ga lectures iitb 09
DESCRIPTION
Geometric AlgTRANSCRIPT
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GENETIC ALGORITHM (GA), MULTI-OBJECTIVE OPTIMIZATION (MOO)
and BIOMIMETIC ADAPTATIONS
SANTOSH K. GUPTASANTOSH K. GUPTA
DEPARTMENT OF CHEMICAL ENGINEERING INDIAN INSTITUTE OF TECHNOLOGY
BOMBAY, POWAI, MUMBAI 400 076, INDIA
GA LECTURES IITB 09
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OPTIMIZATION (SOO) PROBLEM
MAXIMIZE F(x) OR MINIMIZE I(x) MIN I(x) MAX {F ≡ 1/[1+ I(x)]}
S.T.
GET A UNIQUE SOLUTION
L Ui i i parameterx x x ; i 1, 2, ..., n
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MOO: MIN I1 (x); MIN I2 (x)
NORMALLY WE FIND A SET OF EQUALLY-GOOD (NON-DOMINATING) SOLUTIONS, CALLED PARETO SET (e.g., MIN REACTION TIME, MIN SIDE PRODUCT CONCN)
A
B
F2
F1
BB
F1
B
F1
B
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GENETIC ALGORITHM (GA) MIMICS PRINCIPLES OF NATURAL
GENETICS
INVOKES THE DARWINIAN PRINCIPLE OF ‘SURVIVAL OF THE FITTEST’
‘DEVELOPED’ BY PROF. JOHN HOLLAND (U. MICH., ANN ARBOR, USA) IN 1975
BOOKS: HOLLAND, GOLDBERG, COELLO COELLO, K. DEB (IITK), G. RANGAIAH (NUS)
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SIMPLE GA (SOO)MAXIMIZE I(x) S.T.
L Ui i i parameterx x x ; i 1, 2, ..., n
U2X
L2X
U1X
L1X
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DESCRIPTION OF TECHNIQUE (BINARY-CODED)
NO PROOFS; SCHEMA THEORY
GENERATION NO. = 0
GENERATE, RANDOMLY, SEVERAL (NP) SETS OF nparameter DECISION VARIABLES, (x1, x2, ..., xnparameter)1, (x1, x2, ..., xnparameter)2, . . . AS MEMBERS OF A POPULATION
CHOOSE NO. OF BINARIES (SAY lstring = 4) DESCRIBING EACH DECISION VARIABLE
GENERATE (USING RANDOM NO. SUBROUTINE) nparameter lstring (≡ nchr) BINARIES FOR EACH OF THE NP MEMBERS
0.0 ≤ R < 0.5 → USE 0; 0.5 ≤ R ≤ 1.0 → USE 1
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1ST CHROMOSOME OR STRING : 1 0 1 0 0 1 1 1 2ND CHROMOSOME OR STRING : 1 1 0 1 0 1 0 1 * * NP
TH CHROMOSOME OR STRING : 1 1 0 1 0 0 0 1 S1 S2 S3 S4
CONVERT EACH BINARY INTO DECIMAL VALUE
XJ DOMAIN DIVIDED INTO 15 (2lstring - 1) INTERVALS
MAP EACH CHROMOSOME TO GIVE DECIMAL VALUES BETWEEN xJ
L AND xJU
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0 0 0 0 1 0 0 0 0 1 0 0 1 1 1 0 1 0 1 1
0 1 2 3 13 14 15
MAPPING RULE:
SUB-STRING, J
1l
0ii
il
LJ
UJL
JJ s212xxxx
LJX
UJX
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WE NOW HAVE EACH OF THE NP DECISION VARIABLES (VECTORS), xJ, IN TERMS OF REAL NUMBERS, e.g.,
1 (2.71, 3.23)2 (xxxx, xxxx) . .NP (xxxx, xxxx)
ALL BOUNDS ON XJ ARE SATISFIED
ACCURACY OF THE TECHNIQUE DEPENDS ON VALUE SELECTED FOR lstring
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USE MODEL EQUATIONS FOR EACH OF THE NP x, TO COMPUTE I(x)
jth chromosome Decoder Model I(xj)
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REPRODUCTION OR SELECTION TOURNAMENT SELECTION (COPY TO A MATING POOL)
CHOOSE TWO CHROMOSOMES RANDOMLY (FOR 100 CHROMOSOMES: 0.0 ≤ R < 0.01 → USE 1ST; 0.01 ≤ R ≤ 0.02 → USE 2ND, etc.)
COPY (WITHOUT DELETING) THE BETTER OF THE TWO
BAD STRINGS HAVE A CHANCE OF CONTINUING (GBS)
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CROSSOVER CHOOSE TWO CHROMOSOMES RANDOMLY, CHOOSE A
CROSSOVER SITE RANDOMLY, AND CARRY OUT CROSSOVER
0 0 0 1 0 0 1 0 1 0 1 0 → 1 0 0 1
GOOD STRINGS GET PROPAGATED, LESS GOOD ONES SLOWLY DIE DURING COPYING PROCESS IN THE FUTURE
NOT ALL GOOD STRINGS IN MATING POOL UNDERGO CROSSOVER; CROSSOVER PROBABILITY = PC, i.e., 100(1- PC) % OF STRINGS CONTINUE UNCHANGED TO NEXT GENERATION
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MUTATION FOR EXAMPLE, IF WE HAVE
0110 …0011 …0001 …
THE 1ST POSITION CAN NEVER BECOME 1 BY CROSSOVER
TO ACHIEVE SUCH CHANGES, EACH BINARY IN EVERY CHROMOSOME IS SWITCHED OVER (0 ↔ 1) WITH A LOWPROBABILITY, PM
BAD STRINGS, IF CREATED, WOULD DIE SLOWLY
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MATHEMATICAL FOUNDATION (USING SCHEMA THEORY) AVAILABLE IN TEXTBOOKS
GAs WORK WITH SEVERAL SOLUTIONS SIMULTANEOUSLY
MULTIPLE OPTIMAL SOLUTIONS CAN BE CAUGHT
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EXAMPLE 1
HIMMELBLAU FUNCTION
MIN I (X1, X2) = (X12 + X2 - 11)2 + (X1 + X2
2 - 7)2
S.T. 0 ≤ X1, X2 ≤ 6
OPTIMAL SOLUTION: (3, 2)T, I = 0
lstring = 10 BITS, PC = 0.8, PM = 0.05, NP = 20
KNUTH’S RANDOM NUMBER GENERATOR WITH RANDOM SEED = 0.760, USED
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INITIAL POPULATION
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CROSSOVER OPERATION
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MUTATION OPERATION
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POPULATION AT GENERATION 30
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POPULATION-BEST I VS. GENERATION NUMBER
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EXAMPLE 2
CONSTRAINED HIMMELBLAU FUNCTION
MIN I (X1, X2) = (X12 + X2 - 11)2 + (X1 + X2
2 -7)2
S.T. g1(X) ≡ (X1 - 5)2 + X22 - 26 ≥ 0
g2(X) ≡ X1 ≥ 0g3(X) ≡ X2 ≥ 0
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PENALTY FUNCTIONS
MIN F(X1, X2) ≡ I (X1, X2) + w1g1(X) + w2g2(X) + w3g3(X)
w1 = 105 IF g1(X) ≤ 0; w1 = 0 IF g1(X) ≥ 0
w2 = 105 IF X1 ≤ 0; w2 = 0 IF X1 ≥ 0
w3 = 105 IF X2 ≤ 0; w3 = 0 IF X2 ≥ 0
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INITIAL POPULATION AND POPULATION AT GENERATION 30
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MULTI OBJECTIVE OPTIMIZATION (MOO)
K. DEB, MULTI-OBJECTIVE OPTIMIZATION USING EVOLUTIONARY ALGORITHMS, WILEY, CHICHESTER, UK (2001)
K. MITRA, K. DEB AND S. K. GUPTA, J. APPL. POLYM. SCI., 69, 69 (1998)
EXAMPLE (2-OBJECTIVE FUNCTIONS, TWO DECISION VARIABLES)
S.T. XL X XU
I
T
Max I (X) (X X ), I (X , X ) 1 1 2 2 1 2
,
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NORMALLY WE FIND A SET OF EQUALLY-GOOD (NON-DOMINATING) SOLUTIONS, CALLED PARETO SET
A
B
F2
F1
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CONCEPT OF DOMINANCE AND NON-DOMINANCE (MAXIMIZATION)
IF ANY CHROMOSOME’S, I , IS ‘BETTER’ THAN THE I OF THE OTHER IN THE SENSE THAT I1 AS WELL AS I2 ARE LARGER FOR CHR 2 THAN FOR CHR 1, THEN 2 DOMINATES 1
2
1
I2
I1
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NSGA-II-JG ELITIST NON-DOMINATED SORTING
GENETIC ALGORITHM WITH aJG GENERATE NP PARENT CHROMOSOMES (IN
BOX P), NUMBERED 1, 2, …, NP
EVALUATE RANK NUMBER, II,RANK (BASED ON NON-DOMINATION)
CREATE NEW BOX, P’, HAVING NP LOCATIONS
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TAKE CHROMOSOME, II , FROM P (DELETE IT FROM P) AND PUT IT TEMPORARILY IN P’
COMPARE II WITH EACH MEMBER CURRENTLY PRESENT IN P’, ONE BY ONE, AND COLLECT THE NON-DOMINATED MEMBERS IN P’ (RETURN DOMINATED MEMBERS TO THEIR ORIGINAL POSITIONS IN P)
CONTINUE TILL ALL NP MEMBERS OF P HAVE BEEN EXPLORED (IRANK = 1). REPEAT TILL ALL NP ARE PLACED IN DIFFERENT FRONTS IN P’.
ASSIGN RANK NUMBER, II,RANK (= 1, 2, . . . ), TO EACH CHROMOSOME, II, IN P’ (LOW RANKS FOR DIVERSITY)
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EVALUATING CROWDING DISTANCE, II,DIST
IN ANY SELECTED FRONT OF P’, RE-ARRANGE ALL CHROMOSOMES IN ORDER OF INCREASING VALUES OF I1
(OR I2)
FIND THE LARGEST CUBOID ENCLOSING II IN P’, THAT JUST TOUCHES ITS NEAREST NEIGHBORS
CROWDING DISTANCE, II,DIST = SUM OF M SIDES OF THIS CUBOID
I1
I2 II
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BOUNDARY SOLUTIONS → HIGH II,DIST (HIDDEN IN CODE)
HELPS SPREAD OUT PARETO POINTS I1 BETTER THAN I2 IF
I1,RANK I2, RANK
OR
(I1,RANK I2, RANK ) AND (I1,DIST I2,DIST )
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COPYING TO A MATING POOL
TAKE (WITHOUT DELETING) ANY TWO MEMBERS FROM BOX P’ RANDOMLY
MAKE COPY OF THE BETTER ONE IN A NEW BOX, P’’
REPEAT PAIRWISE COMPARISON TILL P’’ HAS NP MEMBERS
NOT ALL MEMBERS IN P’ NEED BE IN P’’
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COPY ALL OF P’’ IN A NEW BOX, D, OF SIZE NP
CARRY OUT CROSSOVER AND MUTATION OF
CHROMOSOMES IN D
THIS GIVES A BOX OF NP DAUGHTER
CHROMOSOMES
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BIOMIMETIC ADAPTATION 1: JUMPING GENE
[KASAT & GUPTA, CACE, 27, 1785 (2003)]
1: Transposon inserted in a chromosome; 2: Genes in the transposon; 3,4: Inverted repeat sequences of bases/nucleotides; 5: Double-stranded
DNA of original chromosome
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JUMPING GENES (McCLINTOCK: 1987; NOBEL PRIZE: 1983 Medicine)
DNA CHUNKS OF 1-2 KILO-BASES THAT CAN JUMP IN AND OUT OF CHROMOSOMES
IMMUNITY TO ANTIBIOTICS
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REPLACEMENT AND REVERSION
JUMPING GENE
REPLACEMENT REVERSION
P
R
Q
S
P
P
Q
Q
R S
Q P
ORIGINALCHROMOSOME
TRANSPOSON
CHROMOSOMEWITH
TRANSPOSON
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JUMPING GENE OPERATORS SELECT A CHROMOSOME (SEQUENTIALLY)
FROM D. CHECK IF JG OPERATION IS NEEDED, USING PJUMP. IF YES:
NSGA-II-JG:
USING TWO INTEGRAL RANDOM NUMBERS, LOCATE TWO LOCATIONS (BEGINNING AND END OF JG OR TRANSPOSON)
REPLACE BY A SET OF NEWLY GENERATED RANDOM BINARIES OF SAME LENGTH
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NSGA-II-aJG:
CHOOSE/SPECIFY LENGTH, fB, OF AN a-JG
USING ONE INTEGRAL RANDOM NUMBER, LOCATE ONE LOCATION (BEGINNING OF THE a-JG)
REPLACE BY A SET OF fB NEWLY GENERATED RANDOM BINARIES
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ELITISM (DEB) COPY ALL THE NP (BETTER) PARENTS (P’’) AND
ALL THE NP DAUGHTERS (D) WITH TRANSPOSONS INTO BOX, PD (SIZE = 2NP)
RECLASSIFY THESE 2NP CHROMOSOMES INTO FRONTS (BOX PD’) USING ONLY NON-DOMINATION
TAKE THE BEST NP FROM PD’ AND PUT INTO BOX P’” (IF WE NEED TO ‘BREAK’ A FRONT, USE CROWDING DISTANCE)
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THIS COMPLETES ONE GENERATION. STOP IF CRITERIA ARE MET
COPY P’” INTO STARTING BOX, P. REPEAT
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SIMPLE EXAMPLE OF NSGA-II-JG (ZDT4)
MIN I1 = X1
MIN I2 = 1 – [I1/G(X)]1/2
WHERE [RASTRIGIN FUNCTION]: G(X) 1 + 10 (N - 1) + ∑i=2
N [Xi2 – 10 COS(4Xi)]
N = 10
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99 LOCAL PARETOS
GLOBAL PARETO HAS
0 X1 1; → 0 ≤ I1 ≤ 1
Xj = 0; j = 2, 3, . . . , 10; → 0 ≤ I2 ≤ 1
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Gen1000(NSGA-II)
f1
0.0 0.1 0.2 0.3 0.4 0.5
f 2
15.5
16.0
16.5
17.0
17.5
18.0
18.5
19.0
Gen 1000 (NSGA-II-JG)
f1
0.0 0.2 0.4 0.6 0.8 1.0 1.2
f 2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
Fig. 7
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f1
0.0 0.2 0.4 0.6 0.8 1.0 1.2
f 2
0.0
0.5
1.0
1.5
2.0
2.5
Pjump =0.1Pjump =0.3Pjump = 0.5 - 1.0
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SEVERAL CHE APPLICATIONS OF SIMULATION AND MOO
INDUSTRIAL NYLON 6 SEMIBATCH REACTORMIN tf; MIN [C2]f s.t. : Xm,d, μm,d USING T and p(t) or Tj(t) and p(t)
INDUSTRIAL THIRD-STAGE WIPED FILM PET REACTOR NSGA-I FAILS TO GIVE PARETO IN ONE-SHOT
APPLICATION; USED MULTIPLE RUNS
SS AND UN-SS INDUSTRIAL STEAM REFORMER CHROMOSOME-SPECIFIC BOUNDS
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INDUSTRIAL FLUIDIZED-BED CAT CRACKER (FCC)
MEMBRANE SEPARATION: LOW ALCOHOL BEER DESALINATION
CYCLONE SEPARATORS
VENTURI SCRUBBERS
PMMA REACTORS (EXPERIMENTAL ON-LINE OPTIMAL CONTROL)
HEAT EXCHANGER NETWORKS (LINHOFF’S PINCH METHOD)
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MOO of an INDUSTRIAL FCCU, B Sankararao & S K Gupta, CACE, 31,
1496 (2007)
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Argn, m2
Make up cat.
Regenerator
cat. withdrawal
Regenerator
Air, Fair, kg/sTair, K
Zdil, m
Zden, m
Riser / Reactor
Tfeed, KFeed, Ffeed, kg/s
Hris, m
Dilute Phase
Dense bedTrgn, K
To mainfractionator
Separator
Aris, m2
Riser
Spent cat.
Regenerated cat.,Fcat, kg/sCrgc, kg coke / kg catalyst
Schematic Diagram of A FCCU
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Gas Oil
Gasoline
LPG
k1
k2
k3
k4
Dry Gas
Coke
k5
k7
k6k8
k9
FIVE-LUMP KINETIC SCHEME USED IN THIS WORK
1, 2, 3, 4 are second order5, 6, 7, 8, 9 are first order
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MULTI-OBJECTIVE OPTIMIZATION PROBLEM: FCCU
Max f1 (Tfeed, Tair, Fcat, Fair) = gasoline yield
Min f2 (Tfeed, Tair, Fcat, Fair) = % CO in the flue gas
Subject to Constraints and Bounds on Tfeed, Tair, Fcat, Fair
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BOUNDS ON DECISION VARIABLES: 575 TFEED 670 K 450 TAIR 525 K 115 FCAT 290 kg/s 11 FAIR 46 kg/s
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51267.23Regenerator Pressure (kPa)
253.85Riser Pressure (kPa)
29.0Feed Rate (kg/s)
34000.0Inventory of Catalyst in Regenerator (kg)
4.5Regenerator Diameter (m)
19.4Regenerator Length (m)
0.685Riser Diameter (m)
37.0Riser Length (m)
VALUEPARAMETER
DESIGN DATA FOR THE INDUSTRIAL FCCU STUDIED
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NSGA-II NSGA-II-JG NSGA-II-aJG
MOSA MOSA-JG MOSA-aJG
30
32.5
35
37.5
40
42.5
45
0.001 0.01 0.1 1 10
% CO in flue gas
Gas
olin
e yi
eld
at e
nd o
f ris
er (%
)
30
32.5
35
37.5
40
42.5
45
0.001 0.01 0.1 1 10
% CO in flue gasG
asol
ine
yiel
d at
end
of r
iser
(%)
30
32.5
35
37.5
40
42.5
45
0.001 0.01 0.1 1 10
% CO in flue gas
Gas
olin
e yi
eld
at e
nd o
f ris
er (%
)30
32.5
35
37.5
40
42.5
45
0.001 0.01 0.1 1 10
% CO in flue gas
Gas
olin
e yi
eld
at e
nd o
f ris
er (%
)
30
32.5
35
37.5
40
42.5
45
0.001 0.01 0.1 1 10
% CO in flue gas
Gas
olin
e yi
eld
at e
nd o
f ris
er (%
)
30
32.5
35
37.5
40
42.5
45
0.001 0.01 0.1 1 10
% CO in flue gas
Gas
olin
e yi
eld
at e
nd o
f ris
er (%
)
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MOO of a (4H/5C) HEN
Min f1 ≡ cost
Min f2 ≡
Point A (MOO): $2.961 × 106/year, utility: 54,805 kW
● SOO: $ 2.934 × 106/ year, utility: 57,062 kW
■ SOO: Linnhoff and Ahmed
10-3 x Utility requirement (kW)
50 52 54 56 5810
-6 x
Ann
ual c
ost (
$/ye
ar)
2.9
3.0
3.1
3.2
3.3
3.4
3.5
3.6
3.7
Point A
, ,1 1
c hS S
cu i hu ii i
q q
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MOO RESULTS FOR A 4Hot/5Cold STREAM HX NETWORK (point A in next
slide)(A. Agarwal and S. K. Gupta, Indus. And Eng.
Chem. Res., 47, 3489-3501 (2008)
327
220
220
160
300
164
138
170
300
40
160
60
45
100
35
85
60
140
113.56
154.0.8
188.0
147.7
127.0 70.5125.4
107.6.8
106.0
193.8
110.0
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55
MOO OF AN INDUSTRIAL NYLON-6 SEMI-BATCH REACTOR (NSGA-II)
K. Mitra, K. Deb and S. K. Gupta, J. Appl. Polym. Sci., 69, 69-87 (1998)
WATER REMOVED TO DRIVE REACTION FORWARD
HISTORIES, p(t), TJ(t), USED
Rv,m
(mol/hr)Rv,w
(mol/hr)
F (kg)
N2To Condenser
SystemVT (t) (mol/hr)
Condensate
Condensing Vapor at TJ(t)
Vapor Phaseat p(t)
Liquid Phase
Stirrer
Valve
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MOO OF AN INDUSTRIAL NYLON-6 REACTOR
M. Ramteke and S. K. Gupta, Polym. Eng. Sci., 48, 2198-2215 (2008)
• MIN I1 [p(t), TJ(t)] = tf/tf,ref
• MIN I2 [p(t), TJ(t)] = [C2]f/[C2]f,ref
• s. t.:
• xm,f = xm,d
• μn,f = μn,d
• T(t) ≤ Tdegradation (= 280 ̊ C)
• MODEL EQUATIONS AND BOUNDS ON p(t), TJ(t) 56
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MOO OF THE INDUSTRIAL NYLON-6 REACTOR
57
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TWO RECENT BIOMIMETIC ADAPTATIONS OF
NSGA-II-aJG
Manojkumar Ramteke and
Santosh K. Gupta
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59
Haikel’s Biogenetic Law (Embryology)
• SOLUTIONS OF AN ‘ORIGINAL’ MOO PROBLEM AVAILABLE OVER ALL GENERATIONS, E.G., TOPT(T) IN A PMMA BATCH REACTOR
• REQUIRE THE SOLUTION FOR ‘ANOTHER’ SIMILAR (NOT THE SAME) MOO PROBLEM, E.G., TRE-OPT(T) AFTER A DISTURBANCE
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60
Ontogeny (9 months)
Phylogeny (Billions of years)
Ontogeny Recapitulates Phylogeny
Haikel’s Biogenetic Law
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HAIKEL’S BIOGENETIC LAW
THE DEVELOPMENTAL STAGES OF EMBRYOS SHOW ALL THE STEPS OF EVOLUTION
MODIFIED PROBLEM:
INITIAL CHROMOSOMES ARE AKIN TO AN EMBRYO, HAVING ALL THE ELEMENTS OF THE STEPS OF EVOLUTION PRIOR TO THAT SPECIES
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62
MIMICKING HAIKEL’S BIO-GENETIC LAW IN NSGA-II-AJG
THE FIRST GENERATION OF THE MODIFIED PROBLEM IS AKIN TO AN EMBRYO
STARTING CHROMOSOMES TAKEN RANDOMLY FROM THE DIFFERENT GENERATIONS OF THE ORIGINAL PROBLEM (SEED !!!)
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63
2
, , ,
2 1 ,2Range of
1
pNNj i j opt i
j i j opt
p
I II
N N
N = NO. OF OBJECTIVE FUNCTIONS
NP = POPULATION SIZE
OPT = OPTIMAL VALUE
MEAN SQUARE DEVIATION
I2
I1
Pareto-optimal set
I1,opt,4
I2,opt, 4
I2, 4
4th point
Interpolated value
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64
THE MEAN SQUARE DEVIATION, σ2, IS A MEASURE OF THE LEVEL OF CONVERGENCE
σ2 SHOULD BE LESS THAN 0.1 FOR ‘CONVERGENCE’
σ2 GREATER THAN 0.1 SHOWS CONVERGENCE TO A LOCAL PARETO FRONT
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65
(PA)(P)(OT)(OX)Phthalic Anhydride
o-Xylene o-Tolualdehyde Phthalide1 4 5
67
Maleic Anhydride (MA)
COx23 8
S4
S3
S2
S1
L1
L2
L3
L4
L5
L9
L1
Coolant
(a)
(b)
S4
S3
S2
S1
L1
L2
L3
L4
L5
L7
AN INDUSTRIAL PHTHALIC ANHYDRIDE REACTOR
• (a) Original Problem having 7 Catalyst Beds
• (b) Modified Problem having 9 beds
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66
• RESULTS IMPROVE WITH THE INCREASE IN THE NUMBER OF CATALYST BEDS
• B-NSGA-II-AJG CONVERGES IN ABOUT 25 GENERATIONS (NSGA-II-AJG DOES NOT CONVERGE EVEN IN 70 GENERATIONS)
Yield of PA
1.08 1.10 1.12 1.14 1.16 1.18
Tota
l cat
alys
t len
gth
(m)
0.4
0.5
0.6
0.7
0.8
0.9
Original Problem,NSGA-II-aJGModified Problem,B-NSGA-II-aJG
Yield of PA
1.08 1.10 1.12 1.14 1.16 1.18
Tota
l cat
alys
t len
gth
(m)
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
B-NSGA-II-aJGNSGA-II-aJG
(a) Gen = 71
(b) Gen = 25, Modified Problem
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67
ALTRUISTIC GENETIC ALGORITHM, ALT-NSGA-II-AJG
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n n Queen Bee(Mother)
n (Single)Father(Stored sperms)
n n n
Meiosis
n n
n n n n n
SeveralEggs
(Different)
SeveralSperms(Identical)
Di
Daughters(Several)
Si
Sons(Several)
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69
EXPLAINING BEE EVOLUTION IS DIFFICULT USING NATURAL SELECTION
QUEEN, DAUGHTER WORKER BEES ARE DIPLOID WHEREAS MALE DRONES ARE HAPLOID. THIS HAPLO-DIPLOID BEHAVIOR GIVES RISE TO ALTRUISM
ALTRUISTIC BEHAVIOR EXPLAINED USING THE CONCEPT OF INCLUSIVE FITNESS
WORKER BEES PREFER TO REAR QUEEN’S OFFSPRINGS (SISTERS) RATHER THAN PRODUCING THEIR OWN DAUGHTERS
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70
MIMICKING HONEY BEE COLONIES: INITIAL ALGORITHM
CROSSOVER BETWEEN A QUEEN CHROMOSOME AND REMAINING CHROMOSOMES; TWO ADAPTATIONS:
ONE-GOOD-QUEEN-NSGA-II-AJG: GOOD QUEEN IS INSERTED PURPOSEFULLY (FROM CONVERGED RESULTS); MEANINGLESS
ONE-BAD-QUEEN-NSGA-II-AJG: QUEEN SELECTED AS THE BEST FROM THE POPULATION
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71
ALT-NSGA-II-AJG
ONE-BAD-QUEEN-ADAPTATION NOT TOO GOOD; EXTEND INTUITIVELY
MULTI-(BAD) QUEEN (IN SOME HYMENOPTERANS)-NSGA-II-AJG WITH TWO-POINT, THREE-MATE CROSSOVERS: ALT-NSGA-II-AJG
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72
THE ZDT4 PROBLEM
1 1
12
12
min
min 1
f x
ff gg
xx
10 1-5 1; 2,3, . . . ., (=10) j
xx j n
2
2
1 10 1 10cos 4n
i ii
g n x x
x
Subject to:
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73
RESULTS
No. of generations
0 50 100 150 200
1e-3
1e-2
1e-1
1e+0
1e+1
1e+2
1e+3
1e+4
1e+5
One-good-queen-Alt-NSGA-II-aJGOne-bad-queen-Alt-NSGA-II-aJG
No. of generations
0 100 200 300 400 500 600
1e-2
1e-1
1e+0
1e+1
1e+2
1e+3
1e+4
1e+5
multi-queen-Alt-NSGA-II-aJG (new crossover)
(a) One queen adaptation (b) Multiple queen adaptation
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Reactor feed
Process gas
Shell and Tube type reactor
Coolant out
Coolantin
Switch Condenser
s
Scrubber/Incinerator
AN INDUSTRIAL PHTHALIC ANHYDRIDE REACTOR
74
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75
(PA)(P)(OT)(OX)Phthalic Anhydride
o-Xylene o-Tolualdehyde Phthalide1 4 5
67
Maleic Anhydride (MA)
COx2
3 8
S4
S3
S2
S1
L1
L2
L3
L4
L5
L9
Coolant
9-ZONE PHTHALIC ANHYDRIDE REACTOR
9 catalyst beds
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76
No. of generations
0 10 20 30 40 50
0.01
0.1
1
10
100
Alt-NSGA-II-aJGNSGA-II-aJG
kg of PA produced/kg of oX consumed
1.10 1.12 1.14 1.16 1.18
Tota
l len
gth
of a
ctua
l cat
alys
t bed
(m)
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
Alt-NSGA-II-aJGNSGA-II-aJG
B
A
(a)
(b)
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77
RAMTEKE, M; GUPTA, S. K. IND. ENG. CHEM. RES., 2009, DOI: 10.1021/IE801592C
RAMTEKE, M; GUPTA, S. K. IND. ENG. CHEM. RES., 2009, IN PRESS
REFERENCES
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78
ON-LINE OPTIMAL CONTROL OF the BULK POLYMERIZATION of MMA
(PLEXIGLAS)
SA Bhat, S Gupta, DN Saraf and SK Gupta, Ind. Eng. Chem. Res., 45, 7530-7539 (2006).
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79
POLYMERIZATION IN A BATCH REACTOR
Initiation
Propagation
Termination
Gel Effect
Time
Conv
ersio
nCalls for On-line Optimizing Control to Ensure Desired End Product Properties !!!
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80
ON-LINE OPTIMAL CONTROL OF A PMMA REACTOR
Polymeri-zationReactor
Disturbance
Data Acquisition: T(t), Power (t)
Model (Parameter)Re-tuning
Soft(ware) Sensing
Computing the Optimal ControlAction, T(t), to get Right Mn at the end
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81
SCHEMATIC DIAGRAM
2
PC with PCI-MIO-16E4
STEPPER MOTOR PI PI
PARR 4842 Ar
COOLINGWATER
NEEDLE VALVE PI
V2
M
V1
V3
COOLING COIL
HEATER 5B Modules
N
I
TTo HeaterController
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82
PARR REACTORSymmetrical Reactor (with Parr Head)
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83
Experimental Result: Solid Line: Optimal Profile with no failureZone 1: Simulation of Heater Failure (complex dual slope)
Control restarted at end of Zone 1Zones 2-5: History as computed and controlled (Note changes as re-
optimization takes place)
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84
Thank You