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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 In this variant of ann_compressor_tanh, the tanh(x) activation function has been replaced by 1-2/(exp(2x)+1) (form 3 in paper).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 gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)
22331.90064000 p1 ( gdx sol )
(infeas: 1e-14)
Other points (infeas > 1e-08)  
Dual Bounds
22331.90061000 (ANTIGONE)
22329.66713000 (BARON)
22331.89883000 (LINDO)
22331.90064000 (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 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
*        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: 2022-06-23 Git hash: c4ba8ecd
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