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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
Primal Bounds (infeas ≤ 1e-08)
276.00000000 p1 ( gdx sol )
(infeas: 0)
278.00000000 p2 ( gdx sol )
(infeas: 0)
282.00000000 p3 ( gdx sol )
(infeas: 0)
Other points (infeas > 1e-08)  
Dual Bounds
303.27272730 (ANTIGONE)
282.00000030 (BARON)
329.00000000 (COUENNE)
298.00000000 (LINDO)
301.87882590 (SCIP)
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
Infeasibility of initial point 0
Sparsity Jacobian Sparsity of Objective Gradient and Jacobian
Sparsity Hessian of Lagrangian Sparsity of 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: 2019-09-10 Git hash: 87a8f78d
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