1 GENETIC ALGORITHM (GA), MULTI-OBJECTIVE OPTIMIZATION (MOO) and BIOMIMETIC ADAPTATIONS SANTOSH SANTOSH K. GUPTA K. GUPTA DEPARTMENT OF CHEMICAL ENGINEERING INDIAN INSTITUTE OF TECHNOLOGY BOMBAY, POWAI, MUMBAI 400 076, INDIA
1
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
2
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
3
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
4
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)
5
SIMPLE GA (SOO)MAXIMIZE I(x) S.T.
L Ui i i parameterx x x ; i 1, 2, ..., n
U2X
L2X
U1X
L1X
6
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
7
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
8
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
9
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
10
USE MODEL EQUATIONS FOR EACH OF THE NP x, TO COMPUTE I(x)
jth chromosome Decoder Model I(xj)
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)
12
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
13
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
14
MATHEMATICAL FOUNDATION (USING SCHEMA THEORY) AVAILABLE IN TEXTBOOKS
GAs WORK WITH SEVERAL SOLUTIONS SIMULTANEOUSLY
MULTIPLE OPTIMAL SOLUTIONS CAN BE CAUGHT
15
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
16
INITIAL POPULATION
17
CROSSOVER OPERATION
18
MUTATION OPERATION
19
POPULATION AT GENERATION 30
20
POPULATION-BEST I VS. GENERATION NUMBER
21
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
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
23
INITIAL POPULATION AND POPULATION AT GENERATION 30
24
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
,
25
NORMALLY WE FIND A SET OF EQUALLY-GOOD (NON-DOMINATING) SOLUTIONS, CALLED PARETO SET
A
B
F2
F1
26
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
27
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
28
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)
29
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
30
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 )
31
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’’
32
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
33
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
34
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
35
REPLACEMENT AND REVERSION
JUMPING GENE
REPLACEMENT REVERSION
P
R
Q
S
P
P
Q
Q
R S
Q P
ORIGINALCHROMOSOME
TRANSPOSON
CHROMOSOMEWITH
TRANSPOSON
36
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
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
38
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)
39
THIS COMPLETES ONE GENERATION. STOP IF CRITERIA ARE MET
COPY P’” INTO STARTING BOX, P. REPEAT
40
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
41
99 LOCAL PARETOS
GLOBAL PARETO HAS
0 X1 1; → 0 ≤ I1 ≤ 1
Xj = 0; j = 2, 3, . . . , 10; → 0 ≤ I2 ≤ 1
42
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
43
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
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
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)
46
MOO of an INDUSTRIAL FCCU, B Sankararao & S K Gupta, CACE, 31,
1496 (2007)
47
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
48
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
49
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
50
BOUNDS ON DECISION VARIABLES: 575 TFEED 670 K 450 TAIR 525 K 115 FCAT 290 kg/s 11 FAIR 46 kg/s
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
52
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 (%
)
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
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
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
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
MOO OF THE INDUSTRIAL NYLON-6 REACTOR
57
TWO RECENT BIOMIMETIC ADAPTATIONS OF
NSGA-II-aJG
Manojkumar Ramteke and
Santosh K. Gupta
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
60
Ontogeny (9 months)
Phylogeny (Billions of years)
Ontogeny Recapitulates Phylogeny
Haikel’s Biogenetic Law
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
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 !!!)
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
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
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
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
67
ALTRUISTIC GENETIC ALGORITHM, ALT-NSGA-II-AJG
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)
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
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
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
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:
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
Reactor feed
Process gas
Shell and Tube type reactor
Coolant out
Coolantin
Switch Condenser
s
Scrubber/Incinerator
AN INDUSTRIAL PHTHALIC ANHYDRIDE REACTOR
74
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
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)
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
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).
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 !!!
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
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
82
PARR REACTORSymmetrical Reactor (with Parr Head)
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)
84
Thank You