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Instance waternd_shamir

Formats ams gms osil py
Primal Bounds (infeas ≤ 1e-08)
419000.00000000 p1 ( gdx sol )
(infeas: 2e-11)
Other points (infeas > 1e-08)  
Dual Bounds
419000.00000000 (LINDO)
419000.00000000 (SCIP)
References D'Ambrosio, Claudia, Bragalli, Cristiana, Lee, Jon, Lodi, Andrea, and Toth, Paolo, Optimal Design of Water Distribution Networks, 2011.
Bragalli, Cristiana, D'Ambrosio, Claudia, Lee, Jon, Lodi, Andrea, and Toth, Paolo, On the optimal design of water distribution networks: a practical MINLP approach, Optimization and Engineering, 13, 2012, 219-246.
Source water.gms from minlp.org model 134
Application Water Network Design
Added to library 25 Sep 2013
Problem type MBNLP
#Variables 135
#Binary Variables 112
#Integer Variables 0
#Nonlinear Variables 23
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 0
Objective Sense min
Objective type linear
Objective curvature linear
#Nonzeros in Objective 112
#Nonlinear Nonzeros in Objective 0
#Constraints 46
#Linear Constraints 38
#Quadratic Constraints 0
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 8
Operands in Gen. Nonlin. Functions mul signpower vcpower
Constraints curvature indefinite
#Nonzeros in Jacobian 311
#Nonlinear Nonzeros in Jacobian 32
#Nonzeros in (Upper-Left) Hessian of Lagrangian 48
#Nonzeros in Diagonal of Hessian of Lagrangian 16
#Blocks in Hessian of Lagrangian 9
Minimal blocksize in Hessian of Lagrangian 1
Maximal blocksize in Hessian of Lagrangian 15
Average blocksize in Hessian of Lagrangian 2.555556
#Semicontinuities 0
#Nonlinear Semicontinuities 0
#SOS type 1 0
#SOS type 2 0
Minimal coefficient 5.0671e-04
Maximal coefficient 5.5000e+05
Infeasibility of initial point 1
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
*         47       31        8        8        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*        136       24      112        0        0        0        0        0
*  FX      1
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        424      392       32        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,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,objvar;

Binary Variables  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;

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;


e1..  - 2000*b24 - 5000*b25 - 8000*b26 - 11000*b27 - 16000*b28 - 23000*b29
      - 32000*b30 - 50000*b31 - 60000*b32 - 90000*b33 - 130000*b34 - 170000*b35
      - 300000*b36 - 550000*b37 - 2000*b38 - 5000*b39 - 8000*b40 - 11000*b41
      - 16000*b42 - 23000*b43 - 32000*b44 - 50000*b45 - 60000*b46 - 90000*b47
      - 130000*b48 - 170000*b49 - 300000*b50 - 550000*b51 - 2000*b52 - 5000*b53
      - 8000*b54 - 11000*b55 - 16000*b56 - 23000*b57 - 32000*b58 - 50000*b59
      - 60000*b60 - 90000*b61 - 130000*b62 - 170000*b63 - 300000*b64
      - 550000*b65 - 2000*b66 - 5000*b67 - 8000*b68 - 11000*b69 - 16000*b70
      - 23000*b71 - 32000*b72 - 50000*b73 - 60000*b74 - 90000*b75 - 130000*b76
      - 170000*b77 - 300000*b78 - 550000*b79 - 2000*b80 - 5000*b81 - 8000*b82
      - 11000*b83 - 16000*b84 - 23000*b85 - 32000*b86 - 50000*b87 - 60000*b88
      - 90000*b89 - 130000*b90 - 170000*b91 - 300000*b92 - 550000*b93
      - 2000*b94 - 5000*b95 - 8000*b96 - 11000*b97 - 16000*b98 - 23000*b99
      - 32000*b100 - 50000*b101 - 60000*b102 - 90000*b103 - 130000*b104
      - 170000*b105 - 300000*b106 - 550000*b107 - 2000*b108 - 5000*b109
      - 8000*b110 - 11000*b111 - 16000*b112 - 23000*b113 - 32000*b114
      - 50000*b115 - 60000*b116 - 90000*b117 - 130000*b118 - 170000*b119
      - 300000*b120 - 550000*b121 - 2000*b122 - 5000*b123 - 8000*b124
      - 11000*b125 - 16000*b126 - 23000*b127 - 32000*b128 - 50000*b129
      - 60000*b130 - 90000*b131 - 130000*b132 - 170000*b133 - 300000*b134
      - 550000*b135 + objvar =E= 0;

e2..  - x8 + x9 + x10 =E= -0.02777;

e3..  - x9 + x11 =E= -0.02777;

e4..  - x10 + x12 + x13 =E= -0.03333;

e5..  - x11 - x12 + x14 =E= -0.075;

e6..  - x13 + x15 =E= -0.09167;

e7..  - x14 - x15 =E= -0.05555;

e8.. SignPower(x8,1.852) - 0.76849192909955*(1.27323954473516*x16)**2.435*(x1
      - x2) =E= 0;

e9.. SignPower(x9,1.852) - 0.76849192909955*(1.27323954473516*x17)**2.435*(x2
      - x3) =E= 0;

e10.. SignPower(x10,1.852) - 0.76849192909955*(1.27323954473516*x18)**2.435*(x2
       - x4) =E= 0;

e11.. SignPower(x11,1.852) - 0.76849192909955*(1.27323954473516*x19)**2.435*(x3
       - x5) =E= 0;

e12.. SignPower(x12,1.852) - 0.76849192909955*(1.27323954473516*x20)**2.435*(x4
       - x5) =E= 0;

e13.. SignPower(x13,1.852) - 0.76849192909955*(1.27323954473516*x21)**2.435*(x4
       - x6) =E= 0;

e14.. SignPower(x14,1.852) - 0.76849192909955*(1.27323954473516*x22)**2.435*(x5
       - x7) =E= 0;

e15.. SignPower(x15,1.852) - 0.76849192909955*(1.27323954473516*x23)**2.435*(x6
       - x7) =E= 0;

e16..    x8 - 2*x16 =L= 0;

e17..    x9 - 2*x17 =L= 0;

e18..    x10 - 2*x18 =L= 0;

e19..    x11 - 2*x19 =L= 0;

e20..    x12 - 2*x20 =L= 0;

e21..    x13 - 2*x21 =L= 0;

e22..    x14 - 2*x22 =L= 0;

e23..    x15 - 2*x23 =L= 0;

e24..    x8 + 2*x16 =G= 0;

e25..    x9 + 2*x17 =G= 0;

e26..    x10 + 2*x18 =G= 0;

e27..    x11 + 2*x19 =G= 0;

e28..    x12 + 2*x20 =G= 0;

e29..    x13 + 2*x21 =G= 0;

e30..    x14 + 2*x22 =G= 0;

e31..    x15 + 2*x23 =G= 0;

e32..    x16 - 0.000506707479097498*b24 - 0.00202682991638999*b25
       - 0.00456036731187748*b26 - 0.00810731966555996*b27
       - 0.0182414692475099*b28 - 0.0324292786622399*b29
       - 0.0506707479097498*b30 - 0.0729658769900397*b31
       - 0.0993146659031096*b32 - 0.129717114648959*b33 - 0.164173223227589*b34
       - 0.202682991638999*b35 - 0.245246419883189*b36 - 0.291863507960159*b37
       =E= 0;

e33..    x17 - 0.000506707479097498*b38 - 0.00202682991638999*b39
       - 0.00456036731187748*b40 - 0.00810731966555996*b41
       - 0.0182414692475099*b42 - 0.0324292786622399*b43
       - 0.0506707479097498*b44 - 0.0729658769900397*b45
       - 0.0993146659031096*b46 - 0.129717114648959*b47 - 0.164173223227589*b48
       - 0.202682991638999*b49 - 0.245246419883189*b50 - 0.291863507960159*b51
       =E= 0;

e34..    x18 - 0.000506707479097498*b52 - 0.00202682991638999*b53
       - 0.00456036731187748*b54 - 0.00810731966555996*b55
       - 0.0182414692475099*b56 - 0.0324292786622399*b57
       - 0.0506707479097498*b58 - 0.0729658769900397*b59
       - 0.0993146659031096*b60 - 0.129717114648959*b61 - 0.164173223227589*b62
       - 0.202682991638999*b63 - 0.245246419883189*b64 - 0.291863507960159*b65
       =E= 0;

e35..    x19 - 0.000506707479097498*b66 - 0.00202682991638999*b67
       - 0.00456036731187748*b68 - 0.00810731966555996*b69
       - 0.0182414692475099*b70 - 0.0324292786622399*b71
       - 0.0506707479097498*b72 - 0.0729658769900397*b73
       - 0.0993146659031096*b74 - 0.129717114648959*b75 - 0.164173223227589*b76
       - 0.202682991638999*b77 - 0.245246419883189*b78 - 0.291863507960159*b79
       =E= 0;

e36..    x20 - 0.000506707479097498*b80 - 0.00202682991638999*b81
       - 0.00456036731187748*b82 - 0.00810731966555996*b83
       - 0.0182414692475099*b84 - 0.0324292786622399*b85
       - 0.0506707479097498*b86 - 0.0729658769900397*b87
       - 0.0993146659031096*b88 - 0.129717114648959*b89 - 0.164173223227589*b90
       - 0.202682991638999*b91 - 0.245246419883189*b92 - 0.291863507960159*b93
       =E= 0;

e37..    x21 - 0.000506707479097498*b94 - 0.00202682991638999*b95
       - 0.00456036731187748*b96 - 0.00810731966555996*b97
       - 0.0182414692475099*b98 - 0.0324292786622399*b99
       - 0.0506707479097498*b100 - 0.0729658769900397*b101
       - 0.0993146659031096*b102 - 0.129717114648959*b103
       - 0.164173223227589*b104 - 0.202682991638999*b105
       - 0.245246419883189*b106 - 0.291863507960159*b107 =E= 0;

e38..    x22 - 0.000506707479097498*b108 - 0.00202682991638999*b109
       - 0.00456036731187748*b110 - 0.00810731966555996*b111
       - 0.0182414692475099*b112 - 0.0324292786622399*b113
       - 0.0506707479097498*b114 - 0.0729658769900397*b115
       - 0.0993146659031096*b116 - 0.129717114648959*b117
       - 0.164173223227589*b118 - 0.202682991638999*b119
       - 0.245246419883189*b120 - 0.291863507960159*b121 =E= 0;

e39..    x23 - 0.000506707479097498*b122 - 0.00202682991638999*b123
       - 0.00456036731187748*b124 - 0.00810731966555996*b125
       - 0.0182414692475099*b126 - 0.0324292786622399*b127
       - 0.0506707479097498*b128 - 0.0729658769900397*b129
       - 0.0993146659031096*b130 - 0.129717114648959*b131
       - 0.164173223227589*b132 - 0.202682991638999*b133
       - 0.245246419883189*b134 - 0.291863507960159*b135 =E= 0;

e40..    b24 + b25 + b26 + b27 + b28 + b29 + b30 + b31 + b32 + b33 + b34 + b35
       + b36 + b37 =E= 1;

e41..    b38 + b39 + b40 + b41 + b42 + b43 + b44 + b45 + b46 + b47 + b48 + b49
       + b50 + b51 =E= 1;

e42..    b52 + b53 + b54 + b55 + b56 + b57 + b58 + b59 + b60 + b61 + b62 + b63
       + b64 + b65 =E= 1;

e43..    b66 + b67 + b68 + b69 + b70 + b71 + b72 + b73 + b74 + b75 + b76 + b77
       + b78 + b79 =E= 1;

e44..    b80 + b81 + b82 + b83 + b84 + b85 + b86 + b87 + b88 + b89 + b90 + b91
       + b92 + b93 =E= 1;

e45..    b94 + b95 + b96 + b97 + b98 + b99 + b100 + b101 + b102 + b103 + b104
       + b105 + b106 + b107 =E= 1;

e46..    b108 + b109 + b110 + b111 + b112 + b113 + b114 + b115 + b116 + b117
       + b118 + b119 + b120 + b121 =E= 1;

e47..    b122 + b123 + b124 + b125 + b126 + b127 + b128 + b129 + b130 + b131
       + b132 + b133 + b134 + b135 =E= 1;

* set non-default bounds
x1.fx = 210;
x2.lo = 180; x2.up = 210;
x3.lo = 190; x3.up = 210;
x4.lo = 185; x4.up = 210;
x5.lo = 180; x5.up = 210;
x6.lo = 195; x6.up = 210;
x7.lo = 190; x7.up = 210;
x16.lo = 0.000506707479097498; x16.up = 0.291863507960159;
x17.lo = 0.000506707479097498; x17.up = 0.291863507960159;
x18.lo = 0.000506707479097498; x18.up = 0.291863507960159;
x19.lo = 0.000506707479097498; x19.up = 0.291863507960159;
x20.lo = 0.000506707479097498; x20.up = 0.291863507960159;
x21.lo = 0.000506707479097498; x21.up = 0.291863507960159;
x22.lo = 0.000506707479097498; x22.up = 0.291863507960159;
x23.lo = 0.000506707479097498; x23.up = 0.291863507960159;

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: 2022-04-26 Git hash: de668763
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