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

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, http://www.logmip.ceride.gov.ar/
References:
Small Model of Type: EMP
$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, http://www.logmip.ceride.gov.ar/ $offtext SETS I PROCESS STREAMS / 1*25 / J PROCESS UNITS / 1*8 / PARAMETERS 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 /; VARIABLES PROF PROFIT ; BINARY VARIABLES Y(J) ; POSITIVE VARIABLES X(I) , CF(J) ; EQUATIONS * 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; ATMOST1.. Y('1') xor Y('2'); LOGIC EQUATION ATMOST2; ATMOST2.. Y('4') xor Y('5'); LOGIC EQUATION ATMOST3; ATMOST3.. Y('6') xor Y('7'); LOGIC EQUATION IMP0; IMP0.. Y('1') -> Y('3') or Y('4') or Y('5'); LOGIC EQUATION IMP1; IMP1.. Y('2') -> Y('3') or Y('4') or Y('5'); LOGIC EQUATION IMP2; IMP2.. Y('3') -> Y('8') ; LOGIC EQUATION IMP3; IMP3.. Y('3') -> Y('1') or Y('2') ; LOGIC EQUATION IMP4; IMP4.. Y('4') -> Y('1') or Y('2') ; LOGIC EQUATION IMP5; IMP5.. Y('4') -> Y('6') or Y('7') ; LOGIC EQUATION IMP6; IMP6.. Y('5') -> Y('1') or Y('2') ; LOGIC EQUATION IMP7; IMP7.. Y('5') -> Y('8') ; LOGIC EQUATION IMP8; IMP8.. Y('6') -> Y('4') ; LOGIC EQUATION IMP9; 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%' 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 ;