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