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Instance sporttournament24
This is a quadratic model for the max-cut problem. The instance arises when minimizing so-called breaks in sports tournaments.
| Formatsⓘ | ams gms lp mod nl osil pip py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | 303.27272730 (ANTIGONE) 282.00000030 (BARON) 329.00000000 (COUENNE) 315.27707000 (CPLEX) 282.00000000 (GUROBI) 298.00000000 (LINDO) 282.00000000 (SCIP) 282.00000000 (SHOT) |
| Referencesⓘ | Elf, Matthias, Jünger, Michael, and Rinaldi, Giovanni, Minimizing Breaks by Maximizing Cuts, Operations Research Letters, 31:5, 2003, 343-349. |
| Sourceⓘ | POLIP instance maxcut/sched-24-4711 |
| Applicationⓘ | Sports Tournament |
| Added to libraryⓘ | 26 Feb 2014 |
| Problem typeⓘ | MBQCP |
| #Variablesⓘ | 277 |
| #Binary Variablesⓘ | 276 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 276 |
| #Nonlinear Binary Variablesⓘ | 276 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | max |
| Objective typeⓘ | linear |
| Objective curvatureⓘ | linear |
| #Nonzeros in Objectiveⓘ | 1 |
| #Nonlinear Nonzeros in Objectiveⓘ | 0 |
| #Constraintsⓘ | 1 |
| #Linear Constraintsⓘ | 0 |
| #Quadratic Constraintsⓘ | 1 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 0 |
| Operands in Gen. Nonlin. Functionsⓘ | |
| Constraints curvatureⓘ | indefinite |
| #Nonzeros in Jacobianⓘ | 277 |
| #Nonlinear Nonzeros in Jacobianⓘ | 276 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 1056 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 0 |
| #Blocks in Hessian of Lagrangianⓘ | 1 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 276 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 276 |
| Average blocksize in Hessian of Lagrangianⓘ | 276.0 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 1.0000e+00 |
| Maximal coefficientⓘ | 4.0000e+00 |
| Infeasibility of initial pointⓘ | 0 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 1 0 0 1 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 277 1 276 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 277 1 276 0
*
* Solve m using MINLP maximizing 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,b151,b152,b153,b154,b155
,b156,b157,b158,b159,b160,b161,b162,b163,b164,b165,b166,b167,b168
,b169,b170,b171,b172,b173,b174,b175,b176,b177,b178,b179,b180,b181
,b182,b183,b184,b185,b186,b187,b188,b189,b190,b191,b192,b193,b194
,b195,b196,b197,b198,b199,b200,b201,b202,b203,b204,b205,b206,b207
,b208,b209,b210,b211,b212,b213,b214,b215,b216,b217,b218,b219,b220
,b221,b222,b223,b224,b225,b226,b227,b228,b229,b230,b231,b232,b233
,b234,b235,b236,b237,b238,b239,b240,b241,b242,b243,b244,b245,b246
,b247,b248,b249,b250,b251,b252,b253,b254,b255,b256,b257,b258,b259
,b260,b261,b262,b263,b264,b265,b266,b267,b268,b269,b270,b271,b272
,b273,b274,b275,b276,objvar;
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,b151,b152,b153
,b154,b155,b156,b157,b158,b159,b160,b161,b162,b163,b164,b165,b166
,b167,b168,b169,b170,b171,b172,b173,b174,b175,b176,b177,b178,b179
,b180,b181,b182,b183,b184,b185,b186,b187,b188,b189,b190,b191,b192
,b193,b194,b195,b196,b197,b198,b199,b200,b201,b202,b203,b204,b205
,b206,b207,b208,b209,b210,b211,b212,b213,b214,b215,b216,b217,b218
,b219,b220,b221,b222,b223,b224,b225,b226,b227,b228,b229,b230,b231
,b232,b233,b234,b235,b236,b237,b238,b239,b240,b241,b242,b243,b244
,b245,b246,b247,b248,b249,b250,b251,b252,b253,b254,b255,b256,b257
,b258,b259,b260,b261,b262,b263,b264,b265,b266,b267,b268,b269,b270
,b271,b272,b273,b274,b275,b276;
Equations e1;
e1.. 2*b1*b2 - 2*b1 - 2*b2 + 2*b1*b105 - 2*b105 + 2*b1*b185 - 2*b1*b189 + 2*b2*
b83 - 4*b83 - 2*b2*b102 + 2*b102 + 2*b2*b186 - 2*b3*b69 - 2*b3 + 4*b69 + 2
*b3*b191 + 2*b3*b203 + 2*b3*b204 + 2*b4*b37 - 2*b4 - 2*b37 - 2*b4*b89 + 4*
b89 + 2*b4*b188 + 2*b4*b191 + 2*b5*b133 - 2*b5 - 2*b133 + 2*b5*b163 - 2*
b163 + 2*b5*b206 - 2*b5*b212 + 2*b6*b54 - 2*b6 - 4*b54 + 2*b6*b72 - 2*b72
- 2*b6*b110 + 4*b110 + 2*b6*b188 + 2*b7*b160 - 2*b7 - 4*b160 + 2*b7*b198
+ 2*b7*b206 - 2*b7*b217 + 2*b8*b70 - 2*b8 - 4*b70 + 2*b8*b72 - 2*b8*b131
+ 2*b131 + 2*b8*b192 + 2*b9*b22 - 2*b9 - 2*b22 - 2*b9*b227 + 2*b9*b228 +
2*b9*b229 + 2*b10*b22 - 2*b10 + 2*b10*b30 - 4*b30 - 2*b10*b235 + 2*b10*
b236 + 2*b11*b57 - 2*b11 - 2*b57 + 2*b11*b75 - 2*b75 + 2*b11*b187 - 2*b11*
b238 + 2*b12*b30 - 2*b12 + 2*b12*b43 - 4*b43 + 2*b12*b96 - 2*b96 - 2*b12*
b239 + 2*b13*b25 - 2*b13 - 2*b25 + 2*b13*b153 - 4*b153 + 2*b14*b57 - 2*b14
- 2*b14*b92 + 2*b92 + 2*b14*b190 + 2*b14*b207 + 2*b15*b43 - 2*b15 + 2*b15
*b60 - 4*b60 + 2*b15*b117 - 4*b117 - 2*b15*b243 - 2*b16*b22 - 2*b16 + 2*
b16*b32 - 4*b32 + 2*b16*b43 + 2*b16*b244 + 2*b17*b60 - 4*b17 + 2*b17*b78
- 4*b78 + 2*b17*b141 - 4*b141 + 2*b17*b243 + 2*b18*b32 - 2*b18 + 2*b18*
b45 - 4*b45 + 2*b18*b60 - 2*b18*b229 + 2*b19*b49 - 2*b19 - 4*b49 + 2*b19*
b241 + 2*b20*b40 - 2*b20 - 2*b40 - 2*b20*b135 - 2*b135 + 2*b20*b163 + 2*
b20*b225 + 2*b21*b78 - 4*b21 + 2*b21*b97 - 4*b97 + 2*b21*b168 - 4*b168 + 2
*b21*b239 + 2*b22*b31 - 4*b31 + 2*b23*b45 - 4*b23 + 2*b23*b62 - 4*b62 + 2*
b23*b78 + 2*b23*b229 - 2*b24*b25 - 2*b24 + 2*b24*b47 - 4*b47 + 2*b24*b65
- 4*b65 + 2*b24*b252 + 2*b25*b26 - 2*b26 + 2*b25*b64 - 4*b64 + 2*b26*b65
+ 2*b27*b28 - 4*b27 - 4*b28 + 2*b27*b197 + 2*b27*b213 + 2*b27*b251 + 2*
b28*b183 + 2*b28*b225 + 2*b28*b227 + 2*b29*b97 - 2*b29 + 2*b29*b119 - 2*
b119 - 2*b29*b183 + 2*b29*b235 + 2*b30*b44 - 4*b44 + 2*b30*b171 - 2*b171
+ 2*b31*b62 + 2*b31*b80 - 4*b80 + 2*b31*b97 + 2*b32*b81 - 4*b81 + 2*b32*
b237 + 2*b33*b34 - 4*b33 - 2*b34 + 2*b33*b248 + 2*b33*b255 + 2*b33*b259 +
2*b34*b63 - 4*b63 + 2*b34*b87 - 4*b87 - 2*b34*b241 + 2*b35*b36 - 2*b35 - 2
*b36 + 2*b35*b86 - 4*b86 - 2*b35*b248 + 2*b35*b249 + 2*b36*b87 + 2*b37*b55
- 2*b55 + 2*b37*b220 - 2*b37*b260 + 2*b38*b55 - 4*b38 + 2*b38*b196 + 2*
b38*b238 + 2*b38*b250 + 2*b39*b41 + 2*b39 - 4*b41 - 2*b39*b76 + 4*b76 - 2*
b39*b94 - 2*b94 - 2*b39*b207 + 2*b40*b193 + 2*b40*b208 - 2*b40*b254 + 2*
b41*b42 + 2*b42 + 2*b41*b205 + 2*b41*b254 - 2*b42*b138 + 2*b138 - 2*b42*
b140 + 2*b140 - 2*b42*b183 + 2*b43*b61 - 2*b61 + 2*b44*b80 + 2*b44*b100 -
4*b100 + 2*b44*b119 + 2*b45*b230 + 2*b45*b245 + 2*b46*b184 - 2*b46 + 2*b46
*b201 + 2*b46*b245 - 2*b46*b256 + 2*b47*b48 - 4*b48 + 2*b47*b84 - 2*b84 +
2*b47*b256 + 2*b48*b85 - 4*b85 + 2*b48*b107 - 4*b107 + 2*b48*b241 + 2*b49*
b50 - 2*b50 + 2*b49*b106 - 4*b106 + 2*b49*b248 + 2*b50*b107 + 2*b51*b67 -
2*b51 - 4*b67 + 2*b51*b260 + 2*b52*b54 - 4*b52 + 2*b52*b157 - 2*b157 + 2*
b52*b221 + 2*b52*b231 - 2*b53*b71 + 2*b53 - 2*b71 - 2*b53*b156 + 4*b156 -
2*b53*b196 + 2*b53*b210 + 2*b54*b71 + 2*b54*b260 + 2*b55*b56 - 2*b56 - 2*
b55*b203 + 2*b56*b71 - 2*b56*b92 + 2*b56*b234 - 2*b57*b165 + 4*b165 + 2*
b57*b197 - 2*b58*b59 + 2*b58 + 2*b59 - 2*b58*b193 + 2*b58*b199 - 2*b58*
b251 + 2*b59*b228 - 2*b59*b239 - 2*b59*b263 + 2*b60*b79 - 2*b79 + 2*b61*
b100 + 2*b61*b122 - 4*b122 - 2*b61*b170 - 2*b170 + 2*b62*b219 + 2*b62*b240
+ 2*b63*b64 + 2*b63*b103 - 2*b103 + 2*b63*b259 + 2*b64*b104 - 4*b104 + 2*
b64*b128 - 2*b128 + 2*b65*b66 - 2*b66 + 2*b65*b179 - 2*b179 + 2*b66*b128
+ 2*b67*b70 + 2*b67*b131 + 2*b67*b215 + 2*b68*b70 + 2*b68 - 2*b68*b203 -
2*b68*b222 - 2*b68*b266 - 2*b69*b90 - 2*b90 - 2*b69*b130 + 2*b130 - 2*b69*
b202 + 2*b70*b90 + 2*b71*b73 - 2*b73 + 2*b72*b187 - 2*b72*b224 + 2*b73*b90
+ 2*b73*b224 - 2*b73*b253 + 2*b74*b163 - 2*b74 + 2*b74*b234 + 2*b74*b250
- 2*b74*b262 - 2*b75*b136 + 2*b136 + 2*b75*b193 + 2*b75*b233 - 2*b76*b77
+ 2*b77 - 2*b76*b197 - 2*b76*b199 + 2*b77*b236 - 2*b77*b243 - 2*b77*b267
+ 2*b78*b99 - 2*b99 + 2*b79*b122 + 2*b79*b144 - 4*b144 - 2*b79*b264 + 2*
b80*b82 - 4*b82 + 2*b80*b237 + 2*b81*b83 + 2*b81*b173 - 4*b173 + 2*b81*
b209 + 2*b82*b83 + 2*b82*b144 + 2*b82*b175 + 2*b175 + 2*b83*b84 + 2*b84*
b85 - 2*b84*b200 + 2*b85*b86 + 2*b85*b126 - 2*b126 + 2*b86*b127 - 4*b127
+ 2*b86*b152 - 2*b152 + 2*b87*b88 - 2*b88 + 2*b87*b151 - 2*b151 + 2*b88*
b152 - 2*b89*b210 - 2*b89*b246 - 2*b89*b269 + 2*b90*b91 - 2*b91 + 2*b91*
b217 - 2*b91*b250 + 2*b91*b269 - 2*b92*b112 - 2*b112 + 2*b92*b132 - 4*b132
+ 2*b93*b94 - 2*b93 + 2*b93*b224 - 2*b93*b238 + 2*b93*b262 + 2*b94*b112
+ 2*b94*b114 + 2*b114 - 2*b95*b165 + 4*b95 - 2*b95*b205 - 2*b95*b208 - 2*
b95*b247 + 2*b96*b118 - 2*b118 - 2*b96*b199 + 2*b96*b247 + 2*b97*b121 - 4*
b121 + 2*b98*b118 - 4*b98 + 2*b98*b121 + 2*b98*b171 + 2*b98*b218 - 2*b99*
b120 - 2*b120 + 2*b99*b144 + 2*b99*b172 - 4*b172 + 2*b100*b101 - 4*b101 +
2*b100*b230 + 2*b101*b147 + 2*b147 + 2*b101*b172 + 2*b101*b265 - 2*b102*
b103 + 2*b102*b146 - 4*b146 - 2*b102*b240 + 2*b103*b104 + 2*b103*b265 + 2*
b104*b106 + 2*b104*b148 - 2*b148 - 2*b105*b128 + 2*b105*b149 - 2*b149 + 2*
b105*b181 - 4*b181 + 2*b106*b150 - 2*b150 + 2*b106*b181 + 2*b107*b108 - 2*
b108 + 2*b107*b180 - 2*b180 + 2*b108*b181 + 2*b109*b130 - 2*b109 + 2*b109*
b202 - 2*b110*b214 - 2*b110*b242 - 2*b110*b272 + 2*b111*b212 - 4*b111 + 2*
b111*b253 + 2*b111*b269 + 2*b111*b272 + 2*b112*b113 - 2*b113 + 2*b112*b217
+ 2*b113*b134 - 2*b134 + 2*b113*b226 - 2*b113*b251 - 2*b114*b138 - 2*b114
*b194 - 2*b114*b271 - 2*b115*b116 + 2*b115 - 2*b116 - 2*b115*b136 + 2*b115
*b166 - 2*b166 - 2*b115*b213 + 2*b116*b117 + 2*b116*b239 + 2*b116*b271 + 2
*b117*b142 - 2*b142 + 2*b117*b199 + 2*b118*b120 - 2*b118*b236 + 2*b119*
b143 - 4*b143 - 2*b119*b257 + 2*b120*b142 + 2*b120*b143 + 2*b121*b123 - 2*
b123 + 2*b121*b172 + 2*b122*b124 - 4*b124 + 2*b122*b219 + 2*b123*b124 + 2*
b123*b143 - 2*b123*b184 + 2*b124*b125 + 2*b125 + 2*b124*b261 - 2*b125*b126
- 2*b125*b189 - 2*b125*b237 + 2*b126*b127 + 2*b126*b261 + 2*b127*b177 - 2
*b177 + 2*b127*b179 + 2*b128*b274 - 2*b129*b202 + 2*b129 - 2*b129*b246 - 2
*b130*b211 - 2*b130*b273 - 2*b131*b158 - 2*b158 - 2*b131*b220 + 2*b132*
b133 + 2*b132*b158 + 2*b132*b272 + 2*b133*b161 - 2*b161 - 2*b133*b204 + 2*
b134*b135 + 2*b134*b212 - 2*b134*b253 + 2*b135*b137 - 2*b137 + 2*b135*b161
+ 2*b136*b262 - 2*b136*b267 + 2*b137*b138 - 2*b137*b206 + 2*b137*b267 - 2
*b138*b139 - 2*b139 + 2*b139*b141 + 2*b139*b235 + 2*b139*b267 - 2*b140*
b169 - 2*b169 - 2*b140*b218 + 2*b140*b254 + 2*b141*b169 + 2*b141*b208 - 2*
b142*b228 + 2*b142*b264 + 2*b143*b145 - 2*b145 + 2*b144*b146 + 2*b145*b146
+ 2*b145*b184 - 2*b145*b276 + 2*b146*b258 - 2*b147*b148 - 2*b147*b195 - 2
*b147*b230 + 2*b148*b150 + 2*b148*b258 - 2*b149*b151 + 2*b149*b189 + 2*
b149*b201 + 2*b150*b151 - 2*b150*b201 + 2*b151*b153 + 2*b152*b154 - 2*b154
- 2*b152*b185 + 2*b153*b154 + 2*b153*b185 - 2*b155*b210 + 2*b155 - 2*b155
*b242 - 2*b156*b216 - 2*b156*b268 - 2*b156*b270 + 2*b157*b196 + 2*b157*
b202 - 2*b157*b232 + 2*b158*b159 - 4*b159 + 2*b158*b273 + 2*b159*b160 + 2*
b159*b232 + 2*b159*b238 + 2*b160*b162 - 2*b162 + 2*b160*b204 + 2*b161*b164
- 4*b164 - 2*b161*b250 + 2*b162*b164 - 2*b162*b207 + 2*b162*b253 - 2*b163
*b166 + 2*b164*b166 + 2*b164*b251 - 2*b165*b262 - 2*b165*b263 + 2*b166*
b263 + 2*b167*b168 - 2*b167 - 2*b167*b225 + 2*b167*b227 + 2*b167*b263 + 2*
b168*b213 + 2*b168*b257 + 2*b169*b170 + 2*b169*b264 + 2*b170*b257 + 2*b170
*b276 + 2*b171*b173 - 2*b171*b244 + 2*b172*b174 - 4*b174 + 2*b173*b174 + 2
*b173*b276 + 2*b174*b176 - 2*b176 + 2*b174*b200 - 2*b175*b177 - 2*b175*
b201 - 2*b175*b219 + 2*b176*b177 - 2*b176*b240 + 2*b176*b255 + 2*b177*b178
- 2*b178 + 2*b178*b179 + 2*b178*b180 - 2*b178*b195 - 2*b179*b275 - 2*b180
*b186 + 2*b180*b275 + 2*b181*b182 - 2*b182 + 2*b182*b275 + 2*b183*b218 - 2
*b184*b209 - 2*b185*b186 + 2*b186*b195 - 2*b187*b188 - 2*b187*b233 - 2*
b188*b217 + 2*b189*b200 - 2*b190*b191 + 2*b190*b192 - 2*b190*b223 - 2*b191
*b212 - 2*b192*b232 - 2*b192*b234 - 2*b193*b194 + 2*b194*b223 + 2*b194*
b233 + 2*b195*b209 - 2*b196*b204 - 2*b197*b198 + 2*b198*b223 - 2*b198*b226
- 2*b200*b245 + 2*b203*b214 - 2*b205*b206 + 2*b205*b207 - 2*b208*b236 - 2
*b209*b259 + 2*b210*b211 - 2*b213*b228 - 2*b214*b215 + 2*b214*b216 - 2*
b218*b229 - 2*b219*b265 - 2*b220*b221 + 2*b220*b222 - 2*b223*b224 - 2*b225
*b226 + 2*b226*b271 - 2*b227*b257 - 2*b230*b261 - 2*b231*b260 + 2*b232*
b270 - 2*b233*b234 - 2*b235*b254 - 2*b237*b258 + 2*b240*b244 - 2*b241*b249
+ 2*b242*b266 + 2*b242*b270 + 2*b243*b247 - 2*b244*b245 + 2*b246*b268 + 2
*b246*b273 - 2*b247*b271 - 2*b248*b252 - 2*b252*b255 + 2*b252*b256 - 2*
b255*b258 - 2*b256*b261 - 2*b259*b265 - 2*b264*b276 - 2*b269*b270 - 2*b272
*b273 - 2*b274*b275 + objvar =L= 0;
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% maximizing objvar;
Last updated: 2025-08-07 Git hash: e62cedfc