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Instance tspn05

Formatsⓘ	ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)ⓘ	191.2552078 p1 ( gdx sol ) (infeas: 5e-13)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	191.2540844 (ANTIGONE) 191.2552075 (BARON) 191.2537001 (COUENNE) 191.2536689 (LINDO) 191.255197 (SCIP) 0. (SHOT)
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ⓘ	tspn5Couenne.nl from minlp.org model 124
Applicationⓘ	Traveling Salesman Problem with Neighborhoods
Added to libraryⓘ	21 Feb 2014
Problem typeⓘ	MBNLP
#Variablesⓘ	20
#Binary Variablesⓘ	10
#Integer Variablesⓘ	0
#Nonlinear Variablesⓘ	20
#Nonlinear Binary Variablesⓘ	10
#Nonlinear Integer Variablesⓘ	0
Objective Senseⓘ	min
Objective typeⓘ	nonlinear
Objective curvatureⓘ	indefinite
#Nonzeros in Objectiveⓘ	20
#Nonlinear Nonzeros in Objectiveⓘ	20
#Constraintsⓘ	10
#Linear Constraintsⓘ	5
#Quadratic Constraintsⓘ	5
#Polynomial Constraintsⓘ	0
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ	mul sqr sqrt
Constraints curvatureⓘ	convex
#Nonzeros in Jacobianⓘ	30
#Nonlinear Nonzeros in Jacobianⓘ	10
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	180
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	10
#Blocks in Hessian of Lagrangianⓘ	1
Minimal blocksize in Hessian of Lagrangianⓘ	20
Maximal blocksize in Hessian of Lagrangianⓘ	20
Average blocksize in Hessian of Lagrangianⓘ	20.0
#Semicontinuitiesⓘ	0
#Nonlinear Semicontinuitiesⓘ	0
#SOS type 1ⓘ	0
#SOS type 2ⓘ	0
Minimal coefficientⓘ	8.2645e-03
Maximal coefficientⓘ	6.1778e+01
Infeasibility of initial pointⓘ	2
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*         11        6        0        5        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         21       11       10        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         51       21       30        0
*
*  Solve m using MINLP minimizing objvar;


Variables  x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,b11,b12,b13,b14,b15,b16,b17,b18,b19
          ,b20,objvar;

Binary Variables  b11,b12,b13,b14,b15,b16,b17,b18,b19,b20;

Equations  e1,e2,e3,e4,e5,e6,e7,e8,e9,e10,e11;


e1.. sqrt(sqr(x1 - x3) + sqr(x2 - x4))*b11 + sqrt(sqr(x1 - x5) + sqr(x2 - x6))*
     b12 + sqrt(sqr(x1 - x7) + sqr(x2 - x8))*b13 + sqrt(sqr(x1 - x9) + sqr(x2
      - x10))*b14 + sqrt(sqr(x3 - x5) + sqr(x4 - x6))*b15 + sqrt(sqr(x3 - x7)
      + sqr(x4 - x8))*b16 + sqrt(sqr(x3 - x9) + sqr(x4 - x10))*b17 + sqrt(sqr(
     x5 - x7) + sqr(x6 - x8))*b18 + sqrt(sqr(x5 - x9) + sqr(x6 - x10))*b19 + 
     sqrt(sqr(x7 - x9) + sqr(x8 - x10))*b20 - objvar =E= 0;

e2.. 0.444444444444444*sqr(x1) - 61.7777777777778*x1 + 0.00826446280991736*sqr(
     x2) - 1.25619834710744*x2 =L= -2193.51331496786;

e3.. 0.0110803324099723*sqr(x3) - 2.58171745152355*x3 + 0.0330578512396694*sqr(
     x4) - 2.87603305785124*x4 =L= -211.938760559511;

e4.. 0.0177777777777778*sqr(x5) - 1.68888888888889*x5 + 0.0204081632653061*sqr(
     x6) - 2.48979591836735*x6 =L= -115.049886621315;

e5.. 0.0204081632653061*sqr(x7) - 4.04081632653061*x7 + 0.25*sqr(x8) - 57.5*x8
      =L= -3505.27040816327;

e6.. 0.16*sqr(x9) - 27.04*x9 + 0.0493827160493827*sqr(x10) - 7.95061728395062*
     x10 =L= -1461.45234567901;

e7..    b11 + b12 + b13 + b14 =E= 2;

e8..    b11 + b15 + b16 + b17 =E= 2;

e9..    b12 + b15 + b18 + b19 =E= 2;

e10..    b13 + b16 + b18 + b20 =E= 2;

e11..    b14 + b17 + b19 + b20 =E= 2;

* set non-default bounds
x1.lo = 68; x1.up = 71;
x2.lo = 65; x2.up = 87;
x3.lo = 107; x3.up = 126;
x4.lo = 38; x4.up = 49;
x5.lo = 40; x5.up = 55;
x6.lo = 54; x6.up = 68;
x7.lo = 92; x7.up = 106;
x8.lo = 113; x8.up = 117;
x9.lo = 82; x9.up = 87;
x10.lo = 76; x10.up = 85;

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;