MINLPLib
A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Instance transswitch0009p
Optimal Transmission Switching problem modeled using trigonometric functions (polar coordinates)
| Formatsⓘ | ams gms mod nl osil py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | 3203.68685600 (COUENNE) 5296.66199800 (GUROBI) 1945.25093600 (LINDO) 4145.75491500 (SCIP) 1188.75000000 (SHOT) 1192.18333100 (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ⓘ | 139 |
| #Linear Constraintsⓘ | 85 |
| #Quadratic Constraintsⓘ | 18 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 36 |
| Operands in Gen. Nonlin. Functionsⓘ | cos mul sin sqr |
| Constraints curvatureⓘ | indefinite |
| #Nonzeros in Jacobianⓘ | 397 |
| #Nonlinear Nonzeros in Jacobianⓘ | 216 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 219 |
| #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
* 140 56 33 51 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
* 401 182 219 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,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;
e1.. 1100*sqr(x64) + 500*x64 + 850*sqr(x65) + 120*x65 + 1225*sqr(x66) + 100*x66
- objvar =E= -1085;
e2.. -17.0648464163823*x3*x6*sin(x48 - x51)*b55 + x10 =E= 0;
e3.. -17.0648464163823*x6*x3*sin(x51 - x48)*b55 + x11 =E= 0;
e4.. -(1.61712247324614*sqr(x7) - 1.61712247324614*x7*x8*cos(x52 - x53) +
13.6979785969084*x7*x8*sin(x52 - x53))*b56 + x12 =E= 0;
e5.. -(1.61712247324614*sqr(x8) - 1.61712247324614*x8*x7*cos(x53 - x52) +
13.6979785969084*x8*x7*sin(x53 - x52))*b56 + x13 =E= 0;
e6.. -(1.28200913842411*sqr(x5) - 1.28200913842411*x5*x6*cos(x50 - x51) +
5.58824496236153*x5*x6*sin(x50 - x51))*b57 + x14 =E= 0;
e7.. -(1.28200913842411*sqr(x6) - 1.28200913842411*x6*x5*cos(x51 - x50) +
5.58824496236153*x6*x5*sin(x51 - x50))*b57 + x15 =E= 0;
e8.. -(1.1550874808901*sqr(x6) - 1.1550874808901*x6*x7*cos(x51 - x52) +
9.78427042636317*x6*x7*sin(x51 - x52))*b58 + x16 =E= 0;
e9.. -(1.1550874808901*sqr(x7) - 1.1550874808901*x7*x6*cos(x52 - x51) +
9.78427042636317*x7*x6*sin(x52 - x51))*b58 + x17 =E= 0;
e10.. -16*x8*x2*sin(x53 - x47)*b59 + x18 =E= 0;
e11.. -16*x2*x8*sin(x47 - x53)*b59 + x19 =E= 0;
e12.. -(1.94219124871473*sqr(x4) - 1.94219124871473*x4*x5*cos(x49 - x50) +
10.5106820518679*x4*x5*sin(x49 - x50))*b60 + x20 =E= 0;
e13.. -(1.94219124871473*sqr(x5) - 1.94219124871473*x5*x4*cos(x50 - x49) +
10.5106820518679*x5*x4*sin(x50 - x49))*b60 + x21 =E= 0;
e14.. -17.3611111111111*x1*x4*sin(x46 - x49)*b61 + x22 =E= 0;
e15.. -17.3611111111111*x4*x1*sin(x49 - x46)*b61 + x23 =E= 0;
e16.. -(1.36518771331058*sqr(x9) - 1.36518771331058*x9*x4*cos(x54 - x49) +
11.6040955631399*x9*x4*sin(x54 - x49))*b62 + x24 =E= 0;
e17.. -(1.36518771331058*sqr(x4) - 1.36518771331058*x4*x9*cos(x49 - x54) +
11.6040955631399*x4*x9*sin(x49 - x54))*b62 + x25 =E= 0;
e18.. -(1.18760437929115*sqr(x8) - 1.18760437929115*x8*x9*cos(x53 - x54) +
5.97513453330859*x8*x9*sin(x53 - x54))*b63 + x26 =E= 0;
e19.. -(1.18760437929115*sqr(x9) - 1.18760437929115*x9*x8*cos(x54 - x53) +
5.97513453330859*x9*x8*sin(x54 - x53))*b63 + x27 =E= 0;
e20.. -(17.0648464163823*sqr(x3) - 17.0648464163823*x3*x6*cos(x48 - x51))*b55
+ x28 =E= 0;
e21.. -(17.0648464163823*sqr(x6) - 17.0648464163823*x6*x3*cos(x51 - x48))*b55
+ x29 =E= 0;
e22.. -(13.6234785969084*sqr(x7) - 13.6979785969084*x7*x8*cos(x52 - x53) -
1.61712247324614*x7*x8*sin(x52 - x53))*b56 + x30 =E= 0;
e23.. -(13.6234785969084*sqr(x8) - 13.6979785969084*x8*x7*cos(x53 - x52) -
1.61712247324614*x8*x7*sin(x53 - x52))*b56 + x31 =E= 0;
e24.. -(5.40924496236153*sqr(x5) - 5.58824496236153*x5*x6*cos(x50 - x51) -
1.28200913842411*x5*x6*sin(x50 - x51))*b57 + x32 =E= 0;
e25.. -(5.40924496236153*sqr(x6) - 5.58824496236153*x6*x5*cos(x51 - x50) -
1.28200913842411*x6*x5*sin(x51 - x50))*b57 + x33 =E= 0;
e26.. -(9.67977042636317*sqr(x6) - 9.78427042636317*x6*x7*cos(x51 - x52) -
1.1550874808901*x6*x7*sin(x51 - x52))*b58 + x34 =E= 0;
e27.. -(9.67977042636317*sqr(x7) - 9.78427042636317*x7*x6*cos(x52 - x51) -
1.1550874808901*x7*x6*sin(x52 - x51))*b58 + x35 =E= 0;
e28.. -(16*sqr(x8) - 16*x8*x2*cos(x53 - x47))*b59 + x36 =E= 0;
e29.. -(16*sqr(x2) - 16*x2*x8*cos(x47 - x53))*b59 + x37 =E= 0;
e30.. -(10.4316820518679*sqr(x4) - 10.5106820518679*x4*x5*cos(x49 - x50) -
1.94219124871473*x4*x5*sin(x49 - x50))*b60 + x38 =E= 0;
e31.. -(10.4316820518679*sqr(x5) - 10.5106820518679*x5*x4*cos(x50 - x49) -
1.94219124871473*x5*x4*sin(x50 - x49))*b60 + x39 =E= 0;
e32.. -(17.3611111111111*sqr(x1) - 17.3611111111111*x1*x4*cos(x46 - x49))*b61
+ x40 =E= 0;
e33.. -(17.3611111111111*sqr(x4) - 17.3611111111111*x4*x1*cos(x49 - x46))*b61
+ x41 =E= 0;
e34.. -(11.5160955631399*sqr(x9) - 11.6040955631399*x9*x4*cos(x54 - x49) -
1.36518771331058*x9*x4*sin(x54 - x49))*b62 + x42 =E= 0;
e35.. -(11.5160955631399*sqr(x4) - 11.6040955631399*x4*x9*cos(x49 - x54) -
1.36518771331058*x4*x9*sin(x49 - x54))*b62 + x43 =E= 0;
e36.. -(5.82213453330859*sqr(x8) - 5.97513453330859*x8*x9*cos(x53 - x54) -
1.18760437929115*x8*x9*sin(x53 - x54))*b63 + x44 =E= 0;
e37.. -(5.82213453330859*sqr(x9) - 5.97513453330859*x9*x8*cos(x54 - x53) -
1.18760437929115*x9*x8*sin(x54 - x53))*b63 + x45 =E= 0;
e38.. sqr(x10) + sqr(x28) =L= 9;
e39.. sqr(x11) + sqr(x29) =L= 9;
e40.. sqr(x12) + sqr(x30) =L= 6.25;
e41.. sqr(x13) + sqr(x31) =L= 6.25;
e42.. sqr(x14) + sqr(x32) =L= 2.25;
e43.. sqr(x15) + sqr(x33) =L= 2.25;
e44.. sqr(x16) + sqr(x34) =L= 2.25;
e45.. sqr(x17) + sqr(x35) =L= 2.25;
e46.. sqr(x18) + sqr(x36) =L= 6.25;
e47.. sqr(x19) + sqr(x37) =L= 6.25;
e48.. sqr(x20) + sqr(x38) =L= 6.25;
e49.. sqr(x21) + sqr(x39) =L= 6.25;
e50.. sqr(x22) + sqr(x40) =L= 6.25;
e51.. sqr(x23) + sqr(x41) =L= 6.25;
e52.. sqr(x24) + sqr(x42) =L= 6.25;
e53.. sqr(x25) + sqr(x43) =L= 6.25;
e54.. sqr(x26) + sqr(x44) =L= 6.25;
e55.. sqr(x27) + sqr(x45) =L= 6.25;
e56.. x64 =L= 2.5;
e57.. x65 =L= 3;
e58.. x66 =L= 2.7;
e59.. x64 =G= 0.1;
e60.. x65 =G= 0.1;
e61.. x66 =G= 0.1;
e62.. x67 =L= 3;
e63.. x68 =L= 3;
e64.. x69 =L= 3;
e65.. x67 =G= -3;
e66.. x68 =G= -3;
e67.. x69 =G= -3;
e68.. x1 =L= 1.1;
e69.. x2 =L= 1.1;
e70.. x3 =L= 1.1;
e71.. x4 =L= 1.1;
e72.. x5 =L= 1.1;
e73.. x6 =L= 1.1;
e74.. x7 =L= 1.1;
e75.. x8 =L= 1.1;
e76.. x9 =L= 1.1;
e77.. x1 =G= 0.9;
e78.. x2 =G= 0.9;
e79.. x3 =G= 0.9;
e80.. x4 =G= 0.9;
e81.. x5 =G= 0.9;
e82.. x6 =G= 0.9;
e83.. x7 =G= 0.9;
e84.. x8 =G= 0.9;
e85.. x9 =G= 0.9;
e86.. x48 - x51 =G= -0.26;
e87.. - x48 + x51 =G= -0.26;
e88.. x52 - x53 =G= -0.26;
e89.. - x52 + x53 =G= -0.26;
e90.. x50 - x51 =G= -0.26;
e91.. - x50 + x51 =G= -0.26;
e92.. x51 - x52 =G= -0.26;
e93.. - x51 + x52 =G= -0.26;
e94.. - x47 + x53 =G= -0.26;
e95.. x47 - x53 =G= -0.26;
e96.. x49 - x50 =G= -0.26;
e97.. - x49 + x50 =G= -0.26;
e98.. x46 - x49 =G= -0.26;
e99.. - x46 + x49 =G= -0.26;
e100.. - x49 + x54 =G= -0.26;
e101.. x49 - x54 =G= -0.26;
e102.. x53 - x54 =G= -0.26;
e103.. - x53 + x54 =G= -0.26;
e104.. x48 - x51 =L= 0.26;
e105.. - x48 + x51 =L= 0.26;
e106.. x52 - x53 =L= 0.26;
e107.. - x52 + x53 =L= 0.26;
e108.. x50 - x51 =L= 0.26;
e109.. - x50 + x51 =L= 0.26;
e110.. x51 - x52 =L= 0.26;
e111.. - x51 + x52 =L= 0.26;
e112.. - x47 + x53 =L= 0.26;
e113.. x47 - x53 =L= 0.26;
e114.. x49 - x50 =L= 0.26;
e115.. - x49 + x50 =L= 0.26;
e116.. x46 - x49 =L= 0.26;
e117.. - x46 + x49 =L= 0.26;
e118.. - x49 + x54 =L= 0.26;
e119.. x49 - x54 =L= 0.26;
e120.. x53 - x54 =L= 0.26;
e121.. - x53 + x54 =L= 0.26;
e122.. x46 =E= 0;
e123.. x22 - x64 =E= 0;
e124.. x19 - x65 =E= 0;
e125.. x10 - x66 =E= 0;
e126.. x40 - x67 =E= 0;
e127.. x37 - x68 =E= 0;
e128.. x28 - x69 =E= 0;
e129.. x20 + x23 + x25 =E= 0;
e130.. x14 + x21 =E= -0.9;
e131.. x11 + x15 + x16 =E= 0;
e132.. x12 + x17 =E= -1;
e133.. x13 + x18 + x26 =E= 0;
e134.. x24 + x27 =E= -1.25;
e135.. x38 + x41 + x43 =E= 0;
e136.. x32 + x39 =E= -0.3;
e137.. x29 + x33 + x34 =E= 0;
e138.. x30 + x35 =E= -0.35;
e139.. x31 + x36 + x44 =E= 0;
e140.. x42 + x45 =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