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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)
225.12607160 (BARON)
214.86665950 (COUENNE)
224.07811870 (GUROBI)
203.45630180 (LINDO)
204.03369990 (SCIP)
0.00000000 (SHOT)
222.49326070 (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 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;


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