logmip3.gms : LogMIP User's Manual Example 3 - Synthesis of 8 Processes

Description

```This model selects optimal processes from within a given superstructure.

References:

MARCO DURAN, PH.D. THESIS, 1984. CARNEGIE-MELLON UNIVERSITY, PITTSBURGH, PA.

Turkay & Grossmann, LOGIC-BASED MINLP ALGORITHMS FOR THE OPTIMAL
SYNTHESIS OF PROCESS NETWORKS, Computers and Chemical Engineering 20,
8, p. 959-978, 1996

Aldo Vecchietti, LogMIP User's Manual, 2007
http://www.logmip.ceride.gov.ar/files/pdfs/logmip_manual.pdf

Keywords: extended mathematical programming, disjunctive programming, logical
constraints, process synthesis
```

Small Model of Type : EMP

Category : GAMS Model library

Main file : logmip3.gms

``````\$title LogMIP User's Manual Example 3 - Synthesis of 8 Processe (LOGMIP3,SEQ=336)

\$onText
This model selects optimal processes from within a given superstructure.

References:

MARCO DURAN, PH.D. THESIS, 1984. CARNEGIE-MELLON UNIVERSITY, PITTSBURGH, PA.

Turkay & Grossmann, LOGIC-BASED MINLP ALGORITHMS FOR THE OPTIMAL
SYNTHESIS OF PROCESS NETWORKS, Computers and Chemical Engineering 20,
8, p. 959-978, 1996

Aldo Vecchietti, LogMIP User's Manual, 2007
http://www.logmip.ceride.gov.ar/files/pdfs/logmip_manual.pdf

Keywords: extended mathematical programming, disjunctive programming, logical
constraints, process synthesis
\$offText

Set
I 'process streams' / 1*25 /
J 'process units'   / 1*8  /;

Parameter CV(I) 'variable cost coeff for process units - streams'
/  3 = -10,  5 = -15,  9 = -40, 19 =  25, 21 =  35, 25 = -35
17 =  80, 14 =  15, 10 =  15,  2 =   1,  4 =   1, 18 = -65
20 = -60, 22 = -80                                         /;

Variable PROF 'profit';

Binary   Variable Y(J);
Positive Variable X(I), CF(J);

Equation
* EQUATIONS COMMON TO NLP SUBPROBLEMS AND MASTER PROBLEMS:
* --------------------------------------------------------
MASSBAL1 'mass balance #1'
MASSBAL2 'mass balance #2'
MASSBAL3 'mass balance #3'
MASSBAL4 'mass balance #4'
MASSBAL5 'mass balance #5'
MASSBAL6 'mass balance #6'
MASSBAL7 'mass balance #7'
MASSBAL8 'mass balance #8'
SPECS1   'design specification 1'
SPECS2   'design specification 2'
SPECS3   'design specification 3'
SPECS4   'design specification 4'

* EQUATIONS FOR THE MASTER PROBLEMS ONLY:
* ---------------------------------------
LOGICAL1 'constraints which allow flow iff unit 1 exists'
LOGICAL2 'constraints which allow flow iff unit 2 exists'
LOGICAL3 'constraints which allow flow iff unit 3 exists'
LOGICAL4 'constraints which allow flow iff unit 4 exists'
LOGICAL5 'constraints which allow flow iff unit 5 exists'
LOGICAL6 'constraints which allow flow iff unit 6 exists'
LOGICAL7 'constraints which allow flow iff unit 7 exists'
LOGICAL8 'constraints which allow flow iff unit 8 exists'

* EQUATIONS FOR THE NLP SUBPROBLEMS ONLY:
* ---------------------------------------
INOUT11  'input-output relations for process unit 1'
INOUT12
INOUT13
INOUT14
INOUT21  'input-output relations for process unit 2'
INOUT22
INOUT23
INOUT24
INOUT31  'input-output relations for process unit 3'
INOUT32
INOUT34
INOUT41  'input-output relations for process unit 4'
INOUT42
INOUT43
INOUT44
INOUT45
INOUT51  'input-output relations for process unit 5'
INOUT52
INOUT53
INOUT54
INOUT61  'input-output relations for process unit 6'
INOUT62
INOUT63
INOUT64
INOUT71  'input-output relations for process unit 7'
INOUT72
INOUT73
INOUT74
INOUT81  'input-output relations for process unit 8'
INOUT82
INOUT83
INOUT84
INOUT85
INOUT86
OBJETIVO 'objective function definition';

* BOUNDS SECTION:
* ---------------
X.up('3')  = 2.0;
X.up('5')  = 2.0;
X.up('9')  = 2.0;
X.up('10') = 1.0;
X.up('14') = 1.0;
X.up('17') = 2.0;
X.up('19') = 2.0;
X.up('21') = 2.0;
X.up('25') = 3.0;

* EQUATIONS COMMON TO NLP SUBPROBLEMS AND MASTER PROBLEMS:
* --------------------------------------------------------
MASSBAL1.. X('13')         =e= X('19') + X('21');
MASSBAL2.. X('17')         =e= X('9')  + X('16') + X('25');
MASSBAL3.. X('11')         =e= X('12') + X('15');
MASSBAL4.. X('3') + X('5') =e= X('6')  + X('11');
MASSBAL5.. X('6')          =e= X('7')  + X('8');
MASSBAL6.. X('23')         =e= X('20') + X('22');
MASSBAL7.. X('23')         =e= X('14') + X('24');
MASSBAL8.. X('1')          =e= X('2')  + X('4');

SPECS1..   X('10') =l= 0.8*X('17');
SPECS2..   X('10') =g= 0.4*X('17');
SPECS3..   X('12') =l= 5.0*X('14');
SPECS4..   X('12') =g= 2.0*X('14');

LOGICAL1.. X('2')  + X('3')  =l= 10.*Y('1');
LOGICAL2.. X('4')  + X('5')  =l= 10.*Y('2');
LOGICAL3.. X('9')            =l= 10.*Y('3');
LOGICAL4.. X('12') + X('14') =l= 10.*Y('4');
LOGICAL5.. X('15')           =l= 10.*Y('5');
LOGICAL6.. X('19')           =l= 10.*Y('6');
LOGICAL7.. X('21')           =l= 10.*Y('7');
LOGICAL8.. X('10') + X('17') =l= 10.*Y('8');

INOUT11..  exp(X('3')) -1.        =e= X('2');
INOUT14..  CF('1')                =e= 5;
INOUT12..  X('2')                 =e= 0;
INOUT13..  X('3')                 =e= 0;
INOUT21..  exp(X('5')/1.2) -1.    =e= X('4');
INOUT24..  CF('2')                =e= 8;
INOUT22..  X('4')                 =e= 0;
INOUT23..  X('5')                 =e= 0;
INOUT31..  1.5*X('9') + X('10')   =e= X('8');
INOUT34..  CF('3')                =e= 6;
INOUT32..  X('9')                 =e= 0;
INOUT41..  1.25*(X('12')+X('14')) =e= X('13');
INOUT45..  CF('4')                =e= 10;
INOUT42..  X('12')                =e= 0;
INOUT43..  X('13')                =e= 0;
INOUT44..  X('14')                =e= 0;
INOUT51..  X('15')                =e= 2.*X('16');
INOUT54..  CF('5')                =e= 6;
INOUT52..  X('15')                =e= 0;
INOUT53..  X('16')                =e= 0;
INOUT61..  exp(X('20')/1.5) -1.   =e= X('19');
INOUT64..  CF('6')                =e= 7;
INOUT62..  X('19')                =e= 0;
INOUT63..  X('20')                =e= 0;
INOUT71..  exp(X('22')) -1.       =e= X('21');
INOUT74..  CF('7')                =e= 4;
INOUT72..  X('21')                =e= 0;
INOUT73..  X('22')                =e= 0;
INOUT81..  exp(X('18')) -1.       =e= X('10') + X('17');
INOUT86..  CF('8')                =e= 5;
INOUT82..  X('10')                =e= 0;
INOUT83..  X('17')                =e= 0;
INOUT84..  X('18')                =e= 0;
INOUT85..  X('25')                =e= 0;

OBJETIVO.. PROF =e= sum(J, CF(J)) + sum(I, X(I)*CV(I)) + 122;

Logic Equation ATMOST1, ATMOST2, ATMOST3;
ATMOST1.. Y('1') xor Y('2');
ATMOST2.. Y('4') xor Y('5');
ATMOST3.. Y('6') xor Y('7');

Logic Equation IMP0, IMP1, IMP2, IMP3, IMP4, IMP5, IMP6, IMP7, IMP8, IMP9;
IMP0.. Y('1') -> Y('3') or Y('4') or Y('5');
IMP1.. Y('2') -> Y('3') or Y('4') or Y('5');
IMP2.. Y('3') -> Y('8');
IMP3.. Y('3') -> Y('1') or Y('2');
IMP4.. Y('4') -> Y('1') or Y('2');
IMP5.. Y('4') -> Y('6') or Y('7');
IMP6.. Y('5') -> Y('1') or Y('2');
IMP7.. Y('5') -> Y('8');
IMP8.. Y('6') -> Y('4');
IMP9.. Y('7') -> Y('4');

* Initialization
Y.l('1') = 1;
Y.l('2') = 0;
Y.l('3') = 1;
Y.l('4') = 0;
Y.l('5') = 0;
Y.l('6') = 0;
Y.l('7') = 0;
Y.l('8') = 1;

\$onEcho > '%LM.INFO%'
default bigm 100
disjunction Y('1') INOUT11 INOUT14 else INOUT12 INOUT13
disjunction Y('2') INOUT21 INOUT24 else INOUT22 INOUT23
disjunction Y('3') INOUT31 INOUT34 else INOUT32
disjunction Y('4') INOUT41 INOUT45 else INOUT42 INOUT43 INOUT44
disjunction Y('5') INOUT51 INOUT54 else INOUT52 INOUT53
disjunction Y('6') INOUT61 INOUT64 else INOUT62 INOUT63
disjunction Y('7') INOUT71 INOUT74 else INOUT72 INOUT73
disjunction Y('8') INOUT81 INOUT86 else INOUT82 INOUT83 INOUT84 INOUT85

* optional, if not set LOGMIP will find the modeltype suitable
modeltype minlp
\$offEcho

option optCr = 0, limCol = 0, limRow = 0, emp = logmip;

Model EXAMPLE3 / all /;

solve EXAMPLE3 using emp minimizing PROF;
``````
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