MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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


Instance tspn10

Formats ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)
225.47373590 p1 ( gdx sol )
(infeas: 0)
225.12607160 p2 ( gdx sol )
(infeas: 5e-13)
Other points (infeas > 1e-08)  
Dual Bounds
202.39445910 (ANTIGONE)
225.12607080 (BARON)
214.86665950 (COUENNE)
203.45630180 (LINDO)
204.03369990 (SCIP)
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 tspn10Couenne.nl from minlp.org model 124
Application Traveling Salesman Problem with Neighborhoods
Added to library 21 Feb 2014
Problem type MBNLP
#Variables 65
#Binary Variables 45
#Integer Variables 0
#Nonlinear Variables 65
#Nonlinear Binary Variables 45
#Nonlinear Integer Variables 0
Objective Sense min
Objective type nonlinear
Objective curvature indefinite
#Nonzeros in Objective 65
#Nonlinear Nonzeros in Objective 65
#Constraints 21
#Linear Constraints 11
#Quadratic Constraints 10
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions mul sqr sqrt
Constraints curvature convex
#Nonzeros in Jacobian 113
#Nonlinear Nonzeros in Jacobian 20
#Nonzeros in (Upper-Left) Hessian of Lagrangian 760
#Nonzeros in Diagonal of Hessian of Lagrangian 20
#Blocks in Hessian of Lagrangian 1
Minimal blocksize in Hessian of Lagrangian 65
Maximal blocksize in Hessian of Lagrangian 65
Average blocksize in Hessian of Lagrangian 65.0
#Semicontinuities 0
#Nonlinear Semicontinuities 0
#SOS type 1 0
#SOS type 2 0
Minimal coefficient 8.2645e-03
Maximal coefficient 6.2667e+01
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
*         22       11        0       11        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         66       21       45        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        179       94       85        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,b21,b22,b23,b24,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,objvar;

Positive Variables  x10;

Binary Variables  b21,b22,b23,b24,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;

Equations  e1,e2,e3,e4,e5,e6,e7,e8,e9,e10,e11,e12,e13,e14,e15,e16,e17,e18,e19
          ,e20,e21,e22;


e1.. sqrt(sqr(x1 - x3) + sqr(x2 - x4))*b21 + sqrt(sqr(x1 - x5) + sqr(x2 - x6))*
     b22 + sqrt(sqr(x1 - x7) + sqr(x2 - x8))*b23 + sqrt(sqr(x1 - x9) + sqr(x2
      - x10))*b24 + sqrt(sqr(x1 - x11) + sqr(x2 - x12))*b25 + sqrt(sqr(x1 - x13
     ) + sqr(x2 - x14))*b26 + sqrt(sqr(x1 - x15) + sqr(x2 - x16))*b27 + sqrt(
     sqr(x1 - x17) + sqr(x2 - x18))*b28 + sqrt(sqr(x1 - x19) + sqr(x2 - x20))*
     b29 + sqrt(sqr(x3 - x5) + sqr(x4 - x6))*b30 + sqrt(sqr(x3 - x7) + sqr(x4
      - x8))*b31 + sqrt(sqr(x3 - x9) + sqr(x4 - x10))*b32 + sqrt(sqr(x3 - x11)
      + sqr(x4 - x12))*b33 + sqrt(sqr(x3 - x13) + sqr(x4 - x14))*b34 + sqrt(
     sqr(x3 - x15) + sqr(x4 - x16))*b35 + sqrt(sqr(x3 - x17) + sqr(x4 - x18))*
     b36 + sqrt(sqr(x3 - x19) + sqr(x4 - x20))*b37 + sqrt(sqr(x5 - x7) + sqr(x6
      - x8))*b38 + sqrt(sqr(x5 - x9) + sqr(x6 - x10))*b39 + sqrt(sqr(x5 - x11)
      + sqr(x6 - x12))*b40 + sqrt(sqr(x5 - x13) + sqr(x6 - x14))*b41 + sqrt(
     sqr(x5 - x15) + sqr(x6 - x16))*b42 + sqrt(sqr(x5 - x17) + sqr(x6 - x18))*
     b43 + sqrt(sqr(x5 - x19) + sqr(x6 - x20))*b44 + sqrt(sqr(x7 - x9) + sqr(x8
      - x10))*b45 + sqrt(sqr(x7 - x11) + sqr(x8 - x12))*b46 + sqrt(sqr(x7 - x13
     ) + sqr(x8 - x14))*b47 + sqrt(sqr(x7 - x15) + sqr(x8 - x16))*b48 + sqrt(
     sqr(x7 - x17) + sqr(x8 - x18))*b49 + sqrt(sqr(x7 - x19) + sqr(x8 - x20))*
     b50 + sqrt(sqr(x9 - x11) + sqr(x10 - x12))*b51 + sqrt(sqr(x9 - x13) + sqr(
     x10 - x14))*b52 + sqrt(sqr(x9 - x15) + sqr(x10 - x16))*b53 + sqrt(sqr(x9
      - x17) + sqr(x10 - x18))*b54 + sqrt(sqr(x9 - x19) + sqr(x10 - x20))*b55
      + sqrt(sqr(x11 - x13) + sqr(x12 - x14))*b56 + sqrt(sqr(x11 - x15) + sqr(
     x12 - x16))*b57 + sqrt(sqr(x11 - x17) + sqr(x12 - x18))*b58 + sqrt(sqr(x11
      - x19) + sqr(x12 - x20))*b59 + sqrt(sqr(x13 - x15) + sqr(x14 - x16))*b60
      + sqrt(sqr(x13 - x17) + sqr(x14 - x18))*b61 + sqrt(sqr(x13 - x19) + sqr(
     x14 - x20))*b62 + sqrt(sqr(x15 - x17) + sqr(x16 - x18))*b63 + sqrt(sqr(x15
      - x19) + sqr(x16 - x20))*b64 + sqrt(sqr(x17 - x19) + sqr(x18 - x20))*b65
      - objvar =E= 0;

e2.. 0.444444444444444*sqr(x1) - 62.6666666666667*x1 + 0.0236686390532544*sqr(
     x2) - 0.63905325443787*x2 =L= -2212.31360946746;

e3.. 0.0204081632653061*sqr(x3) - 4.73469387755102*x3 + 0.0330578512396694*sqr(
     x4) - 5.38842975206612*x4 =L= -493.190757294653;

e4.. 0.0110803324099723*sqr(x5) - 1.14127423822715*x5 + 0.0493827160493827*sqr(
     x6) - 6.66666666666667*x6 =L= -253.387811634349;

e5.. 0.04*sqr(x7) - 7.84*x7 + 0.0625*sqr(x8) - 8*x8 =L= -639.16;

e6.. 0.0177777777777778*sqr(x9) - 3.11111111111111*x9 + 0.013840830449827*sqr(
     x10) - 0.235294117647059*x10 =L= -136.111111111111;

e7.. 0.0090702947845805*sqr(x11) - 1.4421768707483*x11 + 0.04*sqr(x12) - 7.68*
     x12 =L= -424.966530612245;

e8.. 0.0330578512396694*sqr(x13) - 3.27272727272727*x13 + 0.0625*sqr(x14) - 
     7.125*x14 =L= -283.0625;

e9.. 0.0177777777777778*sqr(x15) - 2.57777777777778*x15 + 0.0090702947845805*
     sqr(x16) - 1.80498866213152*x16 =L= -182.242630385488;

e10.. 0.16*sqr(x17) - 38.56*x17 + 0.00826446280991736*sqr(x18) - 
      0.512396694214876*x18 =L= -2330.18214876033;

e11.. 0.0330578512396694*sqr(x19) - 5.52066115702479*x19 + 0.0236686390532544*
      sqr(x20) - 1.82248520710059*x20 =L= -264.570443542472;

e12..    b21 + b22 + b23 + b24 + b25 + b26 + b27 + b28 + b29 =E= 2;

e13..    b21 + b30 + b31 + b32 + b33 + b34 + b35 + b36 + b37 =E= 2;

e14..    b22 + b30 + b38 + b39 + b40 + b41 + b42 + b43 + b44 =E= 2;

e15..    b23 + b31 + b38 + b45 + b46 + b47 + b48 + b49 + b50 =E= 2;

e16..    b24 + b32 + b39 + b45 + b51 + b52 + b53 + b54 + b55 =E= 2;

e17..    b25 + b33 + b40 + b46 + b51 + b56 + b57 + b58 + b59 =E= 2;

e18..    b26 + b34 + b41 + b47 + b52 + b56 + b60 + b61 + b62 =E= 2;

e19..    b27 + b35 + b42 + b48 + b53 + b57 + b60 + b63 + b64 =E= 2;

e20..    b28 + b36 + b43 + b49 + b54 + b58 + b61 + b63 + b65 =E= 2;

e21..    b29 + b37 + b44 + b50 + b55 + b59 + b62 + b64 + b65 =E= 2;

e22..    b24 + b29 + b55 =L= 2;

* set non-default bounds
x1.lo = 69; x1.up = 72;
x2.lo = 7; x2.up = 20;
x3.lo = 109; x3.up = 123;
x4.lo = 76; x4.up = 87;
x5.lo = 42; x5.up = 61;
x6.lo = 63; x6.up = 72;
x7.lo = 93; x7.up = 103;
x8.lo = 60; x8.up = 68;
x9.lo = 80; x9.up = 95;
x10.up = 17;
x11.lo = 69; x11.up = 90;
x12.lo = 91; x12.up = 101;
x13.lo = 44; x13.up = 55;
x14.lo = 53; x14.up = 61;
x15.lo = 65; x15.up = 80;
x16.lo = 89; x16.up = 110;
x17.lo = 118; x17.up = 123;
x18.lo = 20; x18.up = 42;
x19.lo = 78; x19.up = 89;
x20.lo = 32; x20.up = 45;

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: 2022-04-26 Git hash: de668763
Imprint / Privacy Policy / License: CC-BY 4.0