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A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Instance waternd_shamir
| Formatsⓘ | ams gms osil py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | 419000. (LINDO) 419000. (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 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: 2026-09-14 Git hash: 9472b011