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Instance sporttournament22
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ⓘ | 244.86363640 (ANTIGONE) 234.00000020 (BARON) 273.00000000 (COUENNE) 268.36454670 (CPLEX) 234.00000000 (GUROBI) 242.00000000 (LINDO) 234.00000000 (SCIP) 234.00000000 (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-22-4711 |
| Applicationⓘ | Sports Tournament |
| Added to libraryⓘ | 26 Feb 2014 |
| Problem typeⓘ | MBQCP |
| #Variablesⓘ | 232 |
| #Binary Variablesⓘ | 231 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 231 |
| #Nonlinear Binary Variablesⓘ | 231 |
| #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ⓘ | 232 |
| #Nonlinear Nonzeros in Jacobianⓘ | 231 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 880 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 0 |
| #Blocks in Hessian of Lagrangianⓘ | 1 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 231 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 231 |
| Average blocksize in Hessian of Lagrangianⓘ | 231.0 |
| #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
* 232 1 231 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 232 1 231 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,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;
Equations e1;
e1.. 2*b1*b2 - 2*b1 - 2*b2 + 2*b1*b85 - 2*b85 + 2*b1*b166 - 2*b1*b170 + 2*b2*
b62 - 4*b62 - 2*b2*b125 + 2*b125 + 2*b2*b167 - 2*b3*b89 - 2*b3 + 2*b89 + 2
*b3*b172 + 2*b3*b180 + 2*b3*b181 - 2*b4*b110 - 2*b4 + 2*b110 + 2*b4*b169
+ 2*b4*b172 + 2*b4*b186 + 2*b5*b8 - 2*b5 - 4*b8 + 2*b5*b176 + 2*b6*b36 -
2*b6 - 2*b36 + 2*b6*b50 - 2*b50 - 2*b6*b135 + 2*b135 + 2*b6*b169 + 2*b7*
b20 - 2*b7 - 2*b20 - 2*b7*b118 + 2*b118 + 2*b7*b194 + 2*b7*b195 + 2*b8*b48
- 2*b48 + 2*b8*b50 + 2*b8*b173 + 2*b9*b20 - 2*b9 + 2*b9*b29 - 4*b29 + 2*
b9*b76 - 2*b76 - 2*b9*b146 + 2*b146 + 2*b10*b29 - 2*b10 + 2*b10*b40 - 4*
b40 + 2*b10*b99 - 4*b99 - 2*b10*b203 + 2*b11*b23 - 2*b11 - 2*b23 + 2*b11*
b133 - 4*b133 + 2*b12*b40 - 2*b12 + 2*b12*b56 - 4*b56 + 2*b12*b119 - 4*
b119 - 2*b12*b207 - 2*b13*b20 - 2*b13 + 2*b13*b31 - 4*b31 + 2*b13*b40 + 2*
b13*b208 + 2*b14*b56 - 4*b14 + 2*b14*b77 - 4*b77 + 2*b14*b147 - 4*b147 + 2
*b14*b207 + 2*b15*b31 - 2*b15 + 2*b15*b42 - 4*b42 + 2*b15*b56 - 2*b15*b195
+ 2*b16*b46 - 2*b16 - 4*b46 + 2*b16*b205 + 2*b17*b18 - 2*b17 - 2*b18 + 2*
b17*b25 - 2*b25 + 2*b17*b93 - 4*b93 - 2*b17*b182 + 2*b18*b26 - 2*b26 + 2*
b18*b38 - 2*b38 - 2*b18*b214 + 2*b19*b77 - 2*b19 + 2*b19*b101 - 2*b101 - 2
*b19*b163 + 2*b19*b203 + 2*b20*b30 - 4*b30 + 2*b21*b42 - 4*b21 + 2*b21*b58
- 4*b58 + 2*b21*b77 + 2*b21*b195 - 2*b22*b23 - 2*b22 + 2*b22*b44 - 4*b44
+ 2*b22*b66 - 4*b66 + 2*b22*b213 + 2*b23*b24 - 2*b24 + 2*b23*b65 - 4*b65
+ 2*b24*b66 + 2*b25*b27 - 4*b27 + 2*b25*b53 - 2*b53 - 2*b25*b116 + 4*b116
+ 2*b26*b28 - 4*b28 + 2*b26*b164 - 2*b26*b193 + 2*b27*b28 + 2*b27*b164 +
2*b27*b212 + 2*b28*b118 + 2*b28*b163 + 2*b29*b41 - 2*b41 + 2*b29*b150 - 2*
b150 + 2*b30*b58 + 2*b30*b80 - 4*b80 + 2*b30*b101 + 2*b31*b59 - 4*b59 + 2*
b31*b200 + 2*b32*b33 - 4*b32 - 2*b33 + 2*b32*b63 - 2*b63 + 2*b32*b210 + 2*
b32*b216 + 2*b33*b64 - 4*b64 + 2*b33*b87 - 4*b87 - 2*b33*b205 + 2*b34*b35
- 2*b34 - 2*b35 + 2*b34*b86 - 4*b86 - 2*b34*b210 + 2*b34*b211 + 2*b35*b87
+ 2*b36*b49 - 2*b49 + 2*b37*b49 - 4*b37 + 2*b37*b91 - 2*b91 + 2*b37*b176
+ 2*b37*b202 - 2*b38*b39 + 2*b39 + 2*b38*b177 + 2*b38*b189 + 2*b39*b98 +
2*b98 - 2*b39*b146 - 2*b39*b218 + 2*b40*b57 - 2*b57 + 2*b41*b80 + 2*b41*
b104 - 4*b104 - 2*b41*b149 - 2*b149 + 2*b42*b153 + 2*b153 + 2*b42*b196 + 2
*b43*b44 - 2*b43 + 2*b43*b156 - 2*b156 + 2*b43*b213 - 2*b43*b220 + 2*b44*
b45 - 4*b45 + 2*b44*b83 - 2*b83 + 2*b45*b84 - 4*b84 + 2*b45*b109 - 2*b109
+ 2*b45*b205 + 2*b46*b47 - 2*b47 + 2*b46*b159 - 2*b159 + 2*b46*b210 + 2*
b47*b109 + 2*b48*b69 - 2*b69 + 2*b49*b51 - 2*b51 - 2*b49*b186 - 2*b50*b138
+ 2*b138 + 2*b50*b168 + 2*b51*b69 + 2*b51*b138 - 2*b51*b206 + 2*b52*b53
- 2*b52 - 2*b52*b54 + 2*b54 + 2*b52*b171 + 2*b52*b202 - 2*b53*b115 + 2*
b115 + 2*b53*b182 + 2*b54*b115 - 2*b54*b142 + 2*b142 - 2*b54*b221 - 2*b55*
b184 + 2*b55 + 2*b55*b194 - 2*b55*b203 - 2*b55*b222 + 2*b56*b79 - 2*b79 +
2*b57*b104 + 2*b57*b122 - 4*b122 - 2*b57*b219 + 2*b58*b60 - 2*b60 + 2*b58*
b204 + 2*b59*b61 - 2*b61 + 2*b59*b62 + 2*b59*b152 - 4*b152 + 2*b60*b62 + 2
*b60*b122 - 2*b60*b185 - 2*b61*b63 + 2*b61*b127 - 2*b127 + 2*b61*b165 + 2*
b62*b63 + 2*b63*b64 + 2*b64*b65 + 2*b64*b107 - 2*b107 + 2*b65*b108 - 4*
b108 + 2*b65*b132 - 2*b132 + 2*b66*b67 - 2*b67 + 2*b66*b131 - 2*b131 + 2*
b67*b132 - 2*b68*b176 + 2*b68 - 2*b68*b223 + 2*b69*b70 - 2*b70 - 2*b69*
b180 + 2*b70*b197 - 2*b70*b209 + 2*b70*b223 + 2*b71*b72 - 2*b71 - 2*b72 -
2*b71*b73 + 2*b73 + 2*b71*b168 + 2*b71*b206 - 2*b72*b95 + 2*b95 + 2*b72*
b177 + 2*b72*b187 + 2*b73*b95 - 2*b73*b212 - 2*b73*b225 - 2*b74*b75 + 2*
b74 + 2*b75 - 2*b74*b142 - 2*b74*b174 + 2*b74*b178 + 2*b75*b76 - 2*b75*
b207 - 2*b75*b226 + 2*b76*b100 - 2*b100 - 2*b76*b178 + 2*b77*b103 - 4*b103
+ 2*b78*b100 - 4*b78 + 2*b78*b103 + 2*b78*b150 + 2*b78*b190 - 2*b79*b102
- 2*b102 + 2*b79*b122 + 2*b79*b151 - 4*b151 + 2*b80*b81 - 4*b81 + 2*b80*
b200 + 2*b81*b151 + 2*b81*b185 + 2*b81*b220 - 2*b82*b83 + 2*b82 - 2*b82*
b153 - 2*b82*b165 + 2*b82*b175 + 2*b83*b84 + 2*b83*b220 + 2*b84*b86 + 2*
b84*b128 - 2*b128 - 2*b85*b109 + 2*b85*b129 - 2*b129 + 2*b85*b161 - 4*b161
+ 2*b86*b130 - 2*b130 + 2*b86*b161 + 2*b87*b88 - 2*b88 + 2*b87*b160 - 2*
b160 + 2*b88*b161 - 2*b89*b227 - 2*b90*b91 - 2*b90 + 2*b90*b92 - 2*b92 + 2
*b90*b223 + 2*b90*b227 + 2*b91*b93 + 2*b91*b192 + 2*b92*b93 - 2*b92*b172
+ 2*b92*b187 + 2*b93*b214 + 2*b94*b174 - 2*b94 + 2*b94*b191 + 2*b94*b198
- 2*b94*b199 - 2*b95*b116 - 2*b95*b226 - 2*b96*b97 + 4*b96 - 2*b97 - 2*
b96*b115 - 2*b96*b177 - 2*b96*b178 + 2*b97*b99 + 2*b97*b207 + 2*b97*b226
- 2*b98*b120 - 2*b120 - 2*b98*b189 - 2*b98*b190 + 2*b99*b120 + 2*b99*b178
+ 2*b100*b102 - 2*b100*b194 + 2*b101*b121 - 4*b121 - 2*b101*b215 + 2*b102
*b120 + 2*b102*b121 + 2*b103*b105 - 2*b105 + 2*b103*b151 + 2*b104*b106 - 4
*b106 + 2*b104*b196 + 2*b105*b106 + 2*b105*b121 - 2*b105*b165 + 2*b106*
b155 + 2*b155 + 2*b106*b217 + 2*b107*b108 - 2*b107*b179 + 2*b107*b217 + 2*
b108*b157 - 2*b157 + 2*b108*b159 + 2*b109*b229 - 2*b110*b136 - 2*b136 + 2*
b111*b112 - 4*b111 - 2*b112 + 2*b111*b136 + 2*b111*b209 + 2*b111*b227 - 2*
b112*b181 + 2*b112*b182 + 2*b112*b225 - 2*b113*b174 + 2*b113 - 2*b113*b191
+ 2*b113*b192 - 2*b113*b193 - 2*b114*b192 - 2*b114 + 2*b114*b193 + 2*b114
*b212 + 2*b114*b225 - 2*b115*b222 - 2*b116*b117 - 2*b117 - 2*b116*b183 + 2
*b117*b119 + 2*b117*b203 + 2*b117*b222 - 2*b118*b148 - 2*b148 - 2*b118*
b164 + 2*b119*b148 + 2*b119*b183 + 2*b120*b219 + 2*b121*b123 - 2*b123 + 2*
b122*b124 - 4*b124 + 2*b123*b124 + 2*b123*b165 - 2*b123*b231 + 2*b124*b125
+ 2*b124*b126 - 2*b126 - 2*b125*b128 - 2*b125*b200 + 2*b126*b128 - 2*b126
*b204 + 2*b126*b216 + 2*b127*b129 - 2*b127*b130 + 2*b127*b185 + 2*b128*
b130 - 2*b129*b131 + 2*b129*b170 + 2*b130*b131 + 2*b131*b133 + 2*b132*b134
- 2*b134 - 2*b132*b166 + 2*b133*b134 + 2*b133*b166 - 2*b135*b201 + 2*b136
*b137 - 4*b137 + 2*b136*b228 + 2*b137*b139 - 4*b139 + 2*b137*b201 + 2*b137
*b206 - 2*b138*b191 - 2*b138*b221 + 2*b139*b181 + 2*b139*b188 + 2*b139*
b221 - 2*b140*b143 + 2*b140 - 2*b143 - 2*b140*b177 - 2*b140*b187 + 2*b140*
b188 + 2*b141*b142 - 2*b141 + 2*b141*b143 - 2*b141*b188 + 2*b141*b221 - 2*
b142*b218 + 2*b143*b144 + 2*b144 + 2*b143*b218 - 2*b144*b145 - 2*b145 - 2*
b144*b189 - 2*b144*b199 + 2*b145*b146 + 2*b145*b147 + 2*b145*b218 - 2*b146
*b215 + 2*b147*b189 + 2*b147*b215 + 2*b148*b149 + 2*b148*b219 + 2*b149*
b215 + 2*b149*b231 + 2*b150*b152 - 2*b150*b208 + 2*b151*b154 - 4*b154 + 2*
b152*b154 + 2*b152*b231 - 2*b153*b156 - 2*b153*b208 + 2*b154*b156 + 2*b154
*b179 - 2*b155*b157 - 2*b155*b170 - 2*b155*b196 + 2*b156*b157 + 2*b157*
b158 - 2*b158 + 2*b158*b159 + 2*b158*b160 - 2*b158*b175 - 2*b159*b230 - 2*
b160*b167 + 2*b160*b230 + 2*b161*b162 - 2*b162 + 2*b162*b230 - 2*b163*b164
+ 2*b163*b190 - 2*b166*b167 + 2*b167*b175 - 2*b168*b169 - 2*b168*b198 - 2
*b169*b197 + 2*b170*b179 - 2*b171*b172 + 2*b171*b173 - 2*b171*b192 - 2*
b173*b201 - 2*b173*b202 + 2*b174*b184 - 2*b175*b185 - 2*b176*b181 - 2*b179
*b204 - 2*b182*b206 + 2*b183*b184 - 2*b183*b194 - 2*b184*b212 - 2*b187*
b202 - 2*b188*b209 - 2*b190*b195 + 2*b191*b197 + 2*b193*b222 - 2*b196*b220
- 2*b197*b225 + 2*b198*b209 - 2*b198*b214 + 2*b199*b214 + 2*b199*b226 - 2
*b200*b217 + 2*b201*b224 + 2*b204*b208 - 2*b205*b211 - 2*b210*b213 - 2*
b213*b216 - 2*b216*b217 - 2*b219*b231 - 2*b223*b224 - 2*b227*b228 - 2*b229
*b230 + 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: 2024-08-26 Git hash: 6cc1607f