648464163823*(x39*x51 - x42*x48)*b55 + x1 =E= 0;
e3.. -17.0648464163823*(x42*x48 - x39*x51)*b55 + x2 =E= 0;
e4.. -(1.61712247324614*(sqr(x43) + sqr(x52)) - 1.61712247324614*(x43*x44 + x52
*x53) + 13.6979785969084*(x43*x53 - x44*x52))*b56 + x3 =E= 0;
e5.. -(1.61712247324614*(sqr(x44) + sqr(x53)) - 1.61712247324614*(x44*x43 + x53
*x52) + 13.6979785969084*(x44*x52 - x43*x53))*b56 + x4 =E= 0;
e6.. -(1.28200913842411*(sqr(x41) + sqr(x50)) - 1.28200913842411*(x41*x42 + x50
*x51) + 5.58824496236153*(x41*x51 - x42*x50))*b57 + x5 =E= 0;
e7.. -(1.28200913842411*(sqr(x42) + sqr(x51)) - 1.28200913842411*(x42*x41 + x51
*x50) + 5.58824496236153*(x42*x50 - x41*x51))*b57 + x6 =E= 0;
e8.. -(1.1550874808901*(sqr(x42) + sqr(x51)) - 1.1550874808901*(x42*x43 + x51*
x52) + 9.78427042636317*(x42*x52 - x43*x51))*b58 + x7 =E= 0;
e9.. -(1.1550874808901*(sqr(x43) + sqr(x52)) - 1.1550874808901*(x43*x42 + x52*
x51) + 9.78427042636317*(x43*x51 - x42*x52))*b58 + x8 =E= 0;
e10.. -16*(x44*x47 - x38*x53)*b59 + x9 =E= 0;
e11.. -16*(x38*x53 - x44*x47)*b59 + x10 =E= 0;
e12.. -(1.94219124871473*(sqr(x40) + sqr(x49)) - 1.94219124871473*(x40*x41 +
x49*x50) + 10.5106820518679*(x40*x50 - x41*x49))*b60 + x11 =E= 0;
e13.. -(1.94219124871473*(sqr(x41) + sqr(x50)) - 1.94219124871473*(x41*x40 +
x50*x49) + 10.5106820518679*(x41*x49 - x40*x50))*b60 + x12 =E= 0;
e14.. -17.3611111111111*(x37*x49 - x40*x46)*b61 + x13 =E= 0;
e15.. -17.3611111111111*(x40*x46 - x37*x49)*b61 + x14 =E= 0;
e16.. -(1.36518771331058*(sqr(x45) + sqr(x54)) - 1.36518771331058*(x45*x40 +
x54*x49) + 11.6040955631399*(x45*x49 - x40*x54))*b62 + x15 =E= 0;
e17.. -(1.36518771331058*(sqr(x40) + sqr(x49)) - 1.36518771331058*(x40*x45 +
x49*x54) + 11.6040955631399*(x40*x54 - x45*x49))*b62 + x16 =E= 0;
e18.. -(1.18760437929115*(sqr(x44) + sqr(x53)) - 1.18760437929115*(x44*x45 +
x53*x54) + 5.97513453330859*(x44*x54 - x45*x53))*b63 + x17 =E= 0;
e19.. -(1.18760437929115*(sqr(x45) + sqr(x54)) - 1.18760437929115*(x45*x44 +
x54*x53) + 5.97513453330859*(x45*x53 - x44*x54))*b63 + x18 =E= 0;
e20.. -(17.0648464163823*(sqr(x39) + sqr(x48)) - 17.0648464163823*(x39*x42 +
x48*x51))*b55 + x19 =E= 0;
e21.. -(17.0648464163823*(sqr(x42) + sqr(x51)) - 17.0648464163823*(x42*x39 +
x51*x48))*b55 + x20 =E= 0;
e22.. -(13.6234785969084*(sqr(x43) + sqr(x52)) - 13.6979785969084*(x43*x44 +
x52*x53) - 1.61712247324614*(x43*x53 - x44*x52))*b56 + x21 =E= 0;
e23.. -(13.6234785969084*(sqr(x44) + sqr(x53)) - 13.6979785969084*(x44*x43 +
x53*x52) - 1.61712247324614*(x44*x52 - x43*x53))*b56 + x22 =E= 0;
e24.. -(5.40924496236153*(sqr(x41) + sqr(x50)) - 5.58824496236153*(x41*x42 +
x50*x51) - 1.28200913842411*(x41*x51 - x42*x50))*b57 + x23 =E= 0;
e25.. -(5.40924496236153*(sqr(x42) + sqr(x51)) - 5.58824496236153*(x42*x41 +
x51*x50) - 1.28200913842411*(x42*x50 - x41*x51))*b57 + x24 =E= 0;
e26.. -(9.67977042636317*(sqr(x42) + sqr(x51)) - 9.78427042636317*(x42*x43 +
x51*x52) - 1.1550874808901*(x42*x52 - x43*x51))*b58 + x25 =E= 0;
e27.. -(9.67977042636317*(sqr(x43) + sqr(x52)) - 9.78427042636317*(x43*x42 +
x52*x51) - 1.1550874808901*(x43*x51 - x42*x52))*b58 + x26 =E= 0;
e28.. -(16*(sqr(x44) + sqr(x53)) - 16*(x44*x38 + x53*x47))*b59 + x27 =E= 0;
e29.. -(16*(sqr(x38) + sqr(x47)) - 16*(x38*x44 + x47*x53))*b59 + x28 =E= 0;
e30.. -(10.4316820518679*(sqr(x40) + sqr(x49)) - 10.5106820518679*(x40*x41 +
x49*x50) - 1.94219124871473*(x40*x50 - x41*x49))*b60 + x29 =E= 0;
e31.. -(10.4316820518679*(sqr(x41) + sqr(x50)) - 10.5106820518679*(x41*x40 +
x50*x49) - 1.94219124871473*(x41*x49 - x40*x50))*b60 + x30 =E= 0;
e32.. -(17.3611111111111*(sqr(x37) + sqr(x46)) - 17.3611111111111*(x37*x40 +
x46*x49))*b61 + x31 =E= 0;
e33.. -(17.3611111111111*(sqr(x40) + sqr(x49)) - 17.3611111111111*(x40*x37 +
x49*x46))*b61 + x32 =E= 0;
e34.. -(11.5160955631399*(sqr(x45) + sqr(x54)) - 11.6040955631399*(x45*x40 +
x54*x49) - 1.36518771331058*(x45*x49 - x40*x54))*b62 + x33 =E= 0;
e35.. -(11.5160955631399*(sqr(x40) + sqr(x49)) - 11.6040955631399*(x40*x45 +
x49*x54) - 1.36518771331058*(x40*x54 - x45*x49))*b62 + x34 =E= 0;
e36.. -(5.82213453330859*(sqr(x44) + sqr(x53)) - 5.97513453330859*(x44*x45 +
x53*x54) - 1.18760437929115*(x44*x54 - x45*x53))*b63 + x35 =E= 0;
e37.. -(5.82213453330859*(sqr(x45) + sqr(x54)) - 5.97513453330859*(x45*x44 +
x54*x53) - 1.18760437929115*(x45*x53 - x44*x54))*b63 + x36 =E= 0;
e38.. sqr(x1) + sqr(x19) =L= 9;
e39.. sqr(x2) + sqr(x20) =L= 9;
e40.. sqr(x3) + sqr(x21) =L= 6.25;
e41.. sqr(x4) + sqr(x22) =L= 6.25;
e42.. sqr(x5) + sqr(x23) =L= 2.25;
e43.. sqr(x6) + sqr(x24) =L= 2.25;
e44.. sqr(x7) + sqr(x25) =L= 2.25;
e45.. sqr(x8) + sqr(x26) =L= 2.25;
e46.. sqr(x9) + sqr(x27) =L= 6.25;
e47.. sqr(x10) + sqr(x28) =L= 6.25;
e48.. sqr(x11) + sqr(x29) =L= 6.25;
e49.. sqr(x12) + sqr(x30) =L= 6.25;
e50.. sqr(x13) + sqr(x31) =L= 6.25;
e51.. sqr(x14) + sqr(x32) =L= 6.25;
e52.. sqr(x15) + sqr(x33) =L= 6.25;
e53.. sqr(x16) + sqr(x34) =L= 6.25;
e54.. sqr(x17) + sqr(x35) =L= 6.25;
e55.. sqr(x18) + sqr(x36) =L= 6.25;
e56.. sqr(x37) + sqr(x46) =L= 1.21;
e57.. sqr(x38) + sqr(x47) =L= 1.21;
e58.. sqr(x39) + sqr(x48) =L= 1.21;
e59.. sqr(x40) + sqr(x49) =L= 1.21;
e60.. sqr(x41) + sqr(x50) =L= 1.21;
e61.. sqr(x42) + sqr(x51) =L= 1.21;
e62.. sqr(x43) + sqr(x52) =L= 1.21;
e63.. sqr(x44) + sqr(x53) =L= 1.21;
e64.. sqr(x45) + sqr(x54) =L= 1.21;
e65.. sqr(x37) + sqr(x46) =G= 0.81;
e66.. sqr(x38) + sqr(x47) =G= 0.81;
e67.. sqr(x39) + sqr(x48) =G= 0.81;
e68.. sqr(x40) + sqr(x49) =G= 0.81;
e69.. sqr(x41) + sqr(x50) =G= 0.81;
e70.. sqr(x42) + sqr(x51) =G= 0.81;
e71.. sqr(x43) + sqr(x52) =G= 0.81;
e72.. sqr(x44) + sqr(x53) =G= 0.81;
e73.. sqr(x45) + sqr(x54) =G= 0.81;
e74.. x64 =L= 2.5;
e75.. x65 =L= 3;
e76.. x66 =L= 2.7;
e77.. x64 =G= 0.1;
e78.. x65 =G= 0.1;
e79.. x66 =G= 0.1;
e80.. x67 =L= 3;
e81.. x68 =L= 3;
e82.. x69 =L= 3;
e83.. x67 =G= -3;
e84.. x68 =G= -3;
e85.. x69 =G= -3;
e86.. x46 =E= 0;
e87.. x13 - x64 =E= 0;
e88.. x10 - x65 =E= 0;
e89.. x1 - x66 =E= 0;
e90.. x31 - x67 =E= 0;
e91.. x28 - x68 =E= 0;
e92.. x19 - x69 =E= 0;
e93.. x11 + x14 + x16 =E= 0;
e94.. x5 + x12 =E= -0.9;
e95.. x2 + x6 + x7 =E= 0;
e96.. x3 + x8 =E= -1;
e97.. x4 + x9 + x17 =E= 0;
e98.. x15 + x18 =E= -1.25;
e99.. x29 + x32 + x34 =E= 0;
e100.. x23 + x30 =E= -0.3;
e101.. x20 + x24 + x25 =E= 0;
e102.. x21 + x26 =E= -0.35;
e103.. x22 + x27 + x35 =E= 0;
e104.. x33 + x36 =E= -0.5;
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