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Instance ex1244
| Formatsⓘ | ams gms mod nl osil py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | 81958.17906000 (ANTIGONE) 82042.90514000 (BARON) 82042.90522000 (COUENNE) 82042.90522000 (LINDO) 82042.90522000 (SCIP) 0.00000000 (SHOT) |
| Referencesⓘ | Floudas, C A, Pardalos, Panos M, Adjiman, C S, Esposito, W R, Gumus, Zeynep H, Harding, S T, Klepeis, John L, Meyer, Clifford A, and Schweiger, C A, Handbook of Test Problems in Local and Global Optimization, Kluwer Academic Publishers, 1999. Zamora, Juan and Grossmann, I E, A Global MINLP Optimization Algorithm for the Synthesis of Heat Exchanger Networks with No Stream Splits, Computers and Chemical Engineering, 22:3, 1998, 367-384. |
| Sourceⓘ | Test Problem ex12.4.4 of Chapter 12 of Floudas e.a. handbook |
| Applicationⓘ | Simultaneous Optimization for HEN Synthesis |
| Added to libraryⓘ | 01 May 2001 |
| Problem typeⓘ | MBNLP |
| #Variablesⓘ | 95 |
| #Binary Variablesⓘ | 23 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 52 |
| #Nonlinear Binary Variablesⓘ | 0 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | nonlinear |
| Objective curvatureⓘ | indefinite |
| #Nonzeros in Objectiveⓘ | 75 |
| #Nonlinear Nonzeros in Objectiveⓘ | 52 |
| #Constraintsⓘ | 129 |
| #Linear Constraintsⓘ | 129 |
| #Quadratic Constraintsⓘ | 0 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 0 |
| Operands in Gen. Nonlin. Functionsⓘ | div |
| Constraints curvatureⓘ | linear |
| #Nonzeros in Jacobianⓘ | 393 |
| #Nonlinear Nonzeros in Jacobianⓘ | 0 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 147 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 29 |
| #Blocks in Hessian of Lagrangianⓘ | 11 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 2 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 7 |
| Average blocksize in Hessian of Lagrangianⓘ | 4.727273 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 2.0400e-01 |
| Maximal coefficientⓘ | 2.0000e+04 |
| Infeasibility of initial pointⓘ | 288.3 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 130 31 0 99 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 96 73 23 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 469 417 52 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,x64,x65,x66,x67,x68,x69,x70
,x71,x72,b73,b74,b75,b76,b77,b78,b79,b80,b81,b82,b83,b84,b85,b86,b87
,b88,b89,b90,b91,b92,b93,b94,b95,objvar;
Positive Variables x21,x22,x23,x24,x25,x26,x27,x28,x29,x30,x31,x32,x33,x34
,x35,x36,x37,x38,x39,x40,x41,x42,x43;
Binary Variables b73,b74,b75,b76,b77,b78,b79,b80,b81,b82,b83,b84,b85,b86,b87
,b88,b89,b90,b91,b92,b93,b94,b95;
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;
e1.. -(17600*x21/(x44 + x45) + 17600*x22/(x45 + x46) + 17600*x23/(x46 + x47) +
1920*x24/(x48 + x49) + 1920*x25/(x49 + x50) + 1920*x26/(x50 + x51) + 20000
*x27/(x52 + x53) + 20000*x28/(x53 + x54) + 20000*x29/(x54 + x55) + 4320*
x30/(x56 + x57) + 4320*x31/(x57 + x58) + 4320*x32/(x58 + x59) + 16320*x33/
(x60 + x61) + 16320*x34/(x61 + x62) + 16320*x35/(x62 + x63) + 640*x36/(x64
+ x65) + 640*x37/(x65 + x66) + 640*x38/(x66 + x67) + 2400*x39/(57 + x68)
+ 4800*x40/(60 + x69) + 1120*x41/(70 + x70) + 19200*x42/(173 + x71) +
3520*x43/(35 + x72) + 110*x42 + 110*x43 + 10*x39 + 10*x40 + 10*x41)
- 7400*b73 - 7400*b74 - 7400*b75 - 7400*b76 - 7400*b77 - 7400*b78
- 7400*b79 - 7400*b80 - 7400*b81 - 7400*b82 - 7400*b83 - 7400*b84
- 7400*b85 - 7400*b86 - 7400*b87 - 7400*b88 - 7400*b89 - 7400*b90
- 7400*b91 - 7400*b92 - 7400*b93 - 7400*b94 - 7400*b95 + objvar =E= 0;
e2.. x21 + x22 + x23 + x24 + x25 + x26 + x39 =E= 187.37;
e3.. x27 + x28 + x29 + x30 + x31 + x32 + x40 =E= 38.148;
e4.. x33 + x34 + x35 + x36 + x37 + x38 + x41 =E= 136.114;
e5.. x21 + x22 + x23 + x27 + x28 + x29 + x33 + x34 + x35 + x42 =E= 94.233;
e6.. x24 + x25 + x26 + x30 + x31 + x32 + x36 + x37 + x38 + x43 =E= 288.267;
e7.. 2.285*x1 - 2.285*x2 - x21 - x24 =E= 0;
e8.. 2.285*x2 - 2.285*x3 - x22 - x25 =E= 0;
e9.. 2.285*x3 - 2.285*x4 - x23 - x26 =E= 0;
e10.. 0.204*x5 - 0.204*x6 - x27 - x30 =E= 0;
e11.. 0.204*x6 - 0.204*x7 - x28 - x31 =E= 0;
e12.. 0.204*x7 - 0.204*x8 - x29 - x32 =E= 0;
e13.. 0.538*x9 - 0.538*x10 - x33 - x36 =E= 0;
e14.. 0.538*x10 - 0.538*x11 - x34 - x37 =E= 0;
e15.. 0.538*x11 - 0.538*x12 - x35 - x38 =E= 0;
e16.. 0.933*x13 - 0.933*x14 - x21 - x27 - x33 =E= 0;
e17.. 0.933*x14 - 0.933*x15 - x22 - x28 - x34 =E= 0;
e18.. 0.933*x15 - 0.933*x16 - x23 - x29 - x35 =E= 0;
e19.. 1.961*x17 - 1.961*x18 - x24 - x30 - x36 =E= 0;
e20.. 1.961*x18 - 1.961*x19 - x25 - x31 - x37 =E= 0;
e21.. 1.961*x19 - 1.961*x20 - x26 - x32 - x38 =E= 0;
e22.. x1 =E= 159;
e23.. x5 =E= 267;
e24.. x9 =E= 343;
e25.. x15 =E= 26;
e26.. x19 =E= 118;
e27.. - x1 + x2 =L= 0;
e28.. - x2 + x3 =L= 0;
e29.. - x3 + x4 =L= 0;
e30.. - x5 + x6 =L= 0;
e31.. - x6 + x7 =L= 0;
e32.. - x7 + x8 =L= 0;
e33.. - x9 + x10 =L= 0;
e34.. - x10 + x11 =L= 0;
e35.. - x11 + x12 =L= 0;
e36.. - x13 + x14 =L= 0;
e37.. - x14 + x15 =L= 0;
e38.. - x15 + x16 =L= 0;
e39.. - x17 + x18 =L= 0;
e40.. - x18 + x19 =L= 0;
e41.. - x19 + x20 =L= 0;
e42.. - x3 =L= -77;
e43.. - x7 =L= -80;
e44.. - x11 =L= -90;
e45.. x13 =L= 127;
e46.. x17 =L= 265;
e47.. 2.285*x3 - x39 =E= 175.945;
e48.. 0.204*x7 - x40 =E= 16.32;
e49.. 0.538*x11 - x41 =E= 48.42;
e50.. 0.933*x13 + x42 =E= 118.491;
e51.. 1.961*x17 + x43 =E= 519.665;
e52.. x21 - 94.233*b73 =L= 0;
e53.. x22 - 94.233*b74 =L= 0;
e54.. x23 - 94.233*b75 =L= 0;
e55.. x24 - 187.37*b76 =L= 0;
e56.. x25 - 187.37*b77 =L= 0;
e57.. x26 - 187.37*b78 =L= 0;
e58.. x27 - 38.148*b79 =L= 0;
e59.. x28 - 38.148*b80 =L= 0;
e60.. x29 - 38.148*b81 =L= 0;
e61.. x30 - 38.148*b82 =L= 0;
e62.. x31 - 38.148*b83 =L= 0;
e63.. x32 - 38.148*b84 =L= 0;
e64.. x33 - 94.233*b85 =L= 0;
e65.. x34 - 94.233*b86 =L= 0;
e66.. x35 - 94.233*b87 =L= 0;
e67.. x36 - 136.114*b88 =L= 0;
e68.. x37 - 136.114*b89 =L= 0;
e69.. x38 - 136.114*b90 =L= 0;
e70.. x39 - 187.37*b91 =L= 0;
e71.. x40 - 38.148*b92 =L= 0;
e72.. x41 - 136.114*b93 =L= 0;
e73.. x42 - 94.233*b94 =L= 0;
e74.. x43 - 288.267*b95 =L= 0;
e75.. - x1 + x13 + x44 + 133*b73 =L= 133;
e76.. - x2 + x14 + x45 + 133*b74 =L= 133;
e77.. - x3 + x15 + x46 + 133*b75 =L= 133;
e78.. - x1 + x17 + x48 + 41*b76 =L= 41;
e79.. - x2 + x18 + x49 + 41*b77 =L= 41;
e80.. - x3 + x19 + x50 + 41*b78 =L= 41;
e81.. - x5 + x13 + x52 + 241*b79 =L= 241;
e82.. - x6 + x14 + x53 + 241*b80 =L= 241;
e83.. - x7 + x15 + x54 + 241*b81 =L= 241;
e84.. - x5 + x17 + x56 + 149*b82 =L= 149;
e85.. - x6 + x18 + x57 + 149*b83 =L= 149;
e86.. - x7 + x19 + x58 + 149*b84 =L= 149;
e87.. - x9 + x13 + x60 + 317*b85 =L= 317;
e88.. - x10 + x14 + x61 + 317*b86 =L= 317;
e89.. - x11 + x15 + x62 + 317*b87 =L= 317;
e90.. - x9 + x17 + x64 + 225*b88 =L= 225;
e91.. - x10 + x18 + x65 + 225*b89 =L= 225;
e92.. - x11 + x19 + x66 + 225*b90 =L= 225;
e93.. - x2 + x14 + x45 + 133*b73 =L= 133;
e94.. - x3 + x15 + x46 + 133*b74 =L= 133;
e95.. - x4 + x16 + x47 + 133*b75 =L= 133;
e96.. - x2 + x18 + x49 + 41*b76 =L= 41;
e97.. - x3 + x19 + x50 + 41*b77 =L= 41;
e98.. - x4 + x20 + x51 + 41*b78 =L= 41;
e99.. - x6 + x14 + x53 + 241*b79 =L= 241;
e100.. - x7 + x15 + x54 + 241*b80 =L= 241;
e101.. - x8 + x16 + x55 + 241*b81 =L= 241;
e102.. - x6 + x18 + x57 + 149*b82 =L= 149;
e103.. - x7 + x19 + x58 + 149*b83 =L= 149;
e104.. - x8 + x20 + x59 + 149*b84 =L= 149;
e105.. - x10 + x14 + x61 + 317*b85 =L= 317;
e106.. - x11 + x15 + x62 + 317*b86 =L= 317;
e107.. - x12 + x16 + x63 + 317*b87 =L= 317;
e108.. - x10 + x18 + x65 + 225*b88 =L= 225;
e109.. - x11 + x19 + x66 + 225*b89 =L= 225;
e110.. - x12 + x20 + x67 + 225*b90 =L= 225;
e111.. - x3 + x68 =L= -60;
e112.. - x7 + x69 =L= -60;
e113.. - x11 + x70 =L= -60;
e114.. x13 + x71 =L= 300;
e115.. x17 + x72 =L= 300;
e116.. b73 + b79 + b85 =L= 1;
e117.. b74 + b80 + b86 =L= 1;
e118.. b75 + b81 + b87 =L= 1;
e119.. b76 + b82 + b88 =L= 1;
e120.. b77 + b83 + b89 =L= 1;
e121.. b78 + b84 + b90 =L= 1;
e122.. b73 + b76 =L= 1;
e123.. b74 + b77 =L= 1;
e124.. b75 + b78 =L= 1;
e125.. b79 + b82 =L= 1;
e126.. b80 + b83 =L= 1;
e127.. b81 + b84 =L= 1;
e128.. b85 + b88 =L= 1;
e129.. b86 + b89 =L= 1;
e130.. b87 + b90 =L= 1;
* set non-default bounds
x1.lo = 77; x1.up = 159;
x2.lo = 77; x2.up = 159;
x3.lo = 77; x3.up = 159;
x4.lo = 77; x4.up = 159;
x5.lo = 80; x5.up = 267;
x6.lo = 80; x6.up = 267;
x7.lo = 80; x7.up = 267;
x8.lo = 80; x8.up = 267;
x9.lo = 90; x9.up = 343;
x10.lo = 90; x10.up = 343;
x11.lo = 90; x11.up = 343;
x12.lo = 90; x12.up = 343;
x13.lo = 26; x13.up = 127;
x14.lo = 26; x14.up = 127;
x15.lo = 26; x15.up = 127;
x16.lo = 26; x16.up = 127;
x17.lo = 118; x17.up = 265;
x18.lo = 118; x18.up = 265;
x19.lo = 118; x19.up = 265;
x20.lo = 118; x20.up = 265;
x44.lo = 1;
x45.lo = 1;
x46.lo = 1;
x47.lo = 1;
x48.lo = 1;
x49.lo = 1;
x50.lo = 1;
x51.lo = 1;
x52.lo = 1;
x53.lo = 1;
x54.lo = 1;
x55.lo = 1;
x56.lo = 1;
x57.lo = 1;
x58.lo = 1;
x59.lo = 1;
x60.lo = 1;
x61.lo = 1;
x62.lo = 1;
x63.lo = 1;
x64.lo = 1;
x65.lo = 1;
x66.lo = 1;
x67.lo = 1;
x68.lo = 1;
x69.lo = 1;
x70.lo = 1;
x71.lo = 1;
x72.lo = 1;
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: 2025-08-07 Git hash: e62cedfc