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Instance p_ball_20b_5p_2d_m
Select 5-points in 2-dimensional balls, such that the l1-distance between all points is minimized. Only one point can be assigned to each ball, and in total there are 20 balls with radius one. This is a big-M formulation.
| Formatsⓘ | ams gms lp mod nl osil pip py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | 2.43661233 (ALPHAECP) 2.43715272 (ANTIGONE) 2.43717506 (BARON) 2.43717505 (BONMIN) 2.43714878 (COUENNE) 2.43717509 (CPLEX) 2.43716742 (GUROBI) 2.43717509 (LINDO) 2.43717362 (SCIP) 2.43717509 (SHOT) |
| Referencesⓘ | Kronqvist, Jan and Misener, Ruth, A disjunctive cut strengthening technique for convex MINLP, Tech. Rep., 2020. |
| Sourceⓘ | p_ball_20b_5p_2d.gms, contributed by Jan Kronqvist and Ruth Misener |
| Applicationⓘ | Geometry |
| Added to libraryⓘ | 26 Aug 2020 |
| Problem typeⓘ | MBQCP |
| #Variablesⓘ | 130 |
| #Binary Variablesⓘ | 100 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 10 |
| #Nonlinear Binary Variablesⓘ | 0 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | linear |
| Objective curvatureⓘ | linear |
| #Nonzeros in Objectiveⓘ | 20 |
| #Nonlinear Nonzeros in Objectiveⓘ | 0 |
| #Constraintsⓘ | 169 |
| #Linear Constraintsⓘ | 69 |
| #Quadratic Constraintsⓘ | 100 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 0 |
| Operands in Gen. Nonlin. Functionsⓘ | |
| Constraints curvatureⓘ | convex |
| #Nonzeros in Jacobianⓘ | 628 |
| #Nonlinear Nonzeros in Jacobianⓘ | 200 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 10 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 10 |
| #Blocks in Hessian of Lagrangianⓘ | 10 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 1 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 1 |
| Average blocksize in Hessian of Lagrangianⓘ | 1.0 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 2.3675e-02 |
| Maximal coefficientⓘ | 1.3360e+02 |
| Infeasibility of initial pointⓘ | 8.815e-05 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 170 6 0 164 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 131 31 100 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 649 449 200 0
*
* Solve m using MINLP minimizing objvar;
Variables b1,b2,b3,b4,b5,b6,b7,b8,b9,b10,b11,b12,b13,b14,b15,b16,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,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,x101,x102,x103
,x104,x105,x106,x107,x108,x109,x110,x111,x112,x113,x114,x115,x116
,x117,x118,x119,x120,x121,x122,x123,x124,x125,x126,x127,x128,x129
,x130,objvar;
Positive Variables x101,x102,x103,x104,x105,x106,x107,x108,x109,x110,x111
,x112,x113,x114,x115,x116,x117,x118,x119,x120,x121,x122,x123,x124
,x125,x126,x127,x128,x129,x130;
Binary Variables b1,b2,b3,b4,b5,b6,b7,b8,b9,b10,b11,b12,b13,b14,b15,b16,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,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;
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,e36
,e37,e38,e39,e40,e41,e42,e43,e44,e45,e46,e47,e48,e49,e50,e51,e52,e53
,e54,e55,e56,e57,e58,e59,e60,e61,e62,e63,e64,e65,e66,e67,e68,e69,e70
,e71,e72,e73,e74,e75,e76,e77,e78,e79,e80,e81,e82,e83,e84,e85,e86,e87
,e88,e89,e90,e91,e92,e93,e94,e95,e96,e97,e98,e99,e100,e101,e102,e103
,e104,e105,e106,e107,e108,e109,e110,e111,e112,e113,e114,e115,e116
,e117,e118,e119,e120,e121,e122,e123,e124,e125,e126,e127,e128,e129
,e130,e131,e132,e133,e134,e135,e136,e137,e138,e139,e140,e141,e142
,e143,e144,e145,e146,e147,e148,e149,e150,e151,e152,e153,e154,e155
,e156,e157,e158,e159,e160,e161,e162,e163,e164,e165,e166,e167,e168
,e169,e170;
e1.. x101 - x102 - x103 =L= 0;
e2.. - x101 + x102 - x103 =L= 0;
e3.. x104 - x105 - x106 =L= 0;
e4.. - x104 + x105 - x106 =L= 0;
e5.. x101 - x107 - x108 =L= 0;
e6.. - x101 + x107 - x108 =L= 0;
e7.. x104 - x109 - x110 =L= 0;
e8.. - x104 + x109 - x110 =L= 0;
e9.. x101 - x111 - x112 =L= 0;
e10.. - x101 + x111 - x112 =L= 0;
e11.. x104 - x113 - x114 =L= 0;
e12.. - x104 + x113 - x114 =L= 0;
e13.. x101 - x115 - x116 =L= 0;
e14.. - x101 + x115 - x116 =L= 0;
e15.. x104 - x117 - x118 =L= 0;
e16.. - x104 + x117 - x118 =L= 0;
e17.. x102 - x107 - x119 =L= 0;
e18.. - x102 + x107 - x119 =L= 0;
e19.. x105 - x109 - x120 =L= 0;
e20.. - x105 + x109 - x120 =L= 0;
e21.. x102 - x111 - x121 =L= 0;
e22.. - x102 + x111 - x121 =L= 0;
e23.. x105 - x113 - x122 =L= 0;
e24.. - x105 + x113 - x122 =L= 0;
e25.. x102 - x115 - x123 =L= 0;
e26.. - x102 + x115 - x123 =L= 0;
e27.. x105 - x117 - x124 =L= 0;
e28.. - x105 + x117 - x124 =L= 0;
e29.. x107 - x111 - x125 =L= 0;
e30.. - x107 + x111 - x125 =L= 0;
e31.. x109 - x113 - x126 =L= 0;
e32.. - x109 + x113 - x126 =L= 0;
e33.. x107 - x115 - x127 =L= 0;
e34.. - x107 + x115 - x127 =L= 0;
e35.. x109 - x117 - x128 =L= 0;
e36.. - x109 + x117 - x128 =L= 0;
e37.. x111 - x115 - x129 =L= 0;
e38.. - x111 + x115 - x129 =L= 0;
e39.. x113 - x117 - x130 =L= 0;
e40.. - x113 + x117 - x130 =L= 0;
e41.. sqr(0.0236753863366035 - x101) + sqr(0.861938468195851 - x104)
+ 133.598318045686*b1 =L= 134.598318045686;
e42.. sqr(1.43095891437813 - x101) + sqr(5.10831625828775 - x104)
+ 94.8544563231416*b2 =L= 95.8544563231416;
e43.. sqr(1.21379363277567 - x101) + sqr(3.00432848540233 - x104)
+ 87.4797735261255*b3 =L= 88.4797735261255;
e44.. sqr(8.84443217821809 - x101) + sqr(0.384566405581435 - x104)
+ 103.126413671578*b4 =L= 104.126413671578;
e45.. sqr(5.88364087295228 - x101) + sqr(7.44470191338639 - x104)
+ 95.2983106051005*b5 =L= 96.2983106051005;
e46.. sqr(8.07096798042338 - x101) + sqr(5.55715186969177 - x104)
+ 105.43767414173*b6 =L= 106.43767414173;
e47.. sqr(9.60611615222079 - x101) + sqr(3.49008429472371 - x104)
+ 118.60294806901*b7 =L= 119.60294806901;
e48.. sqr(3.8828653966979 - x101) + sqr(5.56627471425883 - x104)
+ 65.8153811229109*b8 =L= 66.8153811229109;
e49.. sqr(3.47709171076729 - x101) + sqr(1.01589173470293 - x104)
+ 81.404902491826*b9 =L= 82.404902491826;
e50.. sqr(3.29737974336435 - x101) + sqr(4.14110922298337 - x104)
+ 58.2801217051105*b10 =L= 59.2801217051105;
e51.. sqr(8.28345883424477 - x101) + sqr(7.50806458757389 - x104)
+ 133.598318045686*b11 =L= 134.598318045686;
e52.. sqr(5.4084966970588 - x101) + sqr(7.74684442267358 - x104)
+ 93.8794468182122*b12 =L= 94.8794468182122;
e53.. sqr(3.43292425314245 - x101) + sqr(7.8299358039566 - x104)
+ 103.126413671578*b13 =L= 104.126413671578;
e54.. sqr(8.35004447905012 - x101) + sqr(1.33263454148094 - x104)
+ 86.2293028346251*b14 =L= 87.2293028346251;
e55.. sqr(2.65420450303518 - x101) + sqr(6.31096321892449 - x104)
+ 90.5806541970954*b15 =L= 91.5806541970954;
e56.. sqr(5.8344315991351 - x101) + sqr(8.56684140863644 - x104)
+ 112.431237492188*b16 =L= 113.431237492188;
e57.. sqr(4.10957657319824 - x101) + sqr(7.8233834211224 - x104)
+ 95.3905990097055*b17 =L= 96.3905990097055;
e58.. sqr(7.39474057003054 - x101) + sqr(2.49738552645804 - x104)
+ 72.1079233169562*b18 =L= 73.1079233169562;
e59.. sqr(6.14221519240217 - x101) + sqr(3.03591203112434 - x104)
+ 55.1492512196064*b19 =L= 56.1492512196064;
e60.. sqr(8.26974385940666 - x101) + sqr(4.22323814320874 - x104)
+ 97.1056389080134*b20 =L= 98.1056389080134;
e61.. b1 + b2 + b3 + b4 + b5 + b6 + b7 + b8 + b9 + b10 + b11 + b12 + b13
+ b14 + b15 + b16 + b17 + b18 + b19 + b20 =E= 1;
e62.. sqr(0.0236753863366035 - x102) + sqr(0.861938468195851 - x105)
+ 133.598318045686*b21 =L= 134.598318045686;
e63.. sqr(1.43095891437813 - x102) + sqr(5.10831625828775 - x105)
+ 94.8544563231416*b22 =L= 95.8544563231416;
e64.. sqr(1.21379363277567 - x102) + sqr(3.00432848540233 - x105)
+ 87.4797735261255*b23 =L= 88.4797735261255;
e65.. sqr(8.84443217821809 - x102) + sqr(0.384566405581435 - x105)
+ 103.126413671578*b24 =L= 104.126413671578;
e66.. sqr(5.88364087295228 - x102) + sqr(7.44470191338639 - x105)
+ 95.2983106051005*b25 =L= 96.2983106051005;
e67.. sqr(8.07096798042338 - x102) + sqr(5.55715186969177 - x105)
+ 105.43767414173*b26 =L= 106.43767414173;
e68.. sqr(9.60611615222079 - x102) + sqr(3.49008429472371 - x105)
+ 118.60294806901*b27 =L= 119.60294806901;
e69.. sqr(3.8828653966979 - x102) + sqr(5.56627471425883 - x105)
+ 65.8153811229109*b28 =L= 66.8153811229109;
e70.. sqr(3.47709171076729 - x102) + sqr(1.01589173470293 - x105)
+ 81.404902491826*b29 =L= 82.404902491826;
e71.. sqr(3.29737974336435 - x102) + sqr(4.14110922298337 - x105)
+ 58.2801217051105*b30 =L= 59.2801217051105;
e72.. sqr(8.28345883424477 - x102) + sqr(7.50806458757389 - x105)
+ 133.598318045686*b31 =L= 134.598318045686;
e73.. sqr(5.4084966970588 - x102) + sqr(7.74684442267358 - x105)
+ 93.8794468182122*b32 =L= 94.8794468182122;
e74.. sqr(3.43292425314245 - x102) + sqr(7.8299358039566 - x105)
+ 103.126413671578*b33 =L= 104.126413671578;
e75.. sqr(8.35004447905012 - x102) + sqr(1.33263454148094 - x105)
+ 86.2293028346251*b34 =L= 87.2293028346251;
e76.. sqr(2.65420450303518 - x102) + sqr(6.31096321892449 - x105)
+ 90.5806541970954*b35 =L= 91.5806541970954;
e77.. sqr(5.8344315991351 - x102) + sqr(8.56684140863644 - x105)
+ 112.431237492188*b36 =L= 113.431237492188;
e78.. sqr(4.10957657319824 - x102) + sqr(7.8233834211224 - x105)
+ 95.3905990097055*b37 =L= 96.3905990097055;
e79.. sqr(7.39474057003054 - x102) + sqr(2.49738552645804 - x105)
+ 72.1079233169562*b38 =L= 73.1079233169562;
e80.. sqr(6.14221519240217 - x102) + sqr(3.03591203112434 - x105)
+ 55.1492512196064*b39 =L= 56.1492512196064;
e81.. sqr(8.26974385940666 - x102) + sqr(4.22323814320874 - x105)
+ 97.1056389080134*b40 =L= 98.1056389080134;
e82.. b21 + b22 + b23 + b24 + b25 + b26 + b27 + b28 + b29 + b30 + b31 + b32
+ b33 + b34 + b35 + b36 + b37 + b38 + b39 + b40 =E= 1;
e83.. sqr(0.0236753863366035 - x107) + sqr(0.861938468195851 - x109)
+ 133.598318045686*b41 =L= 134.598318045686;
e84.. sqr(1.43095891437813 - x107) + sqr(5.10831625828775 - x109)
+ 94.8544563231416*b42 =L= 95.8544563231416;
e85.. sqr(1.21379363277567 - x107) + sqr(3.00432848540233 - x109)
+ 87.4797735261255*b43 =L= 88.4797735261255;
e86.. sqr(8.84443217821809 - x107) + sqr(0.384566405581435 - x109)
+ 103.126413671578*b44 =L= 104.126413671578;
e87.. sqr(5.88364087295228 - x107) + sqr(7.44470191338639 - x109)
+ 95.2983106051005*b45 =L= 96.2983106051005;
e88.. sqr(8.07096798042338 - x107) + sqr(5.55715186969177 - x109)
+ 105.43767414173*b46 =L= 106.43767414173;
e89.. sqr(9.60611615222079 - x107) + sqr(3.49008429472371 - x109)
+ 118.60294806901*b47 =L= 119.60294806901;
e90.. sqr(3.8828653966979 - x107) + sqr(5.56627471425883 - x109)
+ 65.8153811229109*b48 =L= 66.8153811229109;
e91.. sqr(3.47709171076729 - x107) + sqr(1.01589173470293 - x109)
+ 81.404902491826*b49 =L= 82.404902491826;
e92.. sqr(3.29737974336435 - x107) + sqr(4.14110922298337 - x109)
+ 58.2801217051105*b50 =L= 59.2801217051105;
e93.. sqr(8.28345883424477 - x107) + sqr(7.50806458757389 - x109)
+ 133.598318045686*b51 =L= 134.598318045686;
e94.. sqr(5.4084966970588 - x107) + sqr(7.74684442267358 - x109)
+ 93.8794468182122*b52 =L= 94.8794468182122;
e95.. sqr(3.43292425314245 - x107) + sqr(7.8299358039566 - x109)
+ 103.126413671578*b53 =L= 104.126413671578;
e96.. sqr(8.35004447905012 - x107) + sqr(1.33263454148094 - x109)
+ 86.2293028346251*b54 =L= 87.2293028346251;
e97.. sqr(2.65420450303518 - x107) + sqr(6.31096321892449 - x109)
+ 90.5806541970954*b55 =L= 91.5806541970954;
e98.. sqr(5.8344315991351 - x107) + sqr(8.56684140863644 - x109)
+ 112.431237492188*b56 =L= 113.431237492188;
e99.. sqr(4.10957657319824 - x107) + sqr(7.8233834211224 - x109)
+ 95.3905990097055*b57 =L= 96.3905990097055;
e100.. sqr(7.39474057003054 - x107) + sqr(2.49738552645804 - x109)
+ 72.1079233169562*b58 =L= 73.1079233169562;
e101.. sqr(6.14221519240217 - x107) + sqr(3.03591203112434 - x109)
+ 55.1492512196064*b59 =L= 56.1492512196064;
e102.. sqr(8.26974385940666 - x107) + sqr(4.22323814320874 - x109)
+ 97.1056389080134*b60 =L= 98.1056389080134;
e103.. b41 + b42 + b43 + b44 + b45 + b46 + b47 + b48 + b49 + b50 + b51 + b52
+ b53 + b54 + b55 + b56 + b57 + b58 + b59 + b60 =E= 1;
e104.. sqr(0.0236753863366035 - x111) + sqr(0.861938468195851 - x113)
+ 133.598318045686*b61 =L= 134.598318045686;
e105.. sqr(1.43095891437813 - x111) + sqr(5.10831625828775 - x113)
+ 94.8544563231416*b62 =L= 95.8544563231416;
e106.. sqr(1.21379363277567 - x111) + sqr(3.00432848540233 - x113)
+ 87.4797735261255*b63 =L= 88.4797735261255;
e107.. sqr(8.84443217821809 - x111) + sqr(0.384566405581435 - x113)
+ 103.126413671578*b64 =L= 104.126413671578;
e108.. sqr(5.88364087295228 - x111) + sqr(7.44470191338639 - x113)
+ 95.2983106051005*b65 =L= 96.2983106051005;
e109.. sqr(8.07096798042338 - x111) + sqr(5.55715186969177 - x113)
+ 105.43767414173*b66 =L= 106.43767414173;
e110.. sqr(9.60611615222079 - x111) + sqr(3.49008429472371 - x113)
+ 118.60294806901*b67 =L= 119.60294806901;
e111.. sqr(3.8828653966979 - x111) + sqr(5.56627471425883 - x113)
+ 65.8153811229109*b68 =L= 66.8153811229109;
e112.. sqr(3.47709171076729 - x111) + sqr(1.01589173470293 - x113)
+ 81.404902491826*b69 =L= 82.404902491826;
e113.. sqr(3.29737974336435 - x111) + sqr(4.14110922298337 - x113)
+ 58.2801217051105*b70 =L= 59.2801217051105;
e114.. sqr(8.28345883424477 - x111) + sqr(7.50806458757389 - x113)
+ 133.598318045686*b71 =L= 134.598318045686;
e115.. sqr(5.4084966970588 - x111) + sqr(7.74684442267358 - x113)
+ 93.8794468182122*b72 =L= 94.8794468182122;
e116.. sqr(3.43292425314245 - x111) + sqr(7.8299358039566 - x113)
+ 103.126413671578*b73 =L= 104.126413671578;
e117.. sqr(8.35004447905012 - x111) + sqr(1.33263454148094 - x113)
+ 86.2293028346251*b74 =L= 87.2293028346251;
e118.. sqr(2.65420450303518 - x111) + sqr(6.31096321892449 - x113)
+ 90.5806541970954*b75 =L= 91.5806541970954;
e119.. sqr(5.8344315991351 - x111) + sqr(8.56684140863644 - x113)
+ 112.431237492188*b76 =L= 113.431237492188;
e120.. sqr(4.10957657319824 - x111) + sqr(7.8233834211224 - x113)
+ 95.3905990097055*b77 =L= 96.3905990097055;
e121.. sqr(7.39474057003054 - x111) + sqr(2.49738552645804 - x113)
+ 72.1079233169562*b78 =L= 73.1079233169562;
e122.. sqr(6.14221519240217 - x111) + sqr(3.03591203112434 - x113)
+ 55.1492512196064*b79 =L= 56.1492512196064;
e123.. sqr(8.26974385940666 - x111) + sqr(4.22323814320874 - x113)
+ 97.1056389080134*b80 =L= 98.1056389080134;
e124.. b61 + b62 + b63 + b64 + b65 + b66 + b67 + b68 + b69 + b70 + b71 + b72
+ b73 + b74 + b75 + b76 + b77 + b78 + b79 + b80 =E= 1;
e125.. sqr(0.0236753863366035 - x115) + sqr(0.861938468195851 - x117)
+ 133.598318045686*b81 =L= 134.598318045686;
e126.. sqr(1.43095891437813 - x115) + sqr(5.10831625828775 - x117)
+ 94.8544563231416*b82 =L= 95.8544563231416;
e127.. sqr(1.21379363277567 - x115) + sqr(3.00432848540233 - x117)
+ 87.4797735261255*b83 =L= 88.4797735261255;
e128.. sqr(8.84443217821809 - x115) + sqr(0.384566405581435 - x117)
+ 103.126413671578*b84 =L= 104.126413671578;
e129.. sqr(5.88364087295228 - x115) + sqr(7.44470191338639 - x117)
+ 95.2983106051005*b85 =L= 96.2983106051005;
e130.. sqr(8.07096798042338 - x115) + sqr(5.55715186969177 - x117)
+ 105.43767414173*b86 =L= 106.43767414173;
e131.. sqr(9.60611615222079 - x115) + sqr(3.49008429472371 - x117)
+ 118.60294806901*b87 =L= 119.60294806901;
e132.. sqr(3.8828653966979 - x115) + sqr(5.56627471425883 - x117)
+ 65.8153811229109*b88 =L= 66.8153811229109;
e133.. sqr(3.47709171076729 - x115) + sqr(1.01589173470293 - x117)
+ 81.404902491826*b89 =L= 82.404902491826;
e134.. sqr(3.29737974336435 - x115) + sqr(4.14110922298337 - x117)
+ 58.2801217051105*b90 =L= 59.2801217051105;
e135.. sqr(8.28345883424477 - x115) + sqr(7.50806458757389 - x117)
+ 133.598318045686*b91 =L= 134.598318045686;
e136.. sqr(5.4084966970588 - x115) + sqr(7.74684442267358 - x117)
+ 93.8794468182122*b92 =L= 94.8794468182122;
e137.. sqr(3.43292425314245 - x115) + sqr(7.8299358039566 - x117)
+ 103.126413671578*b93 =L= 104.126413671578;
e138.. sqr(8.35004447905012 - x115) + sqr(1.33263454148094 - x117)
+ 86.2293028346251*b94 =L= 87.2293028346251;
e139.. sqr(2.65420450303518 - x115) + sqr(6.31096321892449 - x117)
+ 90.5806541970954*b95 =L= 91.5806541970954;
e140.. sqr(5.8344315991351 - x115) + sqr(8.56684140863644 - x117)
+ 112.431237492188*b96 =L= 113.431237492188;
e141.. sqr(4.10957657319824 - x115) + sqr(7.8233834211224 - x117)
+ 95.3905990097055*b97 =L= 96.3905990097055;
e142.. sqr(7.39474057003054 - x115) + sqr(2.49738552645804 - x117)
+ 72.1079233169562*b98 =L= 73.1079233169562;
e143.. sqr(6.14221519240217 - x115) + sqr(3.03591203112434 - x117)
+ 55.1492512196064*b99 =L= 56.1492512196064;
e144.. sqr(8.26974385940666 - x115) + sqr(4.22323814320874 - x117)
+ 97.1056389080134*b100 =L= 98.1056389080134;
e145.. b81 + b82 + b83 + b84 + b85 + b86 + b87 + b88 + b89 + b90 + b91 + b92
+ b93 + b94 + b95 + b96 + b97 + b98 + b99 + b100 =E= 1;
e146.. b1 + b21 + b41 + b61 + b81 =L= 1;
e147.. b2 + b22 + b42 + b62 + b82 =L= 1;
e148.. b3 + b23 + b43 + b63 + b83 =L= 1;
e149.. b4 + b24 + b44 + b64 + b84 =L= 1;
e150.. b5 + b25 + b45 + b65 + b85 =L= 1;
e151.. b6 + b26 + b46 + b66 + b86 =L= 1;
e152.. b7 + b27 + b47 + b67 + b87 =L= 1;
e153.. b8 + b28 + b48 + b68 + b88 =L= 1;
e154.. b9 + b29 + b49 + b69 + b89 =L= 1;
e155.. b10 + b30 + b50 + b70 + b90 =L= 1;
e156.. b11 + b31 + b51 + b71 + b91 =L= 1;
e157.. b12 + b32 + b52 + b72 + b92 =L= 1;
e158.. b13 + b33 + b53 + b73 + b93 =L= 1;
e159.. b14 + b34 + b54 + b74 + b94 =L= 1;
e160.. b15 + b35 + b55 + b75 + b95 =L= 1;
e161.. b16 + b36 + b56 + b76 + b96 =L= 1;
e162.. b17 + b37 + b57 + b77 + b97 =L= 1;
e163.. b18 + b38 + b58 + b78 + b98 =L= 1;
e164.. b19 + b39 + b59 + b79 + b99 =L= 1;
e165.. b20 + b40 + b60 + b80 + b100 =L= 1;
e166.. x101 - x102 =L= 0;
e167.. x102 - x107 =L= 0;
e168.. x107 - x111 =L= 0;
e169.. x111 - x115 =L= 0;
e170.. - x103 - x106 - x108 - x110 - x112 - x114 - x116 - x118 - x119 - x120
- x121 - x122 - x123 - x124 - x125 - x126 - x127 - x128 - x129 - x130
+ objvar =E= 0;
* set non-default bounds
x101.up = 10;
x102.up = 10;
x103.up = 10;
x104.up = 10;
x105.up = 10;
x106.up = 10;
x107.up = 10;
x108.up = 10;
x109.up = 10;
x110.up = 10;
x111.up = 10;
x112.up = 10;
x113.up = 10;
x114.up = 10;
x115.up = 10;
x116.up = 10;
x117.up = 10;
x118.up = 10;
x119.up = 10;
x120.up = 10;
x121.up = 10;
x122.up = 10;
x123.up = 10;
x124.up = 10;
x125.up = 10;
x126.up = 10;
x127.up = 10;
x128.up = 10;
x129.up = 10;
x130.up = 10;
* set non-default levels
b13.l = 1;
b25.l = 1;
b57.l = 1;
b76.l = 1;
b92.l = 1;
x101.l = 4.42317283955211;
x102.l = 5.03240021704025;
x103.l = 0.609227377488138;
x104.l = 7.96948572261155;
x105.l = 7.96948572261155;
x107.l = 5.03240021704025;
x108.l = 0.609227377488138;
x109.l = 7.96948572261155;
x111.l = 5.03240021704025;
x112.l = 0.609227377488136;
x113.l = 7.96948572261155;
x115.l = 5.03240021704025;
x116.l = 0.609227377488136;
x117.l = 7.96948572261155;
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