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Instance ann_compressor_exp
Compressor plant model where compressor powers are learned by embedded artificial neural networks. In this variant of ann_compressor_tanh, the tanh(x) activation function has been replaced by 1-2/(exp(2x)+1) (form 3 in paper).
| Formatsⓘ | ams gms mod nl osil py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | 22331.90061 (ANTIGONE) 22329.66713 (BARON) 22331.89883 (LINDO) 22331.90064 (SCIP) |
| Referencesⓘ | Schweidtmann, Artur M. and Mitsos, Alexander, Deterministic Global Optimization with Artificial Neural Networks Embedded, Journal of Optimization Theory and Applications, 180:3, 2019, 925-948. |
| Applicationⓘ | Neural Networks |
| Added to libraryⓘ | 29 Nov 2021 |
| Problem typeⓘ | NLP |
| #Variablesⓘ | 96 |
| #Binary Variablesⓘ | 0 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 43 |
| #Nonlinear Binary Variablesⓘ | 0 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | quadratic |
| Objective curvatureⓘ | indefinite |
| #Nonzeros in Objectiveⓘ | 3 |
| #Nonlinear Nonzeros in Objectiveⓘ | 3 |
| #Constraintsⓘ | 95 |
| #Linear Constraintsⓘ | 55 |
| #Quadratic Constraintsⓘ | 0 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 40 |
| Operands in Gen. Nonlin. Functionsⓘ | div exp |
| Constraints curvatureⓘ | indefinite |
| #Nonzeros in Jacobianⓘ | 407 |
| #Nonlinear Nonzeros in Jacobianⓘ | 40 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 44 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 40 |
| #Blocks in Hessian of Lagrangianⓘ | 41 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 1 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 3 |
| Average blocksize in Hessian of Lagrangianⓘ | 1.04878 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 4.5084e-03 |
| Maximal coefficientⓘ | 1.4305e+02 |
| Infeasibility of initial pointⓘ | 173.4 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 96 96 0 0 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 97 97 0 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL
* 411 368 43
* Solve m using NLP minimizing objvar;
Variables
objvar,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,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;
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;
e1.. -120.40939193257074 * x30 * x5 - 120.40939193257074 * x76 * (1 - x5) +
objvar =E= 0;
e2.. x2 =E= 4.5;
e3.. x3 - 100 * x5 =E= 0;
e4.. x4 + 100 * x5 =E= 100;
e5.. -x3 + x6 =E= 0;
e6.. -x2 + x7 =E= 0;
e7.. -0.04 * x6 + x8 =E= -3;
e8.. -0.3448275862068966 * x7 + x9 =E= -1.4137931034482758;
e9.. -3.29883729878545 * x8 - 2.21634281184627 * x9 + x32 =E=
-4.74519636814514;
e10.. -4.39097392620389 * x8 + 2.70229300136141 * x9 + x33 =E=
-4.1794539909462;
e11.. 2.42525489414387 * x8 - 2.14396438801434 * x9 + x34 =E=
1.78401467718833;
e12.. -0.665434334521876 * x8 + 1.29787993619185 * x9 + x35 =E=
-1.11674460513219;
e13.. 2.77766394913542 * x8 + 1.74555017902411 * x9 + x36 =E=
0.597624173984931;
e14.. -4.7733972839648 * x8 + 2.41673394043034 * x9 + x37 =E=
1.42752748364808;
e15.. -2.4663429726711 * x8 + 2.38573916130801 * x9 + x38 =E=
1.17440914003301;
e16.. 5.52466754531544 * x8 - 2.06923017046543 * x9 + x39 =E=
-2.90717074600284;
e17.. -3.61637061682719 * x8 + 5.51456412860865 * x9 + x40 =E=
5.64272390748818;
e18.. 0.995512979228518 * x8 - 4.09187475401507 * x9 + x41 =E=
-3.89340599335458;
e19.. 2 / (exp(2 * x32) + 1) + x10 =E= 1;
e20.. 2 / (exp(2 * x33) + 1) + x11 =E= 1;
e21.. 2 / (exp(2 * x34) + 1) + x12 =E= 1;
e22.. 2 / (exp(2 * x35) + 1) + x13 =E= 1;
e23.. 2 / (exp(2 * x36) + 1) + x14 =E= 1;
e24.. 2 / (exp(2 * x37) + 1) + x15 =E= 1;
e25.. 2 / (exp(2 * x38) + 1) + x16 =E= 1;
e26.. 2 / (exp(2 * x39) + 1) + x17 =E= 1;
e27.. 2 / (exp(2 * x40) + 1) + x18 =E= 1;
e28.. 2 / (exp(2 * x41) + 1) + x19 =E= 1;
e29.. 0.398852142813582 * x10 - 0.725357344120736 * x11 - 0.387983353041334 *
x12 - 0.391659415559979 * x13 + 0.288302309312186 * x14 -
0.849799453052077 * x15 - 0.217992356329322 * x16 + 0.486032972888755 *
x17 + 0.633874608504516 * x18 + 0.650057770234234 * x19 + x42 =E=
1.72952444050299;
e30.. -0.606108375762298 * x10 + 1.05128271107625 * x11 - 0.113407401402558 *
x12 - 0.685128435722532 * x13 - 0.00839355729502805 * x14 +
0.72324079108208 * x15 - 1.54800905346302 * x16 + 0.739614279155593 *
x17 - 0.0672266652749378 * x18 - 0.862069039273904 * x19 + x43 =E=
-1.82152313507679;
e31.. 0.017213005528439 * x10 - 0.432991382826051 * x11 - 0.526615385996248 *
x12 - 1.74111228306707 * x13 + 0.0927253728709128 * x14 - 0.714238249447
* x15 - 2.30412079128021 * x16 - 0.307687532319036 * x17 +
0.685277679084365 * x18 + 0.298152813152174 * x19 + x44 =E=
-1.94871746897132;
e32.. -0.254425130089128 * x10 + 0.982857591863807 * x11 - 1.12188627220446 *
x12 + 0.953177569130776 * x13 + 1.16324832732783 * x14 -
0.583334671787914 * x15 - 1.46286282166184 * x16 - 0.740744196362748 *
x17 + 0.156187890973621 * x18 + 0.473721758540603 * x19 + x45 =E=
0.750110448454269;
e33.. 0.358841679803966 * x10 - 0.909769646581453 * x11 - 0.5400556368999 *
x12 - 1.92581231012236 * x13 - 0.143289578857379 * x14 +
1.11041979527607 * x15 - 0.806556686522453 * x16 + 1.31979752840351 *
x17 - 2.83201899803365 * x18 - 1.4165064435108 * x19 + x46 =E=
-0.155525493921263;
e34.. 0.876963350723843 * x10 + 1.68895367151327 * x11 - 1.01792289921342 *
x12 + 0.481816149447196 * x13 - 0.681037723637203 * x14 -
0.221547242667722 * x15 - 0.153701721119032 * x16 - 0.387789381638438 *
x17 - 0.534863109743709 * x18 + 0.429118392881899 * x19 + x47 =E=
-0.182171157802204;
e35.. 0.295071408357937 * x10 + 0.615013493949934 * x11 - 0.477319899374172 *
x12 + 0.669337407546281 * x13 - 0.659568388812123 * x14 -
2.87966615253197 * x15 - 1.18319325324759 * x16 - 0.317508919826113 *
x17 - 0.0260541413647632 * x18 - 0.613914515498283 * x19 + x48 =E=
-0.525879231367697;
e36.. -0.276877372242598 * x10 - 0.313761370734112 * x11 + 0.437283574367938 *
x12 + 1.40935113091552 * x13 - 0.239224962403201 * x14 +
1.25079738013603 * x15 - 0.862457167086818 * x16 + 0.728247439675487 *
x17 - 0.422374486028782 * x18 - 1.57017436743666 * x19 + x49 =E=
0.851092831485534;
e37.. 0.0222234768795211 * x10 - 0.17355526816404 * x11 + 1.15591927972987 *
x12 + 1.98476876674976 * x13 + 0.10670750595954 * x14 +
0.363095670968738 * x15 + 1.67891067831231 * x16 + 0.581167798267274 *
x17 - 0.201190601410721 * x18 + 0.862612980547481 * x19 + x50 =E=
1.74557292553105;
e38.. 1.5513910853905 * x10 - 1.468539025819 * x11 - 0.106950283907874 * x12
- 2.47794942642174 * x13 - 0.120836180137454 * x14 - 0.189856190121489
* x15 - 0.488776919915584 * x16 - 0.299287142871813 * x17 -
0.786524342476143 * x18 - 0.171942752553922 * x19 + x51 =E=
-1.52550869349925;
e39.. 2 / (exp(2 * x42) + 1) + x20 =E= 1;
e40.. 2 / (exp(2 * x43) + 1) + x21 =E= 1;
e41.. 2 / (exp(2 * x44) + 1) + x22 =E= 1;
e42.. 2 / (exp(2 * x45) + 1) + x23 =E= 1;
e43.. 2 / (exp(2 * x46) + 1) + x24 =E= 1;
e44.. 2 / (exp(2 * x47) + 1) + x25 =E= 1;
e45.. 2 / (exp(2 * x48) + 1) + x26 =E= 1;
e46.. 2 / (exp(2 * x49) + 1) + x27 =E= 1;
e47.. 2 / (exp(2 * x50) + 1) + x28 =E= 1;
e48.. 2 / (exp(2 * x51) + 1) + x29 =E= 1;
e49.. -1.0674 * x20 + 1.2197 * x21 - 1.578 * x22 + 1.4501 * x23 + 1.0611 * x24
+ 0.52263 * x25 + 0.090589 * x26 - 0.78946 * x27 - 1.7347 * x28 +
0.63854 * x29 + x31 =E= -0.523544433780434;
e50.. x30 - 136.23687745314615 * x31 =E= 165.14897153681486;
e51.. -x4 + x52 =E= 0;
e52.. -x2 + x53 =E= 0;
e53.. -0.05714285714285714 * x52 + x54 =E= -1.8571428571428572;
e54.. -0.3448275862068966 * x53 + x55 =E= -1.4137931034482758;
e55.. 4.93640448594107 * x54 + 0.912605578908679 * x55 + x78 =E=
4.1270692338668;
e56.. 0.816777467188004 * x54 + 5.32033684666278 * x55 + x79 =E=
-2.32662461492317;
e57.. 2.66472390799182 * x54 + 0.362343664737007 * x55 + x80 =E=
1.91392918798187;
e58.. 2.02628709921665 * x54 + 0.48093844474148 * x55 + x81 =E=
0.427660620779721;
e59.. -1.14069543363375 * x54 + 3.45428737671842 * x55 + x82 =E=
-1.71791138693198;
e60.. -1.73507877664684 * x54 - 3.91745010409221 * x55 + x83 =E=
1.09025760296775;
e61.. -2.11707508608896 * x54 + 2.33023244949126 * x55 + x84 =E=
1.50363786298596;
e62.. -2.99151042883558 * x54 + 3.93409732391626 * x55 + x85 =E=
-0.0181541866671218;
e63.. -1.5250601954822 * x54 - 3.17883210470949 * x55 + x86 =E=
3.45453898493558;
e64.. -1.46971647430401 * x54 + 3.34372673401725 * x55 + x87 =E=
5.31141965926459;
e65.. 2 / (exp(2 * x78) + 1) + x56 =E= 1;
e66.. 2 / (exp(2 * x79) + 1) + x57 =E= 1;
e67.. 2 / (exp(2 * x80) + 1) + x58 =E= 1;
e68.. 2 / (exp(2 * x81) + 1) + x59 =E= 1;
e69.. 2 / (exp(2 * x82) + 1) + x60 =E= 1;
e70.. 2 / (exp(2 * x83) + 1) + x61 =E= 1;
e71.. 2 / (exp(2 * x84) + 1) + x62 =E= 1;
e72.. 2 / (exp(2 * x85) + 1) + x63 =E= 1;
e73.. 2 / (exp(2 * x86) + 1) + x64 =E= 1;
e74.. 2 / (exp(2 * x87) + 1) + x65 =E= 1;
e75.. -0.19229719566531 * x56 - 0.113229364819046 * x57 - 0.317011984009582 *
x58 - 0.208176499331018 * x59 - 0.0526893135225106 * x60 +
0.00496874764197475 * x61 - 1.11781664691223 * x62 - 0.164747202380028 *
x63 + 0.128801038943437 * x64 - 0.115050980825826 * x65 + x88 =E=
-1.61331605529523;
e76.. -1.39561108328297 * x56 + 0.291294577508309 * x57 + 2.42255053970948 *
x58 + 0.806424775519701 * x59 - 0.24700602376048 * x60 -
2.86528129248516 * x61 + 0.228041341097786 * x62 - 0.919031862096554 *
x63 - 0.331591530574725 * x64 - 0.862221243067094 * x65 + x89 =E=
-1.14616698593978;
e77.. -1.5279242841873 * x56 - 0.698226236065608 * x57 + 1.55481625080507 *
x58 - 0.712477732925898 * x59 - 0.879321205828354 * x60 -
0.999578930453093 * x61 + 0.436064389773445 * x62 - 1.20491503278419 *
x63 + 0.0828027271237818 * x64 + 1.16436684334948 * x65 + x90 =E=
-1.26487905494015;
e78.. -1.31136556313664 * x56 + 0.688090162957568 * x57 - 0.483533126996118 *
x58 + 0.317208594550559 * x59 - 0.987077283548825 * x60 +
2.03966860668343 * x61 - 1.28045374550174 * x62 - 1.17174317918226 * x63
- 1.92490816822108 * x64 + 1.88902014251631 * x65 + x91 =E=
-2.43368306899489;
e79.. 0.663187111420449 * x56 + 0.653673216749544 * x57 - 2.05130150144194 *
x58 - 0.038085494374431 * x59 - 1.47243466819752 * x60 -
2.97625982340582 * x61 + 2.99369146603845 * x62 - 1.41254919999138 * x63
+ 0.792703266075634 * x64 - 1.20920862561178 * x65 + x92 =E=
-0.145245935667929;
e80.. 3.16558479304872 * x56 + 0.610800921707547 * x57 - 3.91566418422506 *
x58 + 0.690696672854988 * x59 - 1.1387592986803 * x60 - 1.55320919936001
* x61 - 0.649315965120837 * x62 - 3.93545445106757 * x63 -
1.72059703275849 * x64 + 0.352306217462982 * x65 + x93 =E=
-0.544825168753145;
e81.. -0.832946328830514 * x56 - 0.261706335203891 * x57 - 1.52961004768381 *
x58 - 0.96278230549486 * x59 - 0.0558260797192328 * x60 +
0.796583270628257 * x61 + 0.231506642471326 * x62 + 0.699291918288105 *
x63 + 0.38426656703623 * x64 + 1.46531125311878 * x65 + x94 =E=
0.336652248890323;
e82.. 1.95060055587423 * x56 + 1.84279061221506 * x57 - 0.225343280513967 *
x58 + 1.32570761854527 * x59 - 0.0145976190506455 * x60 +
2.3127770319283 * x61 - 1.72621008535973 * x62 + 0.913597417647886 * x63
+ 1.22514837154043 * x64 + 0.0387545896912135 * x65 + x95 =E=
-0.182365009499401;
e83.. 0.45472386490334 * x56 - 1.91223566080678 * x57 - 0.537347924651761 *
x58 + 0.98607719903189 * x59 + 0.225915202471944 * x60 +
2.41658375893019 * x61 + 1.5400112823527 * x62 - 0.590930400398464 * x63
- 2.14543603917029 * x64 - 1.15870755844912 * x65 + x96 =E=
3.71721040155117;
e84.. -2.23225023028356 * x56 + 0.327733125529555 * x57 + 0.310848878283525 *
x58 + 1.05010074838177 * x59 - 0.831450614261062 * x60 -
0.501691134298998 * x61 - 3.24606656818691 * x62 + 0.313457236205627 *
x63 - 0.58950348835461 * x64 + 1.96788365310352 * x65 + x97 =E=
0.451617778637158;
e85.. 2 / (exp(2 * x88) + 1) + x66 =E= 1;
e86.. 2 / (exp(2 * x89) + 1) + x67 =E= 1;
e87.. 2 / (exp(2 * x90) + 1) + x68 =E= 1;
e88.. 2 / (exp(2 * x91) + 1) + x69 =E= 1;
e89.. 2 / (exp(2 * x92) + 1) + x70 =E= 1;
e90.. 2 / (exp(2 * x93) + 1) + x71 =E= 1;
e91.. 2 / (exp(2 * x94) + 1) + x72 =E= 1;
e92.. 2 / (exp(2 * x95) + 1) + x73 =E= 1;
e93.. 2 / (exp(2 * x96) + 1) + x74 =E= 1;
e94.. 2 / (exp(2 * x97) + 1) + x75 =E= 1;
e95.. 0.94504 * x66 + 0.063174 * x67 + 1.23 * x68 + 0.0045084 * x69 - 0.080538
* x70 + 0.0086604 * x71 - 0.027211 * x72 + 0.013266 * x73 + 0.27219 *
x74 + 1.7486 * x75 + x77 =E= 0.411768749636318;
e96.. x76 - 143.0487213258034 * x77 =E= 173.4064201136556;
* set non-default bounds
x3.lo = 61.511; x3.up = 100;
x4.lo = 25.3199; x4.up = 44.4401;
x5.lo = 0; x5.up = 1;
Model m / all /;
m.limrow = 0;
m.tolproj=0.0;
m.limcol = 0;
$if NOT '%gams.u1%' == '' $include '%gams.u1%'
$if not set NLP $set NLP NLP
Solve m using %NLP% minimizing objvar;
Last updated: 2026-09-14 Git hash: 9472b011