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R.E.A.C.H.ing Optimum Designs through Processes Inspired by
Principles of Evolution
Partha ChakrobortyProfessor
Department of Civil EngineeringIIT, Kanpur
The Next Half-Hour
Evolution
Genetic Algorithm
Some Applications of Genetic Algorithm
Evolution 101 (I)
Evolution
Evolution is the process by which modern organisms have descended from ancient ones
Microevolution
Microevolution is evolution within a single population; (a population is a group of organisms that share the same gene pool). Often this kind of evolution is looked upon as change in gene frequency within a population
Evolution 101 (II)
For evolution to occur
HeredityInformation needs to be passed on from one generation to the next
Genetic VariationThere has to be differences in the characteristics of individuals in order for change to occur
Differential ReproductionSome individuals need to (get to) reproduce more than others thereby increasing the frequency of their genes in the next generation
Evolution 101 (III)
Heredity
Heredity is the transfer of characteristics (or traits) from parent to offspring through genes
Evolution 101 (IV)
Genetic Variation
Is about variety in the population and hence presence of genetic variation improves chances of coming up with “something new”The primary mechanisms of achieving genetic variation are:
Mutations
Gene Flow
Sexual Reproduction
Evolution 101 (V)
Mutation
It is a random change in DNA
It can be beneficial, neutral or harmful to the organism
Not all mutations matter to evolution
Evolution 101 (VI)
Gene Flow
Migration of genes from one population to another
If the migrating genes did not exist previously in the incident population then such a migration adds to the gene pool
Evolution 101 (VII)
Sexual Reproduction
This type of producing young can introduce new gene combinations through genetic shuffling
Evolution 101 (VIII)
Differential Reproduction
As the genes show up as traits (phenotype) the individuals get affected by what is around; some die young while others live
Those who live compete for mates; only the winners pass on their gene to the next generation
In some sense the fitter (with respect to the current environment) gets to leave more of his/her genes in the next population; often the term fitness is used to describe the relative ability of individuals to pass on their genes
Evolution 101 (IX) Overview
Differential Reproduction
Variation
Heredity
From Organisms to Abstract Beings (I)
110010
111001
000000
010010
101010
000010
110011
The fight to survive (selection operation)
From Organisms to Abstract Beings (II)
110010
111001
010010
101010
110011
The Survivors and Mating Offsprings
111010
110 00 0
1110100
Genetic Algorithms (I)
Basic Questions
How does one decide who survives
How does one decide how successfully each survivor produces offsprings
How are the offsprings related to the parents
How does one ensure that genetic variation is maintained even though with every generation individuals are supposed to become fitter
Genetic Algorithms (II)
Population of individuals or alternative
(feasible) solutions
Next generationof
individuals
Mating pool of“fitter”
individuals
Evaluate individualson their fitness
Select individuals based on fitness
for subsequent mating
Select individuals& exchange charac-
teristics to createnew individuals
Arbitrarily change some characteristic
Differ
entia
l
Repro
ductio
n
HeredityGenetic
Variatio
n
Genetic Algorithms (III)
What is an individual?
x
y
zx,y,z 24,2,11 1001,0000,110
1
ba
d
c
e(a,b)(b,c)(c,d)…(h,i)
a,b,c,d,…if
gh
i
a c
df
i
eb
hg
Genetic Algorithms (IV)
Generation of initial population
Basic Tasks
Evaluation
Selection (Reproduction operation)
Exchange characteristics to develop newindividuals (Crossover operation)
Arbitrarily modify characteristics in newindividuals (Mutation operation)
Genetic Algorithms (V)
Reproduction / Selection Operator
The purpose is to bias the mating pool (those who can pass on their traits to the next generation) with fitter individuals
Assign p as the prob. of choosingan individual for the mating pool
p is proportional to the fitness
Choose an individual with prob. pand place it in the mating pool
Continue till the mating pool sizeis the same as the initial population’s
Choose n individuals randomly
Pick the one with highest fitness
Place n copies of this individual inthe mating pool
Choose n different individuals andrepeat the process till all in the original population have been chosen
Genetic Algorithms (VI)
Crossover operator
1 0 0 1 1 0 1
1 1 0 0 1 1 1
1 0 0 1 1 1 11 1 0 0 1 0 1
Genetic Algorithms (VII)
Mutation
1 0 0 1 1 0 1
1 0 0 0 1 0 1
Genetic Algorithms (VIIIa)
Results from a small example:
6,0
)7()11(),(
21
2221
22
2121
xx
xxxxxxfMinimize
Initial Population Generation 10
Genetic Algorithms (VIIIb)
Gen
era
tion
20
Gen
era
tion
30
Gen
era
tion
40
Gen
era
tion
50
Genetic Algorithms (IX)
Issues
Generation of initial population
Evaluation
Reproduction operation
Crossover and Mutation operations andfeasibility issues
Representation
Genetic Algorithms
Benefits to engineers as an optimization tool
Problem formulation is easier
Allows external procedure based declarations
Can work naturally in a discrete environment
Optimizing with Genetic Algorithms
Some Examples
Some Applications
Engineering component / equipment design
Engineering process optimization
Portfolio optimization
Route optimization; optimal layout; optimal packing
Schedule optimization
Protein structure analysis
Decision making / decision support systems
Transit Routing: Description
Transit Routing: Characterization (I)
The purpose is to determine a set of routes which serve many people quickly and without using too many transfers.
The number of passengers using a particular route depends on the layout of the route as well as the layout of the other routes.
Evaluation of a route set (note, it is not very meaningful to evaluate a route in isolation) is not easy. Obtaining an objective “function” is not possible.
A solution is a “route set;” each route within a route set is a meaningful juxtaposition of links.
Transit Routing: Characterization (II)
Defining “meaningful juxtaposition” (a feasible route) through algebraic relations is difficult.
Traditional MP formulation is at best extremely difficult and most probably impossible.
Procedure based determination of the “goodness” and “feasibility” are more practical.
Transit Routing: Formulation (I)
The problem is formulated for a GA based solution.
The initial population of route sets are created using problem specific information.
Tournament selection is chosen.
Problem specific crossover and mutation operators are devised.
Transit Routing: Formulation (II)
Representation……….
Transit Routing: Formulation (III) Crossover (inter-string)
……….
Parents
Children
Transit Routing: Formulation (IV) Crossover (intra-string)
……….
Transit Routing: Formulation (V) Mutation……
….
Transit Routing: Results
0
1
14
67
13
8
12
4
10
3 5
9
2
11 Mandl’s Swiss network --- a benchmark problem
Single Vehicle Routing: Description (I)
Single Vehicle Routing: Description (II)
Nodes can be visited in any order and at any time
Some nodes cannot be visited before others; no restrictions on visit time
Travelling Salesman Problem
Pick-up and Delivery Problem
Some nodes cannot be visited before others; restrictions on visit time
Dial-a-ride Problem
Single Vehicle Routing: Description (II)
A
B
C
D F
E
K
J
IH
G
A
B
C
D F
E
K
J
IH
G
A-B-C-H-G-D-E-F-I-J-K-A
A-B-C-D-E-F-G-K-J-H-I-A
A-B-C-D-E-F-H-G-I-J-K-A
A-B-C-D-E-F-H-G-K-J-I-A
Single Vehicle Routing: Formulation
A g
en
era
l fo
rmula
tion
for
all
typ
es
of
SV
RP:
A m
uta
tion
-on
ly G
A
app
roach
Single Vehicle Routing: Results (I)
TSP; 202 node problem; geospherical distances, (GR202 --- a benchmark problem)
Opti
mal (r
eport
ed
in
liter.
)N
ear-o
ptim
al (o
bta
ined
h
ere
)
Single Vehicle Routing: Results (II)PDP; 70 node problem; Euclidean
distances, (ST70PD --- a modified benchmark problem)
Opti
mu
m
Single Vehicle Routing: Results (IIIa)GA evolving a good TSP route, Eil51,
Initial Best
Single Vehicle Routing: Results (IIIb)GA evolving a good TSP route, Eil51,
Intermediate
Single Vehicle Routing: Results (IIIc)GA evolving a good TSP route, Eil51,
Intermediate
Single Vehicle Routing: Results (IIId)GA evolving a good TSP route, Eil51,
Intermediate
Single Vehicle Routing: Results (IIIe)GA evolving a good TSP route, Eil51,
Intermediate
Single Vehicle Routing: Results (IIIf)GA evolving a good TSP route, Eil51, Final
Best
Single Vehicle Routing: Results (IIIg)GA evolving a good TSP route, Eil51, Initial
Best
Transit Scheduling: Description (I)
Stops
Transfer stops
Transit Scheduling: Description (II)
From a scheduling standpoint determining theschedule of bus arrivals and departures at a transfer stop is important as these stops typicallyrepresent major stops and also because at thesestops passengers can transfer from one route tothe other.
Given the fleet size, the idea is to determine the schedule such that the total time spent waiting (for a bus) by transferring and non-transferring passengers is minimized.
Transit Scheduling: Characterization (I)
Let’s look at one transfer station with 3 routes ……
time
Transit Scheduling: Characterization (II)
Waiting time for non-transferring passengers ……
Arrival rate
i k
ddki
kiik
ki
ki
dttddtv
1
0
1 ))(( IWT
time
Route i
k-th
bu
s
Transit Scheduling: Characterization (III) Waiting time for transferring passengers ……
time
Route i
k
Route j
i
ijj k l
kij
ki
lj
klij ad )( TT
Transit Scheduling: Formulation (I)
).().( Minimize 21 TTNIWTN Subject to
ijlkjiTad
kihaa
ijkji
ijkjiMad
kisad
kisad
klij
ki
lj
iki
ki
klij
klij
ki
lj
iki
ki
iki
ki
,,,, )(
,
,,, 1
,,,, 0)1()(
,
,
1
min
max
Transit Scheduling: Formulation (II)
The MP formulation is an NLMIP problem. Efficient solution techniques do not exist.
A GA formulation was attempted to solve this and similar problems. The general characteristics of the formulation are:
(a)Headway and stopping times used as variables
(b)Variables d are computed through external procedures
(c)Binary coding, single point crossover, and bitwise mutation used
(d)One set of constraints remained; these were handled using penalty functions
Transit Scheduling: Results (I)
3 routes, 8-10-12 buses, only IWT
3 routes, 8-10-12 buses, TT+IWT
Transit Scheduling: Results (II)
3 transfer stations, 6 routes, 10-12-8-12-8-10 buses, TT+IWT
R1
R5
R4
R3
R2
R6
S3
S2
S1
Transit Scheduling: Results (III) 3 routes, fleet distribution unknown, only IWT
3 routes, fleet distribution unknown, TT+IWT
That’s it !!!!!
Thank you