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Instance: genpooling_meyer04

Formats ams gms lp mod nl osil pip
Primal Bounds
1197394.17200000 p1 ( gdx sol )
(infeas: 4e-11)
1086187.13700000 p2 ( gdx sol )
(infeas: 4e-12)
Dual Bounds
1086187.13700000 (ANTIGONE)
1086187.13700000 (BARON)
857953.45580000 (COUENNE)
1055668.48800000 (LINDO)
692532.38520000 (SCIP)
References Misener, Ruth and Floudas, C A, Generalized Pooling Problem, 2011.
Source generalizedpooling_meyer4.gms from minlp.org model 123
Application Pooling Problem
Added to library 25 Sep 2013
Problem type MBQCP
#Variables 118
#Binary Variables 55
#Integer Variables 0
#Nonlinear Variables 28
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 0
Objective Sense min
Objective type linear
Objective curvature linear
#Nonzeros in Objective 106
#Nonlinear Nonzeros in Objective 0
#Constraints 141
#Linear Constraints 126
#Quadratic Constraints 15
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions  
Constraints curvature indefinite
#Nonzeros in Jacobian 633
#Nonlinear Nonzeros in Jacobian 156
#Nonzeros in (Upper-Left) Hessian of Lagrangian 96
#Nonzeros in Diagonal of Hessian of Lagrangian 0
#Blocks in Hessian of Lagrangian 4
Minimal blocksize in Hessian of Lagrangian 7
Maximal blocksize in Hessian of Lagrangian 7
Average blocksize in Hessian of Lagrangian 7.0
#Semicontinuities 0
#Nonlinear Semicontinuities 0
#SOS type 1 0
#SOS type 2 0
Infeasibility of initial point 300.5
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
*        142       17       51       74        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*        119       64       55        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        740      584      156        0
*
*  Solve m using MINLP minimizing objvar;


Variables  x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,x17,x18,x19
          ,x20,x21,x22,x23,x24,x25,x26,x27,x28,x29,x30,x31,x32,x33,x34,x35,x36
          ,x37,x38,x39,x40,x41,x42,x43,x44,x45,x46,x47,x48,x49,x50,x51,x52,x53
          ,x54,x55,x56,x57,x58,x59,x60,x61,x62,x63,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,objvar;

Positive Variables  x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,x17
          ,x18,x19,x20,x21,x22,x23,x24,x25,x26,x27,x28,x29,x30,x31,x32,x33,x34
          ,x35,x36,x37,x38,x39,x40,x41,x42,x43,x44,x45,x46,x47,x48,x49,x50,x51
          ,x52,x53,x54,x55,x56,x57,x58,x59,x60,x61,x62,x63;

Binary Variables  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;

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;


e1..  - 75.0708333333333*x1 - 150.141666666667*x2 - 280.264444444444*x3
      - 245.231388888889*x4 - 55.0519444444444*x5 - 125.118055555556*x6
      - 260.245555555556*x7 - 215.203055555556*x8 - 30.0283333333333*x9
      - 115.108611111111*x10 - 240.226666666667*x11 - 220.207777777778*x12
      - 55.0519444444444*x13 - 140.132222222222*x14 - 245.231388888889*x15
      - 245.231388888889*x16 - 55.0519444444444*x17 - 40.0377777777778*x18
      - 150.141666666667*x19 - 150.141666666667*x20 - 40.0377777777778*x21
      - 120.113333333333*x22 - 230.217222222222*x23 - 230.217222222222*x24
      - 30.0283333333333*x25 - 60.0566666666667*x26 - 175.165277777778*x27
      - 165.155833333333*x28 - 1177.97083333333*x29 - 2975.27555555556*x30
      - 1263.05111111111*x31 - 1293.07944444444*x32 - 1182.97555555556*x33
      - 1313.09833333333*x34 - 1293.07944444444*x35 - 2975.27555555556*x36
      - 3025.32277777778*x37 - 2995.29444444444*x38 - 1313.09833333333*x39
      - 1233.02277777778*x40 - 1213.00388888889*x41 - 1293.07944444444*x42
      - 1202.99444444444*x43 - 1213.00388888889*x44 - 150.141666666667*x45
      - 135.1275*x46 - 100.094444444444*x47 - 90.085*x48 - 40.0377777777778*x49
      - 70.0661111111111*x50 - 45.0425*x51 - 9345*b64 - 18690*b65 - 34888*b66
      - 30527*b67 - 6853*b68 - 15575*b69 - 32396*b70 - 26789*b71 - 3738*b72
      - 14329*b73 - 29904*b74 - 27412*b75 - 6853*b76 - 17444*b77 - 30527*b78
      - 30527*b79 - 6853*b80 - 4984*b81 - 18690*b82 - 18690*b83 - 4984*b84
      - 14952*b85 - 28658*b86 - 28658*b87 - 3738*b88 - 7476*b89 - 21805*b90
      - 20559*b91 - 9345*b92 - 9968*b93 - 19936*b94 - 23674*b95 - 9968*b96
      - 26166*b97 - 23674*b98 - 9968*b99 - 16198*b100 - 12460*b101 - 26166*b102
      - 16198*b103 - 13706*b104 - 23674*b105 - 12460*b106 - 13706*b107
      - 18690*b108 - 16821*b109 - 12460*b110 - 11214*b111 - 4984*b112
      - 8722*b113 - 5607*b114 - 13972*b115 - 36676*b116 - 13972*b117
      - 13972*b118 + objvar =E= 0;

e2..  - x1 - x2 - x3 - x4 - x45 =L= -20;

e3..  - x5 - x6 - x7 - x8 - x46 =L= -50;

e4..  - x9 - x10 - x11 - x12 - x47 =L= -47.5;

e5..  - x13 - x14 - x15 - x16 - x48 =L= -28;

e6..  - x17 - x18 - x19 - x20 - x49 =L= -100;

e7..  - x21 - x22 - x23 - x24 - x50 =L= -30;

e8..  - x25 - x26 - x27 - x28 - x51 =L= -25;

e9..    x1 + x2 + x3 + x4 + x45 =L= 20;

e10..    x5 + x6 + x7 + x8 + x46 =L= 50;

e11..    x9 + x10 + x11 + x12 + x47 =L= 47.5;

e12..    x13 + x14 + x15 + x16 + x48 =L= 28;

e13..    x17 + x18 + x19 + x20 + x49 =L= 100;

e14..    x21 + x22 + x23 + x24 + x50 =L= 30;

e15..    x25 + x26 + x27 + x28 + x51 =L= 25;

e16..    x29 + x33 + x34 + x35 - 300.5*b115 =L= 0;

e17..    x30 + x36 + x37 + x38 - 300.5*b116 =L= 0;

e18..    x31 + x39 + x40 + x41 - 300.5*b117 =L= 0;

e19..    x32 + x42 + x43 + x44 - 300.5*b118 =L= 0;

e20..  - x29 - x30 - x31 - x32 - x45 - x46 - x47 - x48 - x49 - x50 - x51
       =L= -300.5;

e21..    x29 + x30 + x31 + x32 + x45 + x46 + x47 + x48 + x49 + x50 + x51
       =L= 300.5;

e22..    x1 + x5 + x9 + x13 + x17 + x21 + x25 - x29 - x33 - x34 - x35 + x36
       + x39 + x42 =E= 0;

e23..    x2 + x6 + x10 + x14 + x18 + x22 + x26 - x30 + x33 - x36 - x37 - x38
       + x40 + x43 =E= 0;

e24..    x3 + x7 + x11 + x15 + x19 + x23 + x27 - x31 + x34 + x37 - x39 - x40
       - x41 + x44 =E= 0;

e25..    x4 + x8 + x12 + x16 + x20 + x24 + x28 - x32 + x35 + x38 + x41 - x42
       - x43 - x44 =E= 0;

e26.. 0.01*(x55*x36 + x58*x39 + x61*x42) - (x52*x29 + x52*x33 + x52*x34 + x52*
      x35) + x1 + 8.00000000000001*x5 + 4*x9 + 12*x13 + 5*x17 + 0.5*x21
       + 10*x25 =E= 0;

e27.. 0.1*(x56*x36 + x59*x39 + x62*x42) - (x53*x29 + x53*x33 + x53*x34 + x53*
      x35) + 50*x1 + 175*x5 + 8*x9 + 100*x13 + 70*x17 + 10*x21 + 5*x25 =E= 0;

e28.. 0.05*(x57*x36 + x60*x39 + x63*x42) - (x54*x29 + x54*x33 + x54*x34 + x54*
      x35) + 25*x1 + 100*x5 + 5*x9 + 20*x13 + 12.5*x17 + 2.5*x21
       + 7.50000000000001*x25 =E= 0;

e29.. x52*x33 + x58*x40 + x61*x43 - (x55*x30 + x55*x36 + x55*x37 + x55*x38)
       + 100*x2 + 800*x6 + 400*x10 + 1200*x14 + 500*x18 + 50*x22 + 1000*x26
       =E= 0;

e30.. 0.13*(x53*x33 + x59*x40 + x62*x43) - (x56*x30 + x56*x36 + x56*x37 + x56*
      x38) + 65*x2 + 227.5*x6 + 10.4*x10 + 130*x14 + 91*x18 + 13*x22 + 6.5*x26
       =E= 0;

e31.. 0.1*(x54*x33 + x60*x40 + x63*x43) - (x57*x30 + x57*x36 + x57*x37 + x57*
      x38) + 50*x2 + 200*x6 + 10*x10 + 40*x14 + 25*x18 + 5*x22 + 15*x26 =E= 0;

e32.. 0.9*(x52*x34 + x55*x37 + x61*x44) - (x58*x31 + x58*x39 + x58*x40 + x58*
      x41) + 90*x3 + 720*x7 + 360*x11 + 1080*x15 + 450*x19 + 45*x23 + 900*x27
       =E= 0;

e33.. 0.01*(x53*x34 + x56*x37 + x62*x44) - (x59*x31 + x59*x39 + x59*x40 + x59*
      x41) + 5*x3 + 17.5*x7 + 0.800000000000001*x11 + 10*x15
       + 7.00000000000001*x19 + x23 + 0.5*x27 =E= 0;

e34.. x54*x34 + x57*x37 + x63*x44 - (x60*x31 + x60*x39 + x60*x40 + x60*x41)
       + 500*x3 + 2000*x7 + 100*x11 + 400*x15 + 250*x19 + 50*x23 + 150*x27
       =E= 0;

e35.. 0.3*(x52*x35 + x55*x38 + x58*x41) - (x61*x32 + x61*x42 + x61*x43 + x61*
      x44) + 30*x4 + 240*x8 + 120*x12 + 360*x16 + 150*x20 + 15*x24 + 300*x28
       =E= 0;

e36.. 0.8*(x53*x35 + x56*x38 + x59*x41) - (x62*x32 + x62*x42 + x62*x43 + x62*
      x44) + 400*x4 + 1400*x8 + 64*x12 + 800*x16 + 560*x20 + 80*x24 + 40*x28
       =E= 0;

e37.. 0.7*(x54*x35 + x57*x38 + x60*x41) - (x63*x32 + x63*x42 + x63*x43 + x63*
      x44) + 350*x4 + 1400*x8 + 70*x12 + 280*x16 + 175*x20 + 35*x24 + 105*x28
       =E= 0;

e38.. x52*x29 + x55*x30 + x58*x31 + x61*x32 - 5*x29 - 5*x30 - 5*x31 - 5*x32
       + 95*x45 + 795*x46 + 395*x47 + 1195*x48 + 495*x49 + 45*x50 + 995*x51
       =L= 0;

e39.. x53*x29 + x56*x30 + x59*x31 + x62*x32 - 5*x29 - 5*x30 - 5*x31 - 5*x32
       + 495*x45 + 1745*x46 + 75*x47 + 995*x48 + 695*x49 + 95*x50 + 45*x51
       =L= 0;

e40.. x54*x29 + x57*x30 + x60*x31 + x63*x32 - 10*x29 - 10*x30 - 10*x31 - 10*x32
       + 490*x45 + 1990*x46 + 90*x47 + 390*x48 + 240*x49 + 40*x50 + 140*x51
       =L= 0;

e41..    x1 - 0.2*b64 =G= 0;

e42..    x2 - 0.2*b65 =G= 0;

e43..    x3 - 0.2*b66 =G= 0;

e44..    x4 - 0.2*b67 =G= 0;

e45..    x5 - 0.2*b68 =G= 0;

e46..    x6 - 0.2*b69 =G= 0;

e47..    x7 - 0.2*b70 =G= 0;

e48..    x8 - 0.2*b71 =G= 0;

e49..    x9 - 0.2*b72 =G= 0;

e50..    x10 - 0.2*b73 =G= 0;

e51..    x11 - 0.2*b74 =G= 0;

e52..    x12 - 0.2*b75 =G= 0;

e53..    x13 - 0.2*b76 =G= 0;

e54..    x14 - 0.2*b77 =G= 0;

e55..    x15 - 0.2*b78 =G= 0;

e56..    x16 - 0.2*b79 =G= 0;

e57..    x17 - 0.2*b80 =G= 0;

e58..    x18 - 0.2*b81 =G= 0;

e59..    x19 - 0.2*b82 =G= 0;

e60..    x20 - 0.2*b83 =G= 0;

e61..    x21 - 0.2*b84 =G= 0;

e62..    x22 - 0.2*b85 =G= 0;

e63..    x23 - 0.2*b86 =G= 0;

e64..    x24 - 0.2*b87 =G= 0;

e65..    x25 - 0.2*b88 =G= 0;

e66..    x26 - 0.2*b89 =G= 0;

e67..    x27 - 0.2*b90 =G= 0;

e68..    x28 - 0.2*b91 =G= 0;

e69..    x1 - 20*b64 =L= 0;

e70..    x2 - 20*b65 =L= 0;

e71..    x3 - 20*b66 =L= 0;

e72..    x4 - 20*b67 =L= 0;

e73..    x5 - 50*b68 =L= 0;

e74..    x6 - 50*b69 =L= 0;

e75..    x7 - 50*b70 =L= 0;

e76..    x8 - 50*b71 =L= 0;

e77..    x9 - 47.5*b72 =L= 0;

e78..    x10 - 47.5*b73 =L= 0;

e79..    x11 - 47.5*b74 =L= 0;

e80..    x12 - 47.5*b75 =L= 0;

e81..    x13 - 28*b76 =L= 0;

e82..    x14 - 28*b77 =L= 0;

e83..    x15 - 28*b78 =L= 0;

e84..    x16 - 28*b79 =L= 0;

e85..    x17 - 100*b80 =L= 0;

e86..    x18 - 100*b81 =L= 0;

e87..    x19 - 100*b82 =L= 0;

e88..    x20 - 100*b83 =L= 0;

e89..    x21 - 30*b84 =L= 0;

e90..    x22 - 30*b85 =L= 0;

e91..    x23 - 30*b86 =L= 0;

e92..    x24 - 30*b87 =L= 0;

e93..    x25 - 25*b88 =L= 0;

e94..    x26 - 25*b89 =L= 0;

e95..    x27 - 25*b90 =L= 0;

e96..    x28 - 25*b91 =L= 0;

e97..    x29 - 0.2*b92 =G= 0;

e98..    x30 - 0.2*b93 =G= 0;

e99..    x31 - 0.2*b94 =G= 0;

e100..    x32 - 0.2*b95 =G= 0;

e101..    x29 - 300.5*b92 =L= 0;

e102..    x30 - 300.5*b93 =L= 0;

e103..    x31 - 300.5*b94 =L= 0;

e104..    x32 - 300.5*b95 =L= 0;

e105..    x45 - 0.2*b108 =G= 0;

e106..    x46 - 0.2*b109 =G= 0;

e107..    x47 - 0.2*b110 =G= 0;

e108..    x48 - 0.2*b111 =G= 0;

e109..    x49 - 0.2*b112 =G= 0;

e110..    x50 - 0.2*b113 =G= 0;

e111..    x51 - 0.2*b114 =G= 0;

e112..    x45 - 20*b108 =L= 0;

e113..    x46 - 50*b109 =L= 0;

e114..    x47 - 47.5*b110 =L= 0;

e115..    x48 - 28*b111 =L= 0;

e116..    x49 - 100*b112 =L= 0;

e117..    x50 - 30*b113 =L= 0;

e118..    x51 - 25*b114 =L= 0;

e119..    x36 - 0.2*b99 =G= 0;

e120..    x39 - 0.2*b102 =G= 0;

e121..    x42 - 0.2*b105 =G= 0;

e122..    x33 - 0.2*b96 =G= 0;

e123..    x40 - 0.2*b103 =G= 0;

e124..    x43 - 0.2*b106 =G= 0;

e125..    x34 - 0.2*b97 =G= 0;

e126..    x37 - 0.2*b100 =G= 0;

e127..    x44 - 0.2*b107 =G= 0;

e128..    x35 - 0.2*b98 =G= 0;

e129..    x38 - 0.2*b101 =G= 0;

e130..    x41 - 0.2*b104 =G= 0;

e131..    x36 - 300.5*b99 =L= 0;

e132..    x39 - 300.5*b102 =L= 0;

e133..    x42 - 300.5*b105 =L= 0;

e134..    x33 - 300.5*b96 =L= 0;

e135..    x40 - 300.5*b103 =L= 0;

e136..    x43 - 300.5*b106 =L= 0;

e137..    x34 - 300.5*b97 =L= 0;

e138..    x37 - 300.5*b100 =L= 0;

e139..    x44 - 300.5*b107 =L= 0;

e140..    x35 - 300.5*b98 =L= 0;

e141..    x38 - 300.5*b101 =L= 0;

e142..    x41 - 300.5*b104 =L= 0;

* set non-default bounds
x1.up = 20;
x2.up = 20;
x3.up = 20;
x4.up = 20;
x5.up = 50;
x6.up = 50;
x7.up = 50;
x8.up = 50;
x9.up = 47.5;
x10.up = 47.5;
x11.up = 47.5;
x12.up = 47.5;
x13.up = 28;
x14.up = 28;
x15.up = 28;
x16.up = 28;
x17.up = 100;
x18.up = 100;
x19.up = 100;
x20.up = 100;
x21.up = 30;
x22.up = 30;
x23.up = 30;
x24.up = 30;
x25.up = 25;
x26.up = 25;
x27.up = 25;
x28.up = 25;
x29.up = 300.5;
x30.up = 300.5;
x31.up = 300.5;
x32.up = 300.5;
x33.up = 300.5;
x34.up = 300.5;
x35.up = 300.5;
x36.up = 300.5;
x37.up = 300.5;
x38.up = 300.5;
x39.up = 300.5;
x40.up = 300.5;
x41.up = 300.5;
x42.up = 300.5;
x43.up = 300.5;
x44.up = 300.5;
x45.up = 20;
x46.up = 50;
x47.up = 47.5;
x48.up = 28;
x49.up = 100;
x50.up = 30;
x51.up = 25;
x52.up = 12;
x53.up = 175;
x54.up = 100;
x55.up = 1200;
x56.up = 227.5;
x57.up = 200;
x58.up = 1080;
x59.up = 17.5;
x60.up = 2000;
x61.up = 360;
x62.up = 1400;
x63.up = 1400;

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: 2018-09-14 Git hash: ac5a5314
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