MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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


Instance tspn12

Formats ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)
262.64739570 p1 ( gdx sol )
(infeas: 0)
Other points (infeas > 1e-08)  
Dual Bounds
222.74756250 (ANTIGONE)
262.64739570 (BARON)
240.46669460 (COUENNE)
256.85811000 (GUROBI)
229.72886920 (LINDO)
194.63869960 (SCIP)
0.00000000 (SHOT)
255.11016150 (XPRESS)
References Gentilini, Iacopo, Margot, François, and Shimada, Kenji, The Traveling Salesman Problem with Neighborhoods: MINLP Solution, Optimization Methods and Software, 28:2, 2013, 364-378.
Source tspn12Couenne.nl from minlp.org model 124
Application Traveling Salesman Problem with Neighborhoods
Added to library 21 Feb 2014
Problem type MBNLP
#Variables 90
#Binary Variables 66
#Integer Variables 0
#Nonlinear Variables 90
#Nonlinear Binary Variables 66
#Nonlinear Integer Variables 0
Objective Sense min
Objective type nonlinear
Objective curvature indefinite
#Nonzeros in Objective 90
#Nonlinear Nonzeros in Objective 90
#Constraints 26
#Linear Constraints 14
#Quadratic Constraints 12
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions mul sqr sqrt
Constraints curvature convex
#Nonzeros in Jacobian 165
#Nonlinear Nonzeros in Jacobian 24
#Nonzeros in (Upper-Left) Hessian of Lagrangian 1104
#Nonzeros in Diagonal of Hessian of Lagrangian 24
#Blocks in Hessian of Lagrangian 1
Minimal blocksize in Hessian of Lagrangian 90
Maximal blocksize in Hessian of Lagrangian 90
Average blocksize in Hessian of Lagrangian 90.0
#Semicontinuities 0
#Nonlinear Semicontinuities 0
#SOS type 1 0
#SOS type 2 0
Minimal coefficient 5.9172e-03
Maximal coefficient 9.0370e+00
Infeasibility of initial point 2
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
*         27       13        0       14        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         91       25       66        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        256      142      114        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,b25,b26,b27,b28,b29,b30,b31,b32,b33,b34,b35,b36
          ,b37,b38,b39,b40,b41,b42,b43,b44,b45,b46,b47,b48,b49,b50,b51,b52,b53
          ,b54,b55,b56,b57,b58,b59,b60,b61,b62,b63,b64,b65,b66,b67,b68,b69,b70
          ,b71,b72,b73,b74,b75,b76,b77,b78,b79,b80,b81,b82,b83,b84,b85,b86,b87
          ,b88,b89,b90,objvar;

Positive Variables  x1,x12;

Binary Variables  b25,b26,b27,b28,b29,b30,b31,b32,b33,b34,b35,b36,b37,b38,b39
          ,b40,b41,b42,b43,b44,b45,b46,b47,b48,b49,b50,b51,b52,b53,b54,b55,b56
          ,b57,b58,b59,b60,b61,b62,b63,b64,b65,b66,b67,b68,b69,b70,b71,b72,b73
          ,b74,b75,b76,b77,b78,b79,b80,b81,b82,b83,b84,b85,b86,b87,b88,b89,b90;

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;


e1.. sqrt(sqr(x1 - x3) + sqr(x2 - x4))*b25 + sqrt(sqr(x1 - x5) + sqr(x2 - x6))*
     b26 + sqrt(sqr(x1 - x7) + sqr(x2 - x8))*b27 + sqrt(sqr(x1 - x9) + sqr(x2
      - x10))*b28 + sqrt(sqr(x1 - x11) + sqr(x2 - x12))*b29 + sqrt(sqr(x1 - x13
     ) + sqr(x2 - x14))*b30 + sqrt(sqr(x1 - x15) + sqr(x2 - x16))*b31 + sqrt(
     sqr(x1 - x17) + sqr(x2 - x18))*b32 + sqrt(sqr(x1 - x19) + sqr(x2 - x20))*
     b33 + sqrt(sqr(x1 - x21) + sqr(x2 - x22))*b34 + sqrt(sqr(x1 - x23) + sqr(
     x2 - x24))*b35 + sqrt(sqr(x3 - x5) + sqr(x4 - x6))*b36 + sqrt(sqr(x3 - x7)
      + sqr(x4 - x8))*b37 + sqrt(sqr(x3 - x9) + sqr(x4 - x10))*b38 + sqrt(sqr(
     x3 - x11) + sqr(x4 - x12))*b39 + sqrt(sqr(x3 - x13) + sqr(x4 - x14))*b40
      + sqrt(sqr(x3 - x15) + sqr(x4 - x16))*b41 + sqrt(sqr(x3 - x17) + sqr(x4
      - x18))*b42 + sqrt(sqr(x3 - x19) + sqr(x4 - x20))*b43 + sqrt(sqr(x3 - x21
     ) + sqr(x4 - x22))*b44 + sqrt(sqr(x3 - x23) + sqr(x4 - x24))*b45 + sqrt(
     sqr(x5 - x7) + sqr(x6 - x8))*b46 + sqrt(sqr(x5 - x9) + sqr(x6 - x10))*b47
      + sqrt(sqr(x5 - x11) + sqr(x6 - x12))*b48 + sqrt(sqr(x5 - x13) + sqr(x6
      - x14))*b49 + sqrt(sqr(x5 - x15) + sqr(x6 - x16))*b50 + sqrt(sqr(x5 - x17
     ) + sqr(x6 - x18))*b51 + sqrt(sqr(x5 - x19) + sqr(x6 - x20))*b52 + sqrt(
     sqr(x5 - x21) + sqr(x6 - x22))*b53 + sqrt(sqr(x5 - x23) + sqr(x6 - x24))*
     b54 + sqrt(sqr(x7 - x9) + sqr(x8 - x10))*b55 + sqrt(sqr(x7 - x11) + sqr(x8
      - x12))*b56 + sqrt(sqr(x7 - x13) + sqr(x8 - x14))*b57 + sqrt(sqr(x7 - x15
     ) + sqr(x8 - x16))*b58 + sqrt(sqr(x7 - x17) + sqr(x8 - x18))*b59 + sqrt(
     sqr(x7 - x19) + sqr(x8 - x20))*b60 + sqrt(sqr(x7 - x21) + sqr(x8 - x22))*
     b61 + sqrt(sqr(x7 - x23) + sqr(x8 - x24))*b62 + sqrt(sqr(x9 - x11) + sqr(
     x10 - x12))*b63 + sqrt(sqr(x9 - x13) + sqr(x10 - x14))*b64 + sqrt(sqr(x9
      - x15) + sqr(x10 - x16))*b65 + sqrt(sqr(x9 - x17) + sqr(x10 - x18))*b66
      + sqrt(sqr(x9 - x19) + sqr(x10 - x20))*b67 + sqrt(sqr(x9 - x21) + sqr(x10
      - x22))*b68 + sqrt(sqr(x9 - x23) + sqr(x10 - x24))*b69 + sqrt(sqr(x11 - 
     x13) + sqr(x12 - x14))*b70 + sqrt(sqr(x11 - x15) + sqr(x12 - x16))*b71 + 
     sqrt(sqr(x11 - x17) + sqr(x12 - x18))*b72 + sqrt(sqr(x11 - x19) + sqr(x12
      - x20))*b73 + sqrt(sqr(x11 - x21) + sqr(x12 - x22))*b74 + sqrt(sqr(x11 - 
     x23) + sqr(x12 - x24))*b75 + sqrt(sqr(x13 - x15) + sqr(x14 - x16))*b76 + 
     sqrt(sqr(x13 - x17) + sqr(x14 - x18))*b77 + sqrt(sqr(x13 - x19) + sqr(x14
      - x20))*b78 + sqrt(sqr(x13 - x21) + sqr(x14 - x22))*b79 + sqrt(sqr(x13 - 
     x23) + sqr(x14 - x24))*b80 + sqrt(sqr(x15 - x17) + sqr(x16 - x18))*b81 + 
     sqrt(sqr(x15 - x19) + sqr(x16 - x20))*b82 + sqrt(sqr(x15 - x21) + sqr(x16
      - x22))*b83 + sqrt(sqr(x15 - x23) + sqr(x16 - x24))*b84 + sqrt(sqr(x17 - 
     x19) + sqr(x18 - x20))*b85 + sqrt(sqr(x17 - x21) + sqr(x18 - x22))*b86 + 
     sqrt(sqr(x17 - x23) + sqr(x18 - x24))*b87 + sqrt(sqr(x19 - x21) + sqr(x20
      - x22))*b88 + sqrt(sqr(x19 - x23) + sqr(x20 - x24))*b89 + sqrt(sqr(x21 - 
     x23) + sqr(x22 - x24))*b90 - objvar =E= 0;

e2.. 0.013840830449827*sqr(x1) - 0.235294117647059*x1 + 0.0177777777777778*sqr(
     x2) - 2.00888888888889*x2 =L= -56.7511111111111;

e3.. 0.013840830449827*sqr(x3) - 3.05882352941176*x3 + 0.0625*sqr(x4) - 5.75*x4
      =L= -300.25;

e4.. 0.0204081632653061*sqr(x5) - 1.3469387755102*x5 + 0.0110803324099723*sqr(
     x6) - 1.65096952908587*x6 =L= -82.7231047543671;

e5.. 0.0090702947845805*sqr(x7) - 0.299319727891156*x7 + 0.0277777777777778*
     sqr(x8) - 4.44444444444444*x8 =L= -179.24716553288;

e6.. 0.0277777777777778*sqr(x9) - 2.16666666666667*x9 + 0.015625*sqr(x10) - 
     1.40625*x10 =L= -72.890625;

e7.. 0.0110803324099723*sqr(x11) - 2.29362880886427*x11 + 0.0204081632653061*
     sqr(x12) - 0.285714285714286*x12 =L= -118.695290858726;

e8.. 0.0110803324099723*sqr(x13) - 2.27146814404432*x13 + 0.0204081632653061*
     sqr(x14) - 2.57142857142857*x14 =L= -196.412742382271;

e9.. 0.0330578512396694*sqr(x15) - 4.72727272727273*x15 + 0.0493827160493827*
     sqr(x16) - 9.03703703703704*x16 =L= -581.444444444444;

e10.. 0.0493827160493827*sqr(x17) - 5.48148148148148*x17 + 0.0204081632653061*
      sqr(x18) - 0.775510204081633*x18 =L= -158.478458049887;

e11.. 0.00591715976331361*sqr(x19) - 0.733727810650888*x19 + 0.0236686390532544
      *sqr(x20) - 2.24852071005917*x20 =L= -75.1479289940828;

e12.. 0.0330578512396694*sqr(x21) - 1.48760330578512*x21 + 0.0123456790123457*
      sqr(x22) - 0.839506172839506*x22 =L= -30.0071421283542;

e13.. 0.0277777777777778*sqr(x23) - 5.44444444444444*x23 + 0.0493827160493827*
      sqr(x24) - 8.24691358024691*x24 =L= -610.086419753086;

e14..    b25 + b26 + b27 + b28 + b29 + b30 + b31 + b32 + b33 + b34 + b35 =E= 2;

e15..    b25 + b36 + b37 + b38 + b39 + b40 + b41 + b42 + b43 + b44 + b45 =E= 2;

e16..    b26 + b36 + b46 + b47 + b48 + b49 + b50 + b51 + b52 + b53 + b54 =E= 2;

e17..    b27 + b37 + b46 + b55 + b56 + b57 + b58 + b59 + b60 + b61 + b62 =E= 2;

e18..    b28 + b38 + b47 + b55 + b63 + b64 + b65 + b66 + b67 + b68 + b69 =E= 2;

e19..    b29 + b39 + b48 + b56 + b63 + b70 + b71 + b72 + b73 + b74 + b75 =E= 2;

e20..    b30 + b40 + b49 + b57 + b64 + b70 + b76 + b77 + b78 + b79 + b80 =E= 2;

e21..    b31 + b41 + b50 + b58 + b65 + b71 + b76 + b81 + b82 + b83 + b84 =E= 2;

e22..    b32 + b42 + b51 + b59 + b66 + b72 + b77 + b81 + b85 + b86 + b87 =E= 2;

e23..    b33 + b43 + b52 + b60 + b67 + b73 + b78 + b82 + b85 + b88 + b89 =E= 2;

e24..    b34 + b44 + b53 + b61 + b68 + b74 + b79 + b83 + b86 + b88 + b90 =E= 2;

e25..    b35 + b45 + b54 + b62 + b69 + b75 + b80 + b84 + b87 + b89 + b90 =E= 2;

e26..    b26 + b27 + b34 + b46 + b53 + b61 =L= 3;

e27..    b26 + b27 + b46 =L= 2;

* set non-default bounds
x1.up = 17;
x2.lo = 49; x2.up = 64;
x3.lo = 102; x3.up = 119;
x4.lo = 42; x4.up = 50;
x5.lo = 26; x5.up = 40;
x6.lo = 65; x6.up = 84;
x7.lo = 6; x7.up = 27;
x8.lo = 74; x8.up = 86;
x9.lo = 33; x9.up = 45;
x10.lo = 37; x10.up = 53;
x11.lo = 94; x11.up = 113;
x12.up = 14;
x13.lo = 93; x13.up = 112;
x14.lo = 56; x14.up = 70;
x15.lo = 66; x15.up = 77;
x16.lo = 87; x16.up = 96;
x17.lo = 51; x17.up = 60;
x18.lo = 12; x18.up = 26;
x19.lo = 49; x19.up = 75;
x20.lo = 41; x20.up = 54;
x21.lo = 17; x21.up = 28;
x22.lo = 25; x22.up = 43;
x23.lo = 92; x23.up = 104;
x24.lo = 79; x24.up = 88;

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: 2025-07-31 Git hash: 75b0bef7
Imprint / Privacy Policy / License: CC-BY 4.0