MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

Home // Instances // Documentation // Download // Statistics


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)
5296.68620400 p1 ( gdx sol )
(infeas: 6e-15)
Other points (infeas > 1e-08)  
Dual Bounds
2545.09965900 (ANTIGONE)
3462.56938000 (BARON)
5183.48288300 (COUENNE)
4624.68080100 (LINDO)
5290.04547300 (SCIP)
1188.75000500 (SHOT)
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 of Objective Gradient and Jacobian
Sparsity Hessian of Lagrangian Sparsity of 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: 2022-05-24 Git hash: 1198c186
Imprint / Privacy Policy / License: CC-BY 4.0