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Instance tspn15
| Formatsⓘ | ams gms mod nl osil py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | 300.00356530 (ANTIGONE) 327.13906210 (BARON) 306.61481810 (COUENNE) 322.57102290 (GUROBI) 287.51628750 (LINDO) 257.06819130 (SCIP) 0.00000000 (SHOT) 314.13156950 (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ⓘ | tspn15Couenne.nl from minlp.org model 124 |
| Applicationⓘ | Traveling Salesman Problem with Neighborhoods |
| Added to libraryⓘ | 21 Feb 2014 |
| Problem typeⓘ | MBNLP |
| #Variablesⓘ | 135 |
| #Binary Variablesⓘ | 105 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 135 |
| #Nonlinear Binary Variablesⓘ | 105 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | nonlinear |
| Objective curvatureⓘ | indefinite |
| #Nonzeros in Objectiveⓘ | 135 |
| #Nonlinear Nonzeros in Objectiveⓘ | 135 |
| #Constraintsⓘ | 34 |
| #Linear Constraintsⓘ | 19 |
| #Quadratic Constraintsⓘ | 15 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 0 |
| Operands in Gen. Nonlin. Functionsⓘ | mul sqr sqrt |
| Constraints curvatureⓘ | convex |
| #Nonzeros in Jacobianⓘ | 367 |
| #Nonlinear Nonzeros in Jacobianⓘ | 30 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 1740 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 30 |
| #Blocks in Hessian of Lagrangianⓘ | 1 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 135 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 135 |
| Average blocksize in Hessian of Lagrangianⓘ | 135.0 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 1.5625e-02 |
| Maximal coefficientⓘ | 2.0400e+02 |
| Infeasibility of initial pointⓘ | 2 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 35 16 0 19 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 136 31 105 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 503 338 165 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,x25,x26,x27,x28,x29,x30,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,b91,b92,b93,b94,b95,b96,b97,b98,b99,b100,b101,b102,b103
,b104,b105,b106,b107,b108,b109,b110,b111,b112,b113,b114,b115,b116
,b117,b118,b119,b120,b121,b122,b123,b124,b125,b126,b127,b128,b129
,b130,b131,b132,b133,b134,b135,objvar;
Positive Variables x2,x27;
Binary Variables 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,b91,b92,b93,b94,b95,b96
,b97,b98,b99,b100,b101,b102,b103,b104,b105,b106,b107,b108,b109,b110
,b111,b112,b113,b114,b115,b116,b117,b118,b119,b120,b121,b122,b123
,b124,b125,b126,b127,b128,b129,b130,b131,b132,b133,b134,b135;
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,e28,e29,e30,e31,e32,e33,e34,e35;
e1.. sqrt(sqr(x1 - x3) + sqr(x2 - x4))*b31 + sqrt(sqr(x1 - x5) + sqr(x2 - x6))*
b32 + sqrt(sqr(x1 - x7) + sqr(x2 - x8))*b33 + sqrt(sqr(x1 - x9) + sqr(x2
- x10))*b34 + sqrt(sqr(x1 - x11) + sqr(x2 - x12))*b35 + sqrt(sqr(x1 - x13
) + sqr(x2 - x14))*b36 + sqrt(sqr(x1 - x15) + sqr(x2 - x16))*b37 + sqrt(
sqr(x1 - x17) + sqr(x2 - x18))*b38 + sqrt(sqr(x1 - x19) + sqr(x2 - x20))*
b39 + sqrt(sqr(x1 - x21) + sqr(x2 - x22))*b40 + sqrt(sqr(x1 - x23) + sqr(
x2 - x24))*b41 + sqrt(sqr(x1 - x25) + sqr(x2 - x26))*b42 + sqrt(sqr(x1 -
x27) + sqr(x2 - x28))*b43 + sqrt(sqr(x1 - x29) + sqr(x2 - x30))*b44 +
sqrt(sqr(x3 - x5) + sqr(x4 - x6))*b45 + sqrt(sqr(x3 - x7) + sqr(x4 - x8))*
b46 + sqrt(sqr(x3 - x9) + sqr(x4 - x10))*b47 + sqrt(sqr(x3 - x11) + sqr(x4
- x12))*b48 + sqrt(sqr(x3 - x13) + sqr(x4 - x14))*b49 + sqrt(sqr(x3 - x15
) + sqr(x4 - x16))*b50 + sqrt(sqr(x3 - x17) + sqr(x4 - x18))*b51 + sqrt(
sqr(x3 - x19) + sqr(x4 - x20))*b52 + sqrt(sqr(x3 - x21) + sqr(x4 - x22))*
b53 + sqrt(sqr(x3 - x23) + sqr(x4 - x24))*b54 + sqrt(sqr(x3 - x25) + sqr(
x4 - x26))*b55 + sqrt(sqr(x3 - x27) + sqr(x4 - x28))*b56 + sqrt(sqr(x3 -
x29) + sqr(x4 - x30))*b57 + sqrt(sqr(x5 - x7) + sqr(x6 - x8))*b58 + sqrt(
sqr(x5 - x9) + sqr(x6 - x10))*b59 + sqrt(sqr(x5 - x11) + sqr(x6 - x12))*
b60 + sqrt(sqr(x5 - x13) + sqr(x6 - x14))*b61 + sqrt(sqr(x5 - x15) + sqr(
x6 - x16))*b62 + sqrt(sqr(x5 - x17) + sqr(x6 - x18))*b63 + sqrt(sqr(x5 -
x19) + sqr(x6 - x20))*b64 + sqrt(sqr(x5 - x21) + sqr(x6 - x22))*b65 +
sqrt(sqr(x5 - x23) + sqr(x6 - x24))*b66 + sqrt(sqr(x5 - x25) + sqr(x6 -
x26))*b67 + sqrt(sqr(x5 - x27) + sqr(x6 - x28))*b68 + sqrt(sqr(x5 - x29)
+ sqr(x6 - x30))*b69 + sqrt(sqr(x7 - x9) + sqr(x8 - x10))*b70 + sqrt(sqr(
x7 - x11) + sqr(x8 - x12))*b71 + sqrt(sqr(x7 - x13) + sqr(x8 - x14))*b72
+ sqrt(sqr(x7 - x15) + sqr(x8 - x16))*b73 + sqrt(sqr(x7 - x17) + sqr(x8
- x18))*b74 + sqrt(sqr(x7 - x19) + sqr(x8 - x20))*b75 + sqrt(sqr(x7 - x21
) + sqr(x8 - x22))*b76 + sqrt(sqr(x7 - x23) + sqr(x8 - x24))*b77 + sqrt(
sqr(x7 - x25) + sqr(x8 - x26))*b78 + sqrt(sqr(x7 - x27) + sqr(x8 - x28))*
b79 + sqrt(sqr(x7 - x29) + sqr(x8 - x30))*b80 + sqrt(sqr(x9 - x11) + sqr(
x10 - x12))*b81 + sqrt(sqr(x9 - x13) + sqr(x10 - x14))*b82 + sqrt(sqr(x9
- x15) + sqr(x10 - x16))*b83 + sqrt(sqr(x9 - x17) + sqr(x10 - x18))*b84
+ sqrt(sqr(x9 - x19) + sqr(x10 - x20))*b85 + sqrt(sqr(x9 - x21) + sqr(x10
- x22))*b86 + sqrt(sqr(x9 - x23) + sqr(x10 - x24))*b87 + sqrt(sqr(x9 -
x25) + sqr(x10 - x26))*b88 + sqrt(sqr(x9 - x27) + sqr(x10 - x28))*b89 +
sqrt(sqr(x9 - x29) + sqr(x10 - x30))*b90 + sqrt(sqr(x11 - x13) + sqr(x12
- x14))*b91 + sqrt(sqr(x11 - x15) + sqr(x12 - x16))*b92 + sqrt(sqr(x11 -
x17) + sqr(x12 - x18))*b93 + sqrt(sqr(x11 - x19) + sqr(x12 - x20))*b94 +
sqrt(sqr(x11 - x21) + sqr(x12 - x22))*b95 + sqrt(sqr(x11 - x23) + sqr(x12
- x24))*b96 + sqrt(sqr(x11 - x25) + sqr(x12 - x26))*b97 + sqrt(sqr(x11 -
x27) + sqr(x12 - x28))*b98 + sqrt(sqr(x11 - x29) + sqr(x12 - x30))*b99 +
sqrt(sqr(x13 - x15) + sqr(x14 - x16))*b100 + sqrt(sqr(x13 - x17) + sqr(x14
- x18))*b101 + sqrt(sqr(x13 - x19) + sqr(x14 - x20))*b102 + sqrt(sqr(x13
- x21) + sqr(x14 - x22))*b103 + sqrt(sqr(x13 - x23) + sqr(x14 - x24))*
b104 + sqrt(sqr(x13 - x25) + sqr(x14 - x26))*b105 + sqrt(sqr(x13 - x27) +
sqr(x14 - x28))*b106 + sqrt(sqr(x13 - x29) + sqr(x14 - x30))*b107 + sqrt(
sqr(x15 - x17) + sqr(x16 - x18))*b108 + sqrt(sqr(x15 - x19) + sqr(x16 -
x20))*b109 + sqrt(sqr(x15 - x21) + sqr(x16 - x22))*b110 + sqrt(sqr(x15 -
x23) + sqr(x16 - x24))*b111 + sqrt(sqr(x15 - x25) + sqr(x16 - x26))*b112
+ sqrt(sqr(x15 - x27) + sqr(x16 - x28))*b113 + sqrt(sqr(x15 - x29) + sqr(
x16 - x30))*b114 + sqrt(sqr(x17 - x19) + sqr(x18 - x20))*b115 + sqrt(sqr(
x17 - x21) + sqr(x18 - x22))*b116 + sqrt(sqr(x17 - x23) + sqr(x18 - x24))*
b117 + sqrt(sqr(x17 - x25) + sqr(x18 - x26))*b118 + sqrt(sqr(x17 - x27) +
sqr(x18 - x28))*b119 + sqrt(sqr(x17 - x29) + sqr(x18 - x30))*b120 + sqrt(
sqr(x19 - x21) + sqr(x20 - x22))*b121 + sqrt(sqr(x19 - x23) + sqr(x20 -
x24))*b122 + sqrt(sqr(x19 - x25) + sqr(x20 - x26))*b123 + sqrt(sqr(x19 -
x27) + sqr(x20 - x28))*b124 + sqrt(sqr(x19 - x29) + sqr(x20 - x30))*b125
+ sqrt(sqr(x21 - x23) + sqr(x22 - x24))*b126 + sqrt(sqr(x21 - x25) + sqr(
x22 - x26))*b127 + sqrt(sqr(x21 - x27) + sqr(x22 - x28))*b128 + sqrt(sqr(
x21 - x29) + sqr(x22 - x30))*b129 + sqrt(sqr(x23 - x25) + sqr(x24 - x26))*
b130 + sqrt(sqr(x23 - x27) + sqr(x24 - x28))*b131 + sqrt(sqr(x23 - x29) +
sqr(x24 - x30))*b132 + sqrt(sqr(x25 - x27) + sqr(x26 - x28))*b133 + sqrt(
sqr(x25 - x29) + sqr(x26 - x30))*b134 + sqrt(sqr(x27 - x29) + sqr(x28 -
x30))*b135 - objvar =E= 0;
e2.. 0.0625*sqr(x1) - 8.875*x1 + 0.0177777777777778*sqr(x2) - 0.266666666666667
*x2 =L= -315.0625;
e3.. 0.015625*sqr(x3) - 0.84375*x3 + 0.0625*sqr(x4) - 11.25*x4 =L= -516.640625;
e4.. 0.0330578512396694*sqr(x5) - 0.826446280991736*x5 + 0.0816326530612245*
sqr(x6) - 6.61224489795918*x6 =L= -138.063248439872;
e5.. 0.0493827160493827*sqr(x7) - 8.44444444444444*x7 + 0.0277777777777778*sqr(
x8) - 3.77777777777778*x8 =L= -488.444444444444;
e6.. 0.111111111111111*sqr(x9) - 16.2222222222222*x9 + sqr(x10) - 204*x10
=L= -10995.1111111111;
e7.. 0.04*sqr(x11) - 4.64*x11 + 0.25*sqr(x12) - 23*x12 =L= -662.56;
e8.. 0.04*sqr(x13) - 3.76*x13 + sqr(x14) - 144*x14 =L= -5271.36;
e9.. 0.0816326530612245*sqr(x15) - 16.5714285714286*x15 + 0.0625*sqr(x16) - 2.5
*x16 =L= -865;
e10.. 0.0493827160493827*sqr(x17) - 4.88888888888889*x17 + 0.015625*sqr(x18) -
2.375*x18 =L= -210.25;
e11.. 0.04*sqr(x19) - 6.48*x19 + 0.0330578512396694*sqr(x20) - 2.87603305785124
*x20 =L= -323.993719008264;
e12.. 0.0204081632653061*sqr(x21) - 0.693877551020408*x21 + 0.0816326530612245*
sqr(x22) - 7.91836734693877*x22 =L= -196.918367346939;
e13.. 0.0625*sqr(x23) - 11.375*x23 + 0.444444444444444*sqr(x24) -
76.8888888888889*x24 =L= -3842.00694444444;
e14.. 4*sqr(x25) - 52*x25 + 0.015625*sqr(x26) - 1.1875*x26 =L= -190.5625;
e15.. 0.0816326530612245*sqr(x27) - 0.571428571428571*x27 + 0.0330578512396694*
sqr(x28) - 6.57851239669422*x28 =L= -327.280991735537;
e16.. 0.0625*sqr(x29) - 10.125*x29 + 0.04*sqr(x30) - 2.72*x30 =L= -455.3025;
e17.. b31 + b32 + b33 + b34 + b35 + b36 + b37 + b38 + b39 + b40 + b41 + b42
+ b43 + b44 =E= 2;
e18.. b31 + b45 + b46 + b47 + b48 + b49 + b50 + b51 + b52 + b53 + b54 + b55
+ b56 + b57 =E= 2;
e19.. b32 + b45 + b58 + b59 + b60 + b61 + b62 + b63 + b64 + b65 + b66 + b67
+ b68 + b69 =E= 2;
e20.. b33 + b46 + b58 + b70 + b71 + b72 + b73 + b74 + b75 + b76 + b77 + b78
+ b79 + b80 =E= 2;
e21.. b34 + b47 + b59 + b70 + b81 + b82 + b83 + b84 + b85 + b86 + b87 + b88
+ b89 + b90 =E= 2;
e22.. b35 + b48 + b60 + b71 + b81 + b91 + b92 + b93 + b94 + b95 + b96 + b97
+ b98 + b99 =E= 2;
e23.. b36 + b49 + b61 + b72 + b82 + b91 + b100 + b101 + b102 + b103 + b104
+ b105 + b106 + b107 =E= 2;
e24.. b37 + b50 + b62 + b73 + b83 + b92 + b100 + b108 + b109 + b110 + b111
+ b112 + b113 + b114 =E= 2;
e25.. b38 + b51 + b63 + b74 + b84 + b93 + b101 + b108 + b115 + b116 + b117
+ b118 + b119 + b120 =E= 2;
e26.. b39 + b52 + b64 + b75 + b85 + b94 + b102 + b109 + b115 + b121 + b122
+ b123 + b124 + b125 =E= 2;
e27.. b40 + b53 + b65 + b76 + b86 + b95 + b103 + b110 + b116 + b121 + b126
+ b127 + b128 + b129 =E= 2;
e28.. b41 + b54 + b66 + b77 + b87 + b96 + b104 + b111 + b117 + b122 + b126
+ b130 + b131 + b132 =E= 2;
e29.. b42 + b55 + b67 + b78 + b88 + b97 + b105 + b112 + b118 + b123 + b127
+ b130 + b133 + b134 =E= 2;
e30.. b43 + b56 + b68 + b79 + b89 + b98 + b106 + b113 + b119 + b124 + b128
+ b131 + b133 + b135 =E= 2;
e31.. b44 + b57 + b69 + b80 + b90 + b99 + b107 + b114 + b120 + b125 + b129
+ b132 + b134 + b135 =E= 2;
e32.. b35 + b37 + b39 + b44 + b92 + b94 + b99 + b109 + b114 + b125 =L= 4;
e33.. b37 + b39 + b44 + b109 + b114 + b125 =L= 3;
e34.. b31 + b33 + b34 + b35 + b36 + b37 + b38 + b39 + b41 + b43 + b44 + b46
+ b47 + b48 + b49 + b50 + b51 + b52 + b54 + b56 + b57 + b70 + b71 + b72
+ b73 + b74 + b75 + b77 + b79 + b80 + b81 + b82 + b83 + b84 + b85 + b87
+ b89 + b90 + b91 + b92 + b93 + b94 + b96 + b98 + b99 + b100 + b101
+ b102 + b104 + b106 + b107 + b108 + b109 + b111 + b113 + b114 + b115
+ b117 + b119 + b120 + b122 + b124 + b125 + b131 + b132 + b135 =L= 11;
e35.. b33 + b34 + b35 + b36 + b37 + b38 + b39 + b41 + b44 + b70 + b71 + b72
+ b73 + b74 + b75 + b77 + b80 + b81 + b82 + b83 + b84 + b85 + b87 + b90
+ b91 + b92 + b93 + b94 + b96 + b99 + b100 + b101 + b102 + b104 + b107
+ b108 + b109 + b111 + b114 + b115 + b117 + b120 + b122 + b125 + b132
=L= 9;
* set non-default bounds
x1.lo = 67; x1.up = 75;
x2.up = 15;
x3.lo = 19; x3.up = 35;
x4.lo = 86; x4.up = 94;
x5.lo = 7; x5.up = 18;
x6.lo = 37; x6.up = 44;
x7.lo = 81; x7.up = 90;
x8.lo = 62; x8.up = 74;
x9.lo = 70; x9.up = 76;
x10.lo = 101; x10.up = 103;
x11.lo = 53; x11.up = 63;
x12.lo = 44; x12.up = 48;
x13.lo = 42; x13.up = 52;
x14.lo = 71; x14.up = 73;
x15.lo = 98; x15.up = 105;
x16.lo = 16; x16.up = 24;
x17.lo = 45; x17.up = 54;
x18.lo = 68; x18.up = 84;
x19.lo = 76; x19.up = 86;
x20.lo = 38; x20.up = 49;
x21.lo = 10; x21.up = 24;
x22.lo = 45; x22.up = 52;
x23.lo = 87; x23.up = 95;
x24.lo = 85; x24.up = 88;
x25.lo = 6; x25.up = 7;
x26.lo = 30; x26.up = 46;
x27.up = 7;
x28.lo = 94; x28.up = 105;
x29.lo = 77; x29.up = 85;
x30.lo = 29; x30.up = 39;
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: 2025-08-07 Git hash: e62cedfc