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Instance p_ball_30b_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 30 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ⓘ | 0.29012034 (ALPHAECP) 0.29160024 (ANTIGONE) 0.29159961 (BARON) 0.29162937 (BONMIN) 0.29160300 (COUENNE) 0.29162944 (CPLEX) 0.29162520 (GUROBI) 0.29162942 (LINDO) 0.29162566 (SCIP) 0.29162944 (SHOT) |
| Referencesⓘ | Kronqvist, Jan and Misener, Ruth, A disjunctive cut strengthening technique for convex MINLP, Tech. Rep., 2020. |
| Sourceⓘ | p_ball_30b_5p_2d.gms, contributed by Jan Kronqvist and Ruth Misener |
| Applicationⓘ | Geometry |
| Added to libraryⓘ | 26 Aug 2020 |
| Problem typeⓘ | MBQCP |
| #Variablesⓘ | 180 |
| #Binary Variablesⓘ | 150 |
| #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ⓘ | 229 |
| #Linear Constraintsⓘ | 79 |
| #Quadratic Constraintsⓘ | 150 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 0 |
| Operands in Gen. Nonlin. Functionsⓘ | |
| Constraints curvatureⓘ | convex |
| #Nonzeros in Jacobianⓘ | 878 |
| #Nonlinear Nonzeros in Jacobianⓘ | 300 |
| #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ⓘ | 2.7294e-01 |
| Maximal coefficientⓘ | 1.6061e+02 |
| Infeasibility of initial pointⓘ | 9.933e-05 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 230 6 0 224 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 181 31 150 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 899 599 300 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,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,b136,b137,b138,b139,b140,b141,b142
,b143,b144,b145,b146,b147,b148,b149,b150,x151,x152,x153,x154,x155
,x156,x157,x158,x159,x160,x161,x162,x163,x164,x165,x166,x167,x168
,x169,x170,x171,x172,x173,x174,x175,x176,x177,x178,x179,x180,objvar;
Positive Variables x151,x152,x153,x154,x155,x156,x157,x158,x159,x160,x161
,x162,x163,x164,x165,x166,x167,x168,x169,x170,x171,x172,x173,x174
,x175,x176,x177,x178,x179,x180;
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,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,b136,b137,b138,b139,b140
,b141,b142,b143,b144,b145,b146,b147,b148,b149,b150;
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,e171,e172,e173,e174,e175,e176,e177,e178,e179,e180,e181
,e182,e183,e184,e185,e186,e187,e188,e189,e190,e191,e192,e193,e194
,e195,e196,e197,e198,e199,e200,e201,e202,e203,e204,e205,e206,e207
,e208,e209,e210,e211,e212,e213,e214,e215,e216,e217,e218,e219,e220
,e221,e222,e223,e224,e225,e226,e227,e228,e229,e230;
e1.. x151 - x152 - x153 =L= 0;
e2.. - x151 + x152 - x153 =L= 0;
e3.. x154 - x155 - x156 =L= 0;
e4.. - x154 + x155 - x156 =L= 0;
e5.. x151 - x157 - x158 =L= 0;
e6.. - x151 + x157 - x158 =L= 0;
e7.. x154 - x159 - x160 =L= 0;
e8.. - x154 + x159 - x160 =L= 0;
e9.. x151 - x161 - x162 =L= 0;
e10.. - x151 + x161 - x162 =L= 0;
e11.. x154 - x163 - x164 =L= 0;
e12.. - x154 + x163 - x164 =L= 0;
e13.. x151 - x165 - x166 =L= 0;
e14.. - x151 + x165 - x166 =L= 0;
e15.. x154 - x167 - x168 =L= 0;
e16.. - x154 + x167 - x168 =L= 0;
e17.. x152 - x157 - x169 =L= 0;
e18.. - x152 + x157 - x169 =L= 0;
e19.. x155 - x159 - x170 =L= 0;
e20.. - x155 + x159 - x170 =L= 0;
e21.. x152 - x161 - x171 =L= 0;
e22.. - x152 + x161 - x171 =L= 0;
e23.. x155 - x163 - x172 =L= 0;
e24.. - x155 + x163 - x172 =L= 0;
e25.. x152 - x165 - x173 =L= 0;
e26.. - x152 + x165 - x173 =L= 0;
e27.. x155 - x167 - x174 =L= 0;
e28.. - x155 + x167 - x174 =L= 0;
e29.. x157 - x161 - x175 =L= 0;
e30.. - x157 + x161 - x175 =L= 0;
e31.. x159 - x163 - x176 =L= 0;
e32.. - x159 + x163 - x176 =L= 0;
e33.. x157 - x165 - x177 =L= 0;
e34.. - x157 + x165 - x177 =L= 0;
e35.. x159 - x167 - x178 =L= 0;
e36.. - x159 + x167 - x178 =L= 0;
e37.. x161 - x165 - x179 =L= 0;
e38.. - x161 + x165 - x179 =L= 0;
e39.. x163 - x167 - x180 =L= 0;
e40.. - x163 + x167 - x180 =L= 0;
e41.. sqr(3.58392835071893 - x151) + sqr(0.44370753979378 - x154)
+ 117.37605108924*b1 =L= 118.37605108924;
e42.. sqr(1.95628884344 - x151) + sqr(0.390503036650278 - x154)
+ 140.241701004457*b2 =L= 141.241701004457;
e43.. sqr(4.55035690490668 - x151) + sqr(7.27185840240323 - x154)
+ 71.5594363053072*b3 =L= 72.5594363053072;
e44.. sqr(6.2100872388646 - x151) + sqr(6.48745936675473 - x154)
+ 70.1361240423208*b4 =L= 71.1361240423208;
e45.. sqr(3.1786343207553 - x151) + sqr(2.35630065859291 - x154)
+ 91.0983527000505*b5 =L= 92.0983527000505;
e46.. sqr(2.77208272832737 - x151) + sqr(6.63537019621518 - x154)
+ 78.1787285426132*b6 =L= 79.1787285426132;
e47.. sqr(5.05196451835929 - x151) + sqr(9.78029757859562 - x154)
+ 117.525315958044*b7 =L= 118.525315958044;
e48.. sqr(4.91358831690657 - x151) + sqr(9.95200766490468 - x154)
+ 120.184782975767*b8 =L= 121.184782975767;
e49.. sqr(1.82270973029123 - x151) + sqr(3.08924661212034 - x154)
+ 100.562560044535*b9 =L= 101.562560044535;
e50.. sqr(8.90416070287928 - x151) + sqr(8.76903198117563 - x154)
+ 140.241701004457*b10 =L= 141.241701004457;
e51.. sqr(9.55691722438547 - x151) + sqr(7.67982230145412 - x154)
+ 131.965894836477*b11 =L= 132.965894836477;
e52.. sqr(5.63154215917614 - x151) + sqr(5.19669129629487 - x154)
+ 61.1865070415458*b12 =L= 62.1865070415458;
e53.. sqr(1.22506785607057 - x151) + sqr(1.73643838760701 - x154)
+ 129.251385415199*b13 =L= 130.251385415199;
e54.. sqr(3.56742024375224 - x151) + sqr(9.67716416398758 - x154)
+ 122.549628719203*b14 =L= 123.549628719203;
e55.. sqr(6.4469689992634 - x151) + sqr(3.27001587839258 - x154)
+ 94.7662927771576*b15 =L= 95.7662927771576;
e56.. sqr(6.10753237542196 - x151) + sqr(4.19206922588061 - x154)
+ 78.2445398454346*b16 =L= 79.2445398454346;
e57.. sqr(3.65877473332061 - x151) + sqr(3.63421268850839 - x154)
+ 68.5611029512265*b17 =L= 69.5611029512265;
e58.. sqr(1.2178860076098 - x151) + sqr(2.16125505734127 - x154)
+ 123.013834343708*b18 =L= 124.013834343708;
e59.. sqr(0.592074869235123 - x151) + sqr(4.93671199500253 - x154)
+ 106.643311548917*b19 =L= 107.643311548917;
e60.. sqr(6.7402850724876 - x151) + sqr(1.57064570718754 - x154)
+ 125.533092608851*b20 =L= 126.533092608851;
e61.. sqr(4.86197880938116 - x151) + sqr(0.383551455477691 - x154)
+ 125.003682175941*b21 =L= 126.003682175941;
e62.. sqr(1.8799102211015 - x151) + sqr(8.11097800063776 - x154)
+ 111.618317672146*b22 =L= 112.618317672146;
e63.. sqr(7.64684982583741 - x151) + sqr(0.420960467093494 - x154)
+ 160.611756853376*b23 =L= 161.611756853376;
e64.. sqr(3.86587305838289 - x151) + sqr(3.43289089140431 - x154)
+ 68.5364474973792*b24 =L= 69.5364474973792;
e65.. sqr(1.93085934314818 - x151) + sqr(3.48739999687651 - x154)
+ 94.0180040498471*b25 =L= 95.0180040498471;
e66.. sqr(8.14411066658926 - x151) + sqr(3.28390698782521 - x154)
+ 120.943028096043*b26 =L= 121.943028096043;
e67.. sqr(3.92781648828775 - x151) + sqr(4.5879692218008 - x154)
+ 55.2445625258556*b27 =L= 56.2445625258556;
e68.. sqr(9.43530528332928 - x151) + sqr(6.2115811426888 - x154)
+ 114.385124970594*b28 =L= 115.385124970594;
e69.. sqr(5.94277300911337 - x151) + sqr(2.72126258813597 - x154)
+ 96.0912915355006*b29 =L= 97.0912915355006;
e70.. sqr(0.272938801260022 - x151) + sqr(9.52106324081905 - x154)
+ 160.611756853376*b30 =L= 161.611756853376;
e71.. 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 =E= 1;
e72.. sqr(3.58392835071893 - x152) + sqr(0.44370753979378 - x155)
+ 117.37605108924*b31 =L= 118.37605108924;
e73.. sqr(1.95628884344 - x152) + sqr(0.390503036650278 - x155)
+ 140.241701004457*b32 =L= 141.241701004457;
e74.. sqr(4.55035690490668 - x152) + sqr(7.27185840240323 - x155)
+ 71.5594363053072*b33 =L= 72.5594363053072;
e75.. sqr(6.2100872388646 - x152) + sqr(6.48745936675473 - x155)
+ 70.1361240423208*b34 =L= 71.1361240423208;
e76.. sqr(3.1786343207553 - x152) + sqr(2.35630065859291 - x155)
+ 91.0983527000505*b35 =L= 92.0983527000505;
e77.. sqr(2.77208272832737 - x152) + sqr(6.63537019621518 - x155)
+ 78.1787285426132*b36 =L= 79.1787285426132;
e78.. sqr(5.05196451835929 - x152) + sqr(9.78029757859562 - x155)
+ 117.525315958044*b37 =L= 118.525315958044;
e79.. sqr(4.91358831690657 - x152) + sqr(9.95200766490468 - x155)
+ 120.184782975767*b38 =L= 121.184782975767;
e80.. sqr(1.82270973029123 - x152) + sqr(3.08924661212034 - x155)
+ 100.562560044535*b39 =L= 101.562560044535;
e81.. sqr(8.90416070287928 - x152) + sqr(8.76903198117563 - x155)
+ 140.241701004457*b40 =L= 141.241701004457;
e82.. sqr(9.55691722438547 - x152) + sqr(7.67982230145412 - x155)
+ 131.965894836477*b41 =L= 132.965894836477;
e83.. sqr(5.63154215917614 - x152) + sqr(5.19669129629487 - x155)
+ 61.1865070415458*b42 =L= 62.1865070415458;
e84.. sqr(1.22506785607057 - x152) + sqr(1.73643838760701 - x155)
+ 129.251385415199*b43 =L= 130.251385415199;
e85.. sqr(3.56742024375224 - x152) + sqr(9.67716416398758 - x155)
+ 122.549628719203*b44 =L= 123.549628719203;
e86.. sqr(6.4469689992634 - x152) + sqr(3.27001587839258 - x155)
+ 94.7662927771576*b45 =L= 95.7662927771576;
e87.. sqr(6.10753237542196 - x152) + sqr(4.19206922588061 - x155)
+ 78.2445398454346*b46 =L= 79.2445398454346;
e88.. sqr(3.65877473332061 - x152) + sqr(3.63421268850839 - x155)
+ 68.5611029512265*b47 =L= 69.5611029512265;
e89.. sqr(1.2178860076098 - x152) + sqr(2.16125505734127 - x155)
+ 123.013834343708*b48 =L= 124.013834343708;
e90.. sqr(0.592074869235123 - x152) + sqr(4.93671199500253 - x155)
+ 106.643311548917*b49 =L= 107.643311548917;
e91.. sqr(6.7402850724876 - x152) + sqr(1.57064570718754 - x155)
+ 125.533092608851*b50 =L= 126.533092608851;
e92.. sqr(4.86197880938116 - x152) + sqr(0.383551455477691 - x155)
+ 125.003682175941*b51 =L= 126.003682175941;
e93.. sqr(1.8799102211015 - x152) + sqr(8.11097800063776 - x155)
+ 111.618317672146*b52 =L= 112.618317672146;
e94.. sqr(7.64684982583741 - x152) + sqr(0.420960467093494 - x155)
+ 160.611756853376*b53 =L= 161.611756853376;
e95.. sqr(3.86587305838289 - x152) + sqr(3.43289089140431 - x155)
+ 68.5364474973792*b54 =L= 69.5364474973792;
e96.. sqr(1.93085934314818 - x152) + sqr(3.48739999687651 - x155)
+ 94.0180040498471*b55 =L= 95.0180040498471;
e97.. sqr(8.14411066658926 - x152) + sqr(3.28390698782521 - x155)
+ 120.943028096043*b56 =L= 121.943028096043;
e98.. sqr(3.92781648828775 - x152) + sqr(4.5879692218008 - x155)
+ 55.2445625258556*b57 =L= 56.2445625258556;
e99.. sqr(9.43530528332928 - x152) + sqr(6.2115811426888 - x155)
+ 114.385124970594*b58 =L= 115.385124970594;
e100.. sqr(5.94277300911337 - x152) + sqr(2.72126258813597 - x155)
+ 96.0912915355006*b59 =L= 97.0912915355006;
e101.. sqr(0.272938801260022 - x152) + sqr(9.52106324081905 - x155)
+ 160.611756853376*b60 =L= 161.611756853376;
e102.. 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 =E= 1;
e103.. sqr(3.58392835071893 - x157) + sqr(0.44370753979378 - x159)
+ 117.37605108924*b61 =L= 118.37605108924;
e104.. sqr(1.95628884344 - x157) + sqr(0.390503036650278 - x159)
+ 140.241701004457*b62 =L= 141.241701004457;
e105.. sqr(4.55035690490668 - x157) + sqr(7.27185840240323 - x159)
+ 71.5594363053072*b63 =L= 72.5594363053072;
e106.. sqr(6.2100872388646 - x157) + sqr(6.48745936675473 - x159)
+ 70.1361240423208*b64 =L= 71.1361240423208;
e107.. sqr(3.1786343207553 - x157) + sqr(2.35630065859291 - x159)
+ 91.0983527000505*b65 =L= 92.0983527000505;
e108.. sqr(2.77208272832737 - x157) + sqr(6.63537019621518 - x159)
+ 78.1787285426132*b66 =L= 79.1787285426132;
e109.. sqr(5.05196451835929 - x157) + sqr(9.78029757859562 - x159)
+ 117.525315958044*b67 =L= 118.525315958044;
e110.. sqr(4.91358831690657 - x157) + sqr(9.95200766490468 - x159)
+ 120.184782975767*b68 =L= 121.184782975767;
e111.. sqr(1.82270973029123 - x157) + sqr(3.08924661212034 - x159)
+ 100.562560044535*b69 =L= 101.562560044535;
e112.. sqr(8.90416070287928 - x157) + sqr(8.76903198117563 - x159)
+ 140.241701004457*b70 =L= 141.241701004457;
e113.. sqr(9.55691722438547 - x157) + sqr(7.67982230145412 - x159)
+ 131.965894836477*b71 =L= 132.965894836477;
e114.. sqr(5.63154215917614 - x157) + sqr(5.19669129629487 - x159)
+ 61.1865070415458*b72 =L= 62.1865070415458;
e115.. sqr(1.22506785607057 - x157) + sqr(1.73643838760701 - x159)
+ 129.251385415199*b73 =L= 130.251385415199;
e116.. sqr(3.56742024375224 - x157) + sqr(9.67716416398758 - x159)
+ 122.549628719203*b74 =L= 123.549628719203;
e117.. sqr(6.4469689992634 - x157) + sqr(3.27001587839258 - x159)
+ 94.7662927771576*b75 =L= 95.7662927771576;
e118.. sqr(6.10753237542196 - x157) + sqr(4.19206922588061 - x159)
+ 78.2445398454346*b76 =L= 79.2445398454346;
e119.. sqr(3.65877473332061 - x157) + sqr(3.63421268850839 - x159)
+ 68.5611029512265*b77 =L= 69.5611029512265;
e120.. sqr(1.2178860076098 - x157) + sqr(2.16125505734127 - x159)
+ 123.013834343708*b78 =L= 124.013834343708;
e121.. sqr(0.592074869235123 - x157) + sqr(4.93671199500253 - x159)
+ 106.643311548917*b79 =L= 107.643311548917;
e122.. sqr(6.7402850724876 - x157) + sqr(1.57064570718754 - x159)
+ 125.533092608851*b80 =L= 126.533092608851;
e123.. sqr(4.86197880938116 - x157) + sqr(0.383551455477691 - x159)
+ 125.003682175941*b81 =L= 126.003682175941;
e124.. sqr(1.8799102211015 - x157) + sqr(8.11097800063776 - x159)
+ 111.618317672146*b82 =L= 112.618317672146;
e125.. sqr(7.64684982583741 - x157) + sqr(0.420960467093494 - x159)
+ 160.611756853376*b83 =L= 161.611756853376;
e126.. sqr(3.86587305838289 - x157) + sqr(3.43289089140431 - x159)
+ 68.5364474973792*b84 =L= 69.5364474973792;
e127.. sqr(1.93085934314818 - x157) + sqr(3.48739999687651 - x159)
+ 94.0180040498471*b85 =L= 95.0180040498471;
e128.. sqr(8.14411066658926 - x157) + sqr(3.28390698782521 - x159)
+ 120.943028096043*b86 =L= 121.943028096043;
e129.. sqr(3.92781648828775 - x157) + sqr(4.5879692218008 - x159)
+ 55.2445625258556*b87 =L= 56.2445625258556;
e130.. sqr(9.43530528332928 - x157) + sqr(6.2115811426888 - x159)
+ 114.385124970594*b88 =L= 115.385124970594;
e131.. sqr(5.94277300911337 - x157) + sqr(2.72126258813597 - x159)
+ 96.0912915355006*b89 =L= 97.0912915355006;
e132.. sqr(0.272938801260022 - x157) + sqr(9.52106324081905 - x159)
+ 160.611756853376*b90 =L= 161.611756853376;
e133.. 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 =E= 1;
e134.. sqr(3.58392835071893 - x161) + sqr(0.44370753979378 - x163)
+ 117.37605108924*b91 =L= 118.37605108924;
e135.. sqr(1.95628884344 - x161) + sqr(0.390503036650278 - x163)
+ 140.241701004457*b92 =L= 141.241701004457;
e136.. sqr(4.55035690490668 - x161) + sqr(7.27185840240323 - x163)
+ 71.5594363053072*b93 =L= 72.5594363053072;
e137.. sqr(6.2100872388646 - x161) + sqr(6.48745936675473 - x163)
+ 70.1361240423208*b94 =L= 71.1361240423208;
e138.. sqr(3.1786343207553 - x161) + sqr(2.35630065859291 - x163)
+ 91.0983527000505*b95 =L= 92.0983527000505;
e139.. sqr(2.77208272832737 - x161) + sqr(6.63537019621518 - x163)
+ 78.1787285426132*b96 =L= 79.1787285426132;
e140.. sqr(5.05196451835929 - x161) + sqr(9.78029757859562 - x163)
+ 117.525315958044*b97 =L= 118.525315958044;
e141.. sqr(4.91358831690657 - x161) + sqr(9.95200766490468 - x163)
+ 120.184782975767*b98 =L= 121.184782975767;
e142.. sqr(1.82270973029123 - x161) + sqr(3.08924661212034 - x163)
+ 100.562560044535*b99 =L= 101.562560044535;
e143.. sqr(8.90416070287928 - x161) + sqr(8.76903198117563 - x163)
+ 140.241701004457*b100 =L= 141.241701004457;
e144.. sqr(9.55691722438547 - x161) + sqr(7.67982230145412 - x163)
+ 131.965894836477*b101 =L= 132.965894836477;
e145.. sqr(5.63154215917614 - x161) + sqr(5.19669129629487 - x163)
+ 61.1865070415458*b102 =L= 62.1865070415458;
e146.. sqr(1.22506785607057 - x161) + sqr(1.73643838760701 - x163)
+ 129.251385415199*b103 =L= 130.251385415199;
e147.. sqr(3.56742024375224 - x161) + sqr(9.67716416398758 - x163)
+ 122.549628719203*b104 =L= 123.549628719203;
e148.. sqr(6.4469689992634 - x161) + sqr(3.27001587839258 - x163)
+ 94.7662927771576*b105 =L= 95.7662927771576;
e149.. sqr(6.10753237542196 - x161) + sqr(4.19206922588061 - x163)
+ 78.2445398454346*b106 =L= 79.2445398454346;
e150.. sqr(3.65877473332061 - x161) + sqr(3.63421268850839 - x163)
+ 68.5611029512265*b107 =L= 69.5611029512265;
e151.. sqr(1.2178860076098 - x161) + sqr(2.16125505734127 - x163)
+ 123.013834343708*b108 =L= 124.013834343708;
e152.. sqr(0.592074869235123 - x161) + sqr(4.93671199500253 - x163)
+ 106.643311548917*b109 =L= 107.643311548917;
e153.. sqr(6.7402850724876 - x161) + sqr(1.57064570718754 - x163)
+ 125.533092608851*b110 =L= 126.533092608851;
e154.. sqr(4.86197880938116 - x161) + sqr(0.383551455477691 - x163)
+ 125.003682175941*b111 =L= 126.003682175941;
e155.. sqr(1.8799102211015 - x161) + sqr(8.11097800063776 - x163)
+ 111.618317672146*b112 =L= 112.618317672146;
e156.. sqr(7.64684982583741 - x161) + sqr(0.420960467093494 - x163)
+ 160.611756853376*b113 =L= 161.611756853376;
e157.. sqr(3.86587305838289 - x161) + sqr(3.43289089140431 - x163)
+ 68.5364474973792*b114 =L= 69.5364474973792;
e158.. sqr(1.93085934314818 - x161) + sqr(3.48739999687651 - x163)
+ 94.0180040498471*b115 =L= 95.0180040498471;
e159.. sqr(8.14411066658926 - x161) + sqr(3.28390698782521 - x163)
+ 120.943028096043*b116 =L= 121.943028096043;
e160.. sqr(3.92781648828775 - x161) + sqr(4.5879692218008 - x163)
+ 55.2445625258556*b117 =L= 56.2445625258556;
e161.. sqr(9.43530528332928 - x161) + sqr(6.2115811426888 - x163)
+ 114.385124970594*b118 =L= 115.385124970594;
e162.. sqr(5.94277300911337 - x161) + sqr(2.72126258813597 - x163)
+ 96.0912915355006*b119 =L= 97.0912915355006;
e163.. sqr(0.272938801260022 - x161) + sqr(9.52106324081905 - x163)
+ 160.611756853376*b120 =L= 161.611756853376;
e164.. 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 =E= 1;
e165.. sqr(3.58392835071893 - x165) + sqr(0.44370753979378 - x167)
+ 117.37605108924*b121 =L= 118.37605108924;
e166.. sqr(1.95628884344 - x165) + sqr(0.390503036650278 - x167)
+ 140.241701004457*b122 =L= 141.241701004457;
e167.. sqr(4.55035690490668 - x165) + sqr(7.27185840240323 - x167)
+ 71.5594363053072*b123 =L= 72.5594363053072;
e168.. sqr(6.2100872388646 - x165) + sqr(6.48745936675473 - x167)
+ 70.1361240423208*b124 =L= 71.1361240423208;
e169.. sqr(3.1786343207553 - x165) + sqr(2.35630065859291 - x167)
+ 91.0983527000505*b125 =L= 92.0983527000505;
e170.. sqr(2.77208272832737 - x165) + sqr(6.63537019621518 - x167)
+ 78.1787285426132*b126 =L= 79.1787285426132;
e171.. sqr(5.05196451835929 - x165) + sqr(9.78029757859562 - x167)
+ 117.525315958044*b127 =L= 118.525315958044;
e172.. sqr(4.91358831690657 - x165) + sqr(9.95200766490468 - x167)
+ 120.184782975767*b128 =L= 121.184782975767;
e173.. sqr(1.82270973029123 - x165) + sqr(3.08924661212034 - x167)
+ 100.562560044535*b129 =L= 101.562560044535;
e174.. sqr(8.90416070287928 - x165) + sqr(8.76903198117563 - x167)
+ 140.241701004457*b130 =L= 141.241701004457;
e175.. sqr(9.55691722438547 - x165) + sqr(7.67982230145412 - x167)
+ 131.965894836477*b131 =L= 132.965894836477;
e176.. sqr(5.63154215917614 - x165) + sqr(5.19669129629487 - x167)
+ 61.1865070415458*b132 =L= 62.1865070415458;
e177.. sqr(1.22506785607057 - x165) + sqr(1.73643838760701 - x167)
+ 129.251385415199*b133 =L= 130.251385415199;
e178.. sqr(3.56742024375224 - x165) + sqr(9.67716416398758 - x167)
+ 122.549628719203*b134 =L= 123.549628719203;
e179.. sqr(6.4469689992634 - x165) + sqr(3.27001587839258 - x167)
+ 94.7662927771576*b135 =L= 95.7662927771576;
e180.. sqr(6.10753237542196 - x165) + sqr(4.19206922588061 - x167)
+ 78.2445398454346*b136 =L= 79.2445398454346;
e181.. sqr(3.65877473332061 - x165) + sqr(3.63421268850839 - x167)
+ 68.5611029512265*b137 =L= 69.5611029512265;
e182.. sqr(1.2178860076098 - x165) + sqr(2.16125505734127 - x167)
+ 123.013834343708*b138 =L= 124.013834343708;
e183.. sqr(0.592074869235123 - x165) + sqr(4.93671199500253 - x167)
+ 106.643311548917*b139 =L= 107.643311548917;
e184.. sqr(6.7402850724876 - x165) + sqr(1.57064570718754 - x167)
+ 125.533092608851*b140 =L= 126.533092608851;
e185.. sqr(4.86197880938116 - x165) + sqr(0.383551455477691 - x167)
+ 125.003682175941*b141 =L= 126.003682175941;
e186.. sqr(1.8799102211015 - x165) + sqr(8.11097800063776 - x167)
+ 111.618317672146*b142 =L= 112.618317672146;
e187.. sqr(7.64684982583741 - x165) + sqr(0.420960467093494 - x167)
+ 160.611756853376*b143 =L= 161.611756853376;
e188.. sqr(3.86587305838289 - x165) + sqr(3.43289089140431 - x167)
+ 68.5364474973792*b144 =L= 69.5364474973792;
e189.. sqr(1.93085934314818 - x165) + sqr(3.48739999687651 - x167)
+ 94.0180040498471*b145 =L= 95.0180040498471;
e190.. sqr(8.14411066658926 - x165) + sqr(3.28390698782521 - x167)
+ 120.943028096043*b146 =L= 121.943028096043;
e191.. sqr(3.92781648828775 - x165) + sqr(4.5879692218008 - x167)
+ 55.2445625258556*b147 =L= 56.2445625258556;
e192.. sqr(9.43530528332928 - x165) + sqr(6.2115811426888 - x167)
+ 114.385124970594*b148 =L= 115.385124970594;
e193.. sqr(5.94277300911337 - x165) + sqr(2.72126258813597 - x167)
+ 96.0912915355006*b149 =L= 97.0912915355006;
e194.. sqr(0.272938801260022 - x165) + sqr(9.52106324081905 - x167)
+ 160.611756853376*b150 =L= 161.611756853376;
e195.. b121 + b122 + b123 + b124 + b125 + b126 + b127 + b128 + b129 + b130
+ b131 + b132 + b133 + b134 + b135 + b136 + b137 + b138 + b139 + b140
+ b141 + b142 + b143 + b144 + b145 + b146 + b147 + b148 + b149 + b150
=E= 1;
e196.. b1 + b31 + b61 + b91 + b121 =L= 1;
e197.. b2 + b32 + b62 + b92 + b122 =L= 1;
e198.. b3 + b33 + b63 + b93 + b123 =L= 1;
e199.. b4 + b34 + b64 + b94 + b124 =L= 1;
e200.. b5 + b35 + b65 + b95 + b125 =L= 1;
e201.. b6 + b36 + b66 + b96 + b126 =L= 1;
e202.. b7 + b37 + b67 + b97 + b127 =L= 1;
e203.. b8 + b38 + b68 + b98 + b128 =L= 1;
e204.. b9 + b39 + b69 + b99 + b129 =L= 1;
e205.. b10 + b40 + b70 + b100 + b130 =L= 1;
e206.. b11 + b41 + b71 + b101 + b131 =L= 1;
e207.. b12 + b42 + b72 + b102 + b132 =L= 1;
e208.. b13 + b43 + b73 + b103 + b133 =L= 1;
e209.. b14 + b44 + b74 + b104 + b134 =L= 1;
e210.. b15 + b45 + b75 + b105 + b135 =L= 1;
e211.. b16 + b46 + b76 + b106 + b136 =L= 1;
e212.. b17 + b47 + b77 + b107 + b137 =L= 1;
e213.. b18 + b48 + b78 + b108 + b138 =L= 1;
e214.. b19 + b49 + b79 + b109 + b139 =L= 1;
e215.. b20 + b50 + b80 + b110 + b140 =L= 1;
e216.. b21 + b51 + b81 + b111 + b141 =L= 1;
e217.. b22 + b52 + b82 + b112 + b142 =L= 1;
e218.. b23 + b53 + b83 + b113 + b143 =L= 1;
e219.. b24 + b54 + b84 + b114 + b144 =L= 1;
e220.. b25 + b55 + b85 + b115 + b145 =L= 1;
e221.. b26 + b56 + b86 + b116 + b146 =L= 1;
e222.. b27 + b57 + b87 + b117 + b147 =L= 1;
e223.. b28 + b58 + b88 + b118 + b148 =L= 1;
e224.. b29 + b59 + b89 + b119 + b149 =L= 1;
e225.. b30 + b60 + b90 + b120 + b150 =L= 1;
e226.. x151 - x152 =L= 0;
e227.. x152 - x157 =L= 0;
e228.. x157 - x161 =L= 0;
e229.. x161 - x165 =L= 0;
e230.. - x153 - x156 - x158 - x160 - x162 - x164 - x166 - x168 - x169 - x170
- x171 - x172 - x173 - x174 - x175 - x176 - x177 - x178 - x179 - x180
+ objvar =E= 0;
* set non-default bounds
x151.up = 10;
x152.up = 10;
x153.up = 10;
x154.up = 10;
x155.up = 10;
x156.up = 10;
x157.up = 10;
x158.up = 10;
x159.up = 10;
x160.up = 10;
x161.up = 10;
x162.up = 10;
x163.up = 10;
x164.up = 10;
x165.up = 10;
x166.up = 10;
x167.up = 10;
x168.up = 10;
x169.up = 10;
x170.up = 10;
x171.up = 10;
x172.up = 10;
x173.up = 10;
x174.up = 10;
x175.up = 10;
x176.up = 10;
x177.up = 10;
x178.up = 10;
x179.up = 10;
x180.up = 10;
* set non-default levels
b25.l = 1;
b35.l = 1;
b69.l = 1;
b107.l = 1;
b144.l = 1;
x151.l = 2.80824226248558;
x152.l = 2.80824226248558;
x154.l = 3.25902574907896;
x155.l = 3.25902574907896;
x157.l = 2.80824226248558;
x159.l = 3.25902574907896;
x161.l = 2.80824226248558;
x163.l = 3.25902574907896;
x165.l = 2.88110099828265;
x166.l = 0.072858735797072;
x167.l = 3.25902574907896;
x173.l = 0.072858735797072;
x177.l = 0.072858735797072;
x179.l = 0.072858735797072;
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