MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

Home // Instances // Documentation // Download // Statistics


Instance ann_compressor_tanh

Compressor plant model where compressor powers are learned by embedded artificial neural networks.
Formats gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)
22331.90064000 p1 ( gdx sol )
(infeas: 9e-16)
Other points (infeas > 1e-08)  
Dual Bounds
22331.89765000 (LINDO)
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 tanh
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..  -tanh(x32) + x10 =E= 0;
e20..  -tanh(x33) + x11 =E= 0;
e21..  -tanh(x34) + x12 =E= 0;
e22..  -tanh(x35) + x13 =E= 0;
e23..  -tanh(x36) + x14 =E= 0;
e24..  -tanh(x37) + x15 =E= 0;
e25..  -tanh(x38) + x16 =E= 0;
e26..  -tanh(x39) + x17 =E= 0;
e27..  -tanh(x40) + x18 =E= 0;
e28..  -tanh(x41) + x19 =E= 0;
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..  -tanh(x42) + x20 =E= 0;
e40..  -tanh(x43) + x21 =E= 0;
e41..  -tanh(x44) + x22 =E= 0;
e42..  -tanh(x45) + x23 =E= 0;
e43..  -tanh(x46) + x24 =E= 0;
e44..  -tanh(x47) + x25 =E= 0;
e45..  -tanh(x48) + x26 =E= 0;
e46..  -tanh(x49) + x27 =E= 0;
e47..  -tanh(x50) + x28 =E= 0;
e48..  -tanh(x51) + x29 =E= 0;
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..  -tanh(x78) + x56 =E= 0;
e66..  -tanh(x79) + x57 =E= 0;
e67..  -tanh(x80) + x58 =E= 0;
e68..  -tanh(x81) + x59 =E= 0;
e69..  -tanh(x82) + x60 =E= 0;
e70..  -tanh(x83) + x61 =E= 0;
e71..  -tanh(x84) + x62 =E= 0;
e72..  -tanh(x85) + x63 =E= 0;
e73..  -tanh(x86) + x64 =E= 0;
e74..  -tanh(x87) + x65 =E= 0;
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..  -tanh(x88) + x66 =E= 0;
e86..  -tanh(x89) + x67 =E= 0;
e87..  -tanh(x90) + x68 =E= 0;
e88..  -tanh(x91) + x69 =E= 0;
e89..  -tanh(x92) + x70 =E= 0;
e90..  -tanh(x93) + x71 =E= 0;
e91..  -tanh(x94) + x72 =E= 0;
e92..  -tanh(x95) + x73 =E= 0;
e93..  -tanh(x96) + x74 =E= 0;
e94..  -tanh(x97) + x75 =E= 0;
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
Imprint / Privacy Policy / License: CC-BY 4.0