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Instance tspn08

Formatsⓘ	ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)ⓘ	290.56685390 p1 ( gdx sol ) (infeas: 0)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	266.38129820 (ANTIGONE) 290.56685390 (BARON) 285.75075350 (COUENNE) 288.68966410 (GUROBI) 264.99874910 (LINDO) 284.90970650 (SCIP) 0.00000000 (SHOT) 289.64297140 (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ⓘ	tspn8Couenne.nl from minlp.org model 124
Applicationⓘ	Traveling Salesman Problem with Neighborhoods
Added to libraryⓘ	21 Feb 2014
Problem typeⓘ	MBNLP
#Variablesⓘ	44
#Binary Variablesⓘ	28
#Integer Variablesⓘ	0
#Nonlinear Variablesⓘ	44
#Nonlinear Binary Variablesⓘ	28
#Nonlinear Integer Variablesⓘ	0
Objective Senseⓘ	min
Objective typeⓘ	nonlinear
Objective curvatureⓘ	indefinite
#Nonzeros in Objectiveⓘ	44
#Nonlinear Nonzeros in Objectiveⓘ	44
#Constraintsⓘ	18
#Linear Constraintsⓘ	10
#Quadratic Constraintsⓘ	8
#Polynomial Constraintsⓘ	0
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ	mul sqr sqrt
Constraints curvatureⓘ	convex
#Nonzeros in Jacobianⓘ	92
#Nonlinear Nonzeros in Jacobianⓘ	16
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	480
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	16
#Blocks in Hessian of Lagrangianⓘ	1
Minimal blocksize in Hessian of Lagrangianⓘ	44
Maximal blocksize in Hessian of Lagrangianⓘ	44
Average blocksize in Hessian of Lagrangianⓘ	44.0
#Semicontinuitiesⓘ	0
#Nonlinear Semicontinuitiesⓘ	0
#SOS type 1ⓘ	0
#SOS type 2ⓘ	0
Minimal coefficientⓘ	5.9172e-03
Maximal coefficientⓘ	8.5432e+00
Infeasibility of initial pointⓘ	2
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*         19        9        0       10        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         45       17       28        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        137       77       60        0
*
*  Solve m using MINLP minimizing objvar;


Variables  x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,b17,b18,b19
          ,b20,b21,b22,b23,b24,b25,b26,b27,b28,b29,b30,b31,b32,b33,b34,b35,b36
          ,b37,b38,b39,b40,b41,b42,b43,b44,objvar;

Positive Variables  x8,x13;

Binary Variables  b17,b18,b19,b20,b21,b22,b23,b24,b25,b26,b27,b28,b29,b30,b31
          ,b32,b33,b34,b35,b36,b37,b38,b39,b40,b41,b42,b43,b44;

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


e1.. sqrt(sqr(x1 - x3) + sqr(x2 - x4))*b17 + sqrt(sqr(x1 - x5) + sqr(x2 - x6))*
     b18 + sqrt(sqr(x1 - x7) + sqr(x2 - x8))*b19 + sqrt(sqr(x1 - x9) + sqr(x2
      - x10))*b20 + sqrt(sqr(x1 - x11) + sqr(x2 - x12))*b21 + sqrt(sqr(x1 - x13
     ) + sqr(x2 - x14))*b22 + sqrt(sqr(x1 - x15) + sqr(x2 - x16))*b23 + sqrt(
     sqr(x3 - x5) + sqr(x4 - x6))*b24 + sqrt(sqr(x3 - x7) + sqr(x4 - x8))*b25
      + sqrt(sqr(x3 - x9) + sqr(x4 - x10))*b26 + sqrt(sqr(x3 - x11) + sqr(x4 - 
     x12))*b27 + sqrt(sqr(x3 - x13) + sqr(x4 - x14))*b28 + sqrt(sqr(x3 - x15)
      + sqr(x4 - x16))*b29 + sqrt(sqr(x5 - x7) + sqr(x6 - x8))*b30 + sqrt(sqr(
     x5 - x9) + sqr(x6 - x10))*b31 + sqrt(sqr(x5 - x11) + sqr(x6 - x12))*b32 + 
     sqrt(sqr(x5 - x13) + sqr(x6 - x14))*b33 + sqrt(sqr(x5 - x15) + sqr(x6 - 
     x16))*b34 + sqrt(sqr(x7 - x9) + sqr(x8 - x10))*b35 + sqrt(sqr(x7 - x11) + 
     sqr(x8 - x12))*b36 + sqrt(sqr(x7 - x13) + sqr(x8 - x14))*b37 + sqrt(sqr(x7
      - x15) + sqr(x8 - x16))*b38 + sqrt(sqr(x9 - x11) + sqr(x10 - x12))*b39 + 
     sqrt(sqr(x9 - x13) + sqr(x10 - x14))*b40 + sqrt(sqr(x9 - x15) + sqr(x10 - 
     x16))*b41 + sqrt(sqr(x11 - x13) + sqr(x12 - x14))*b42 + sqrt(sqr(x11 - x15
     ) + sqr(x12 - x16))*b43 + sqrt(sqr(x13 - x15) + sqr(x14 - x16))*b44
      - objvar =E= 0;

e2.. 0.013840830449827*sqr(x1) - 0.318339100346021*x1 + 0.0236686390532544*sqr(
     x2) - 2.9112426035503*x2 =L= -90.3511598861612;

e3.. 0.0493827160493827*sqr(x3) - 3.30864197530864*x3 + 0.04*sqr(x4) - 1.36*x4
      =L= -65.9797530864197;

e4.. 0.0330578512396694*sqr(x5) - 0.694214876033058*x5 + 0.0493827160493827*
     sqr(x6) - 8.54320987654321*x6 =L= -372.138455259667;

e5.. 0.0330578512396694*sqr(x7) - 6.57851239669422*x7 + 0.013840830449827*sqr(
     x8) - 0.235294117647059*x8 =L= -327.280991735537;

e6.. 0.00826446280991736*sqr(x9) - 0.446280991735537*x9 + 0.013840830449827*
     sqr(x10) - 2.92041522491349*x10 =L= -159.076696502617;

e7.. 0.0330578512396694*sqr(x11) - 4.13223140495868*x11 + 0.013840830449827*
     sqr(x12) - 3.22491349480969*x12 =L= -315.983442477623;

e8.. 0.00756143667296786*sqr(x13) - 0.173913043478261*x13 + 0.0123456790123457*
     sqr(x14) - 0.395061728395062*x14 =L= -3.16049382716049;

e9.. 0.00591715976331361*sqr(x15) - 0.72189349112426*x15 + 0.00694444444444444*
     sqr(x16) - 1.38888888888889*x16 =L= -90.4621959237344;

e10..    b17 + b18 + b19 + b20 + b21 + b22 + b23 =E= 2;

e11..    b17 + b24 + b25 + b26 + b27 + b28 + b29 =E= 2;

e12..    b18 + b24 + b30 + b31 + b32 + b33 + b34 =E= 2;

e13..    b19 + b25 + b30 + b35 + b36 + b37 + b38 =E= 2;

e14..    b20 + b26 + b31 + b35 + b39 + b40 + b41 =E= 2;

e15..    b21 + b27 + b32 + b36 + b39 + b42 + b43 =E= 2;

e16..    b22 + b28 + b33 + b37 + b40 + b42 + b44 =E= 2;

e17..    b23 + b29 + b34 + b38 + b41 + b43 + b44 =E= 2;

e18..    b18 + b20 + b21 + b23 + b31 + b32 + b34 + b39 + b41 + b43 =L= 4;

e19..    b17 + b18 + b19 + b22 + b24 + b25 + b28 + b30 + b33 + b37 =L= 4;

* set non-default bounds
x1.lo = 3; x1.up = 20;
x2.lo = 55; x2.up = 68;
x3.lo = 29; x3.up = 38;
x4.lo = 12; x4.up = 22;
x5.lo = 5; x5.up = 16;
x6.lo = 82; x6.up = 91;
x7.lo = 94; x7.up = 105;
x8.up = 17;
x9.lo = 16; x9.up = 38;
x10.lo = 97; x10.up = 114;
x11.lo = 57; x11.up = 68;
x12.lo = 108; x12.up = 125;
x13.up = 23;
x14.lo = 7; x14.up = 25;
x15.lo = 48; x15.up = 74;
x16.lo = 88; x16.up = 112;

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;