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Instance heatexch_gen2
| Formatsⓘ | ams gms mod nl osil py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | 579611.43810000 (ANTIGONE) 585255.58350000 (BARON) 579990.01250000 (COUENNE) 579990.01250000 (GUROBI) 627371.49820000 (LINDO) 583986.90980000 (SCIP) 1590.01250800 (SHOT) 581889.75610000 (XPRESS) |
| Referencesⓘ | Escobar, Marcelo and Grossmann, I E, Mixed-Integer Nonlinear Programming Models for Optimal Simultaneous Synthesis of Heat Exchangers Network, 2010. |
| Sourceⓘ | General_Model_Case2.gms from minlp.org model 93 |
| Applicationⓘ | Heat Exchanger Network |
| Added to libraryⓘ | 25 Sep 2013 |
| Problem typeⓘ | MBNLP |
| #Variablesⓘ | 148 |
| #Binary Variablesⓘ | 16 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 126 |
| #Nonlinear Binary Variablesⓘ | 0 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | nonlinear |
| Objective curvatureⓘ | concave |
| #Nonzeros in Objectiveⓘ | 43 |
| #Nonlinear Nonzeros in Objectiveⓘ | 21 |
| #Constraintsⓘ | 166 |
| #Linear Constraintsⓘ | 102 |
| #Quadratic Constraintsⓘ | 32 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 32 |
| Operands in Gen. Nonlin. Functionsⓘ | div log vcpower |
| Constraints curvatureⓘ | indefinite |
| #Nonzeros in Jacobianⓘ | 484 |
| #Nonlinear Nonzeros in Jacobianⓘ | 158 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 190 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 58 |
| #Blocks in Hessian of Lagrangianⓘ | 60 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 1 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 11 |
| Average blocksize in Hessian of Lagrangianⓘ | 2.1 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 1.0000e-06 |
| Maximal coefficientⓘ | 6.6600e+03 |
| Infeasibility of initial pointⓘ | 1.08e+05 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 167 107 18 42 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 149 133 16 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 528 349 179 0
*
* Solve m using MINLP minimizing objvar;
Variables b1,b2,b3,b4,b5,b6,b7,b8,b9,b10,b11,b12,b13,b14,b15,b16,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,x73,x74,x75,x76,x77,x78,x79,x80,x81,x82,x83,x84,x85,x86,x87
,x88,x89,x90,x91,x92,x93,x94,x95,x96,x97,x98,x99,x100,x101,x102,x103
,x104,x105,x106,x107,x108,x109,x110,x111,x112,x113,x114,x115,x116
,x117,x118,x119,x120,x121,x122,x123,x124,x125,x126,x127,x128,x129
,x130,x131,x132,x133,x134,x135,x136,x137,x138,x139,x140,x141,x142
,x143,x144,x145,x146,x147,x148,objvar;
Positive Variables x35,x36,x37,x38,x39,x40,x41,x42,x43,x44,x45,x46,x47,x48
,x49,x50,x72,x73,x74,x75,x76,x77,x78,x79,x80,x81,x82,x83,x84,x85,x86
,x87,x88,x89,x90,x91,x112,x113,x114,x115,x116,x117,x118,x119,x120
,x121,x122,x123,x124,x125,x126,x127,x128,x129,x130,x131,x132,x133
,x134,x135,x136,x137,x138,x139,x140,x141,x142,x143,x144,x145,x146
,x147,x148;
Binary Variables b1,b2,b3,b4,b5,b6,b7,b8,b9,b10,b11,b12,b13,b14,b15,b16;
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
,e143,e144,e145,e146,e147,e148,e149,e150,e151,e152,e153,e154,e155
,e156,e157,e158,e159,e160,e161,e162,e163,e164,e165,e166,e167;
e1.. 6*x17 - 6*x18 - x35 =E= 0;
e2.. 6*x18 - 6*x19 - x36 =E= 0;
e3.. 4*x20 - 4*x21 - x37 =E= 0;
e4.. 4*x21 - 4*x22 - x38 =E= 0;
e5.. 6*x23 - 6*x24 - x39 =E= 0;
e6.. 6*x24 - 6*x25 - x40 =E= 0;
e7.. 20*x26 - 20*x27 - x41 =E= 0;
e8.. 20*x27 - 20*x28 - x42 =E= 0;
e9.. 12*x29 - 12*x30 - x43 =E= 0;
e10.. 12*x30 - 12*x31 - x44 =E= 0;
e11.. 18*x32 - 18*x33 - x35 - x37 - x39 - x41 - x43 =E= 0;
e12.. 18*x33 - 18*x34 - x36 - x38 - x40 - x42 - x44 =E= 0;
e13.. 6*x19 - x45 =E= 1920;
e14.. 4*x22 - x46 =E= 1520;
e15.. 6*x25 - x47 =E= 2160;
e16.. 20*x28 - x48 =E= 7200;
e17.. 12*x31 - x49 =E= 3840;
e18.. - x35 - x36 - x45 =E= -1080;
e19.. - x37 - x38 - x46 =E= -400;
e20.. - x39 - x40 - x47 =E= -600;
e21.. - x41 - x42 - x48 =E= -400;
e22.. - x43 - x44 - x49 =E= -720;
e23.. - 18*x32 - x50 =E= -11880;
e24.. - x35 - x36 - x37 - x38 - x39 - x40 - x41 - x42 - x43 - x44 - x50
=E= -6660;
e25.. x17 - x18 =G= 0;
e26.. x18 - x19 =G= 0;
e27.. x20 - x21 =G= 0;
e28.. x21 - x22 =G= 0;
e29.. x23 - x24 =G= 0;
e30.. x24 - x25 =G= 0;
e31.. x26 - x27 =G= 0;
e32.. x27 - x28 =G= 0;
e33.. x29 - x30 =G= 0;
e34.. x30 - x31 =G= 0;
e35.. x32 - x33 =G= 0;
e36.. x33 - x34 =G= 0;
e37.. x19 =G= 320;
e38.. x22 =G= 380;
e39.. x25 =G= 360;
e40.. x28 =G= 360;
e41.. x31 =G= 320;
e42.. - x32 =G= -660;
e43.. - x17 =E= -500;
e44.. - x20 =E= -480;
e45.. - x23 =E= -460;
e46.. - x26 =E= -380;
e47.. - x29 =E= -380;
e48.. - x34 =E= -290;
e49.. - x72 =E= -6;
e50.. - x73 =E= -6;
e51.. - x74 =E= -4;
e52.. - x75 =E= -4;
e53.. - x76 =E= -6;
e54.. - x77 =E= -6;
e55.. - x78 =E= -20;
e56.. - x79 =E= -20;
e57.. - x80 =E= -12;
e58.. - x81 =E= -12;
e59.. - x82 - x84 - x86 - x88 - x90 =E= -18;
e60.. - x83 - x85 - x87 - x89 - x91 =E= -18;
e61.. -x72*(x17 - x92) + x35 =E= 0;
e62.. -x73*(x18 - x93) + x36 =E= 0;
e63.. -x74*(x20 - x94) + x37 =E= 0;
e64.. -x75*(x21 - x95) + x38 =E= 0;
e65.. -x76*(x23 - x96) + x39 =E= 0;
e66.. -x77*(x24 - x97) + x40 =E= 0;
e67.. -x78*(x26 - x98) + x41 =E= 0;
e68.. -x79*(x27 - x99) + x42 =E= 0;
e69.. -x80*(x29 - x100) + x43 =E= 0;
e70.. -x81*(x30 - x101) + x44 =E= 0;
e71.. -x82*(x102 - x33) + x35 =E= 0;
e72.. -x83*(x103 - x34) + x36 =E= 0;
e73.. -x84*(x104 - x33) + x37 =E= 0;
e74.. -x85*(x105 - x34) + x38 =E= 0;
e75.. -x86*(x106 - x33) + x39 =E= 0;
e76.. -x87*(x107 - x34) + x40 =E= 0;
e77.. -x88*(x108 - x33) + x41 =E= 0;
e78.. -x89*(x109 - x34) + x42 =E= 0;
e79.. -x90*(x110 - x33) + x43 =E= 0;
e80.. -x91*(x111 - x34) + x44 =E= 0;
e81.. -x72*x92 + 6*x18 =E= 0;
e82.. -x73*x93 + 6*x19 =E= 0;
e83.. -x74*x94 + 4*x21 =E= 0;
e84.. -x75*x95 + 4*x22 =E= 0;
e85.. -x76*x96 + 6*x24 =E= 0;
e86.. -x77*x97 + 6*x25 =E= 0;
e87.. -x78*x98 + 20*x27 =E= 0;
e88.. -x79*x99 + 20*x28 =E= 0;
e89.. -x80*x100 + 12*x30 =E= 0;
e90.. -x81*x101 + 12*x31 =E= 0;
e91.. -(x82*x102 + x84*x104 + x86*x106 + x88*x108 + x90*x110) + 18*x32 =E= 0;
e92.. -(x83*x103 + x85*x105 + x87*x107 + x89*x109 + x91*x111) + 18*x33 =E= 0;
e93.. -(x51 - x52)/log(x51/(1e-6 + x52)) + x112 =E= 0;
e94.. -(x52 - x53)/log(x52/(1e-6 + x53)) + x113 =E= 0;
e95.. -(x54 - x55)/log(x54/(1e-6 + x55)) + x114 =E= 0;
e96.. -(x55 - x56)/log(x55/(1e-6 + x56)) + x115 =E= 0;
e97.. -(x57 - x58)/log(x57/(1e-6 + x58)) + x116 =E= 0;
e98.. -(x58 - x59)/log(x58/(1e-6 + x59)) + x117 =E= 0;
e99.. -(x60 - x61)/log(x60/(1e-6 + x61)) + x118 =E= 0;
e100.. -(x61 - x62)/log(x61/(1e-6 + x62)) + x119 =E= 0;
e101.. -(x63 - x64)/log(x63/(1e-6 + x64)) + x120 =E= 0;
e102.. -(x64 - x65)/log(x64/(1e-6 + x65)) + x121 =E= 0;
e103.. -x35/(0.01 + x112) + x128 =E= 0;
e104.. -x36/(0.01 + x113) + x129 =E= 0;
e105.. -x37/(0.01 + x114) + x131 =E= 0;
e106.. -x38/(0.01 + x115) + x132 =E= 0;
e107.. -x39/(0.01 + x116) + x134 =E= 0;
e108.. -x40/(0.01 + x117) + x135 =E= 0;
e109.. -x41/(0.01 + x118) + x137 =E= 0;
e110.. -x42/(0.01 + x119) + x138 =E= 0;
e111.. -x43/(0.01 + x120) + x140 =E= 0;
e112.. -x44/(0.01 + x121) + x141 =E= 0;
e113.. -(-20 + x66)/log(0.0499999975000001*x66) + x122 =E= 0;
e114.. -(-80 + x67)/log(0.01249999984375*x67) + x123 =E= 0;
e115.. -(-60 + x68)/log(0.0166666663888889*x68) + x124 =E= 0;
e116.. -(-60 + x69)/log(0.0166666663888889*x69) + x125 =E= 0;
e117.. -(-20 + x70)/log(0.0499999975000001*x70) + x126 =E= 0;
e118.. -(-40 + x71)/log(0.024999999375*x71) + x127 =E= 0;
e119.. -x45/(0.01 + x122) + x143 =E= 0;
e120.. -x46/(0.01 + x123) + x144 =E= 0;
e121.. -x47/(0.01 + x124) + x145 =E= 0;
e122.. -x48/(0.01 + x125) + x146 =E= 0;
e123.. -x49/(0.01 + x126) + x147 =E= 0;
e124.. -x50/(0.01 + x127) + x148 =E= 0;
e125.. - 1080*b1 + x35 =L= 0;
e126.. - 1080*b2 + x36 =L= 0;
e127.. - 400*b3 + x37 =L= 0;
e128.. - 400*b4 + x38 =L= 0;
e129.. - 600*b5 + x39 =L= 0;
e130.. - 600*b6 + x40 =L= 0;
e131.. - 400*b7 + x41 =L= 0;
e132.. - 400*b8 + x42 =L= 0;
e133.. - 720*b9 + x43 =L= 0;
e134.. - 720*b10 + x44 =L= 0;
e135.. - 6660*b16 + x50 =L= 0;
e136.. - 1080*b11 + x45 =L= 0;
e137.. - 400*b12 + x46 =L= 0;
e138.. - 600*b13 + x47 =L= 0;
e139.. - 400*b14 + x48 =L= 0;
e140.. - 720*b15 + x49 =L= 0;
e141.. 340*b1 - x17 + x32 + x51 =L= 340;
e142.. 340*b2 - x18 + x33 + x52 =L= 340;
e143.. 280*b3 - x20 + x32 + x54 =L= 280;
e144.. 280*b4 - x21 + x33 + x55 =L= 280;
e145.. 300*b5 - x23 + x32 + x57 =L= 300;
e146.. 300*b6 - x24 + x33 + x58 =L= 300;
e147.. 300*b7 - x26 + x32 + x60 =L= 300;
e148.. 300*b8 - x27 + x33 + x61 =L= 300;
e149.. 340*b9 - x29 + x32 + x63 =L= 340;
e150.. 340*b10 - x30 + x33 + x64 =L= 340;
e151.. 340*b1 - x18 + x33 + x52 =L= 340;
e152.. 340*b2 - x19 + x34 + x53 =L= 340;
e153.. 280*b3 - x21 + x33 + x55 =L= 280;
e154.. 280*b4 - x22 + x34 + x56 =L= 280;
e155.. 300*b5 - x24 + x33 + x58 =L= 300;
e156.. 300*b6 - x25 + x34 + x59 =L= 300;
e157.. 300*b7 - x27 + x33 + x61 =L= 300;
e158.. 300*b8 - x28 + x34 + x62 =L= 300;
e159.. 340*b9 - x30 + x33 + x64 =L= 340;
e160.. 340*b10 - x31 + x34 + x65 =L= 340;
e161.. - x19 + x66 =L= -320;
e162.. - x22 + x67 =L= -320;
e163.. - x25 + x68 =L= -320;
e164.. - x28 + x69 =L= -320;
e165.. - x31 + x70 =L= -320;
e166.. x32 + x71 =L= 700;
e167.. -(1200*(0.01 + x128)**0.6 + 1200*(0.01 + x129)**0.6 + 1200*(0.01 + x130)
**0.6 + 1200*(0.01 + x131)**0.6 + 1200*(0.01 + x132)**0.6 + 1200*(0.01
+ x133)**0.6 + 1200*(0.01 + x134)**0.6 + 1200*(0.01 + x135)**0.6 + 1200
*(0.01 + x136)**0.6 + 1200*(0.01 + x137)**0.6 + 1200*(0.01 + x138)**0.6
+ 1200*(0.01 + x139)**0.6 + 1200*(0.01 + x140)**0.6 + 1200*(0.01 + x141
)**0.6 + 1200*(0.01 + x142)**0.6 + 1200*(0.01 + x143)**0.6 + 1200*(0.01
+ x144)**0.6 + 1200*(0.01 + x145)**0.6 + 1200*(0.01 + x146)**0.6 + 1200
*(0.01 + x147)**0.6 + 1200*(0.01 + x148)**0.6) - 5500*b1 - 5500*b2
- 5500*b3 - 5500*b4 - 5500*b5 - 5500*b6 - 5500*b7 - 5500*b8 - 5500*b9
- 5500*b10 - 5500*b11 - 5500*b12 - 5500*b13 - 5500*b14 - 5500*b15
- 5500*b16 - 10*x45 - 10*x46 - 10*x47 - 10*x48 - 10*x49 - 140*x50
+ objvar =E= 0;
* set non-default bounds
x17.lo = 320; x17.up = 500;
x18.lo = 320; x18.up = 500;
x19.lo = 320; x19.up = 500;
x20.lo = 380; x20.up = 480;
x21.lo = 380; x21.up = 480;
x22.lo = 380; x22.up = 480;
x23.lo = 360; x23.up = 460;
x24.lo = 360; x24.up = 460;
x25.lo = 360; x25.up = 460;
x26.lo = 360; x26.up = 380;
x27.lo = 360; x27.up = 380;
x28.lo = 360; x28.up = 380;
x29.lo = 320; x29.up = 380;
x30.lo = 320; x30.up = 380;
x31.lo = 320; x31.up = 380;
x32.lo = 290; x32.up = 660;
x33.lo = 290; x33.up = 660;
x34.lo = 290; x34.up = 660;
x51.lo = 10;
x52.lo = 10;
x53.lo = 10;
x54.lo = 10;
x55.lo = 10;
x56.lo = 10;
x57.lo = 10;
x58.lo = 10;
x59.lo = 10;
x60.lo = 10;
x61.lo = 10;
x62.lo = 10;
x63.lo = 10;
x64.lo = 10;
x65.lo = 10;
x66.lo = 10;
x67.lo = 10;
x68.lo = 10;
x69.lo = 10;
x70.lo = 10;
x71.lo = 10;
x72.up = 6;
x73.up = 6;
x74.up = 4;
x75.up = 4;
x76.up = 6;
x77.up = 6;
x78.up = 20;
x79.up = 20;
x80.up = 12;
x81.up = 12;
x82.up = 18;
x83.up = 18;
x84.up = 18;
x85.up = 18;
x86.up = 18;
x87.up = 18;
x88.up = 18;
x89.up = 18;
x90.up = 18;
x91.up = 18;
x92.lo = 320; x92.up = 500;
x93.lo = 320; x93.up = 500;
x94.lo = 380; x94.up = 480;
x95.lo = 380; x95.up = 480;
x96.lo = 360; x96.up = 460;
x97.lo = 360; x97.up = 460;
x98.lo = 360; x98.up = 380;
x99.lo = 360; x99.up = 380;
x100.lo = 320; x100.up = 380;
x101.lo = 320; x101.up = 380;
x102.lo = 290; x102.up = 660;
x103.lo = 290; x103.up = 660;
x104.lo = 290; x104.up = 660;
x105.lo = 290; x105.up = 660;
x106.lo = 290; x106.up = 660;
x107.lo = 290; x107.up = 660;
x108.lo = 290; x108.up = 660;
x109.lo = 290; x109.up = 660;
x110.lo = 290; x110.up = 660;
x111.lo = 290; x111.up = 660;
* set non-default levels
x17.l = 500;
x18.l = 500;
x19.l = 500;
x20.l = 480;
x21.l = 480;
x22.l = 480;
x23.l = 460;
x24.l = 460;
x25.l = 460;
x26.l = 380;
x27.l = 380;
x28.l = 380;
x29.l = 380;
x30.l = 380;
x31.l = 380;
x35.l = 1080;
x36.l = 1080;
x37.l = 400;
x38.l = 400;
x39.l = 600;
x40.l = 600;
x41.l = 400;
x42.l = 400;
x43.l = 720;
x44.l = 720;
x51.l = 210;
x52.l = 210;
x53.l = 210;
x54.l = 190;
x55.l = 190;
x56.l = 190;
x57.l = 170;
x58.l = 170;
x59.l = 170;
x60.l = 90;
x61.l = 90;
x62.l = 90;
x63.l = 90;
x64.l = 90;
x65.l = 90;
x66.l = 180;
x67.l = 160;
x68.l = 140;
x69.l = 60;
x70.l = 60;
x71.l = 410;
x72.l = 6;
x73.l = 6;
x74.l = 4;
x75.l = 4;
x76.l = 6;
x77.l = 6;
x78.l = 20;
x79.l = 20;
x80.l = 12;
x81.l = 12;
x82.l = 18;
x83.l = 18;
x84.l = 18;
x85.l = 18;
x86.l = 18;
x87.l = 18;
x88.l = 18;
x89.l = 18;
x90.l = 18;
x91.l = 18;
x92.l = 500;
x93.l = 500;
x94.l = 480;
x95.l = 480;
x96.l = 460;
x97.l = 460;
x98.l = 380;
x99.l = 380;
x100.l = 380;
x101.l = 380;
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