Presentation defining the usage of genetic algorithm,how it works and its implementation which is well explained using a numerical problem.

1. GENETIC
ALGORITMS
By:
Saloni Bhatia Dutta

2. Defination
 GA are heuristic search algorithms based
on the evolutionary ideas of natural
selection and genetics.
 Exploit historical information to direct the
search into the region of better performance
within the search space.
 Follows the principles of Charles Darwin, “
survival of fittest”

3. Why GA ?
 More robust
 Do not break easily even if inputs are changed
slightly or in presence of reasonable noise.
 Provide significant benefits over typical
optimization techniques.

4. Basic Terminologies
1. INDIVIDUALS:
 Single Solution
Solutions
Genotype
(chromosome)
Genes
Phenotype
(model form of
chromosomes)

5. SOLUTION SET PHENOTYPE
Factor
1
Factor
2
Factor
3
Factor
4
……….. Factor
N
Gene 1 Gene 2 Gene
3
Gene 4 …………. Gene N
CHROMOSOME GENOTYPE
Morphogenes
is Function
NOTE: When different chromosomes can encode the
same
solution it is called degenerative Morphogenesis
Function

6. 2. GENES:
 A possible solution to a problem.
 Binary representation(bit string) of number of
intervals of arbitary length.
Phenotype Parameter: instructions for mapping
between genotype and phenotype.
CHROMOSOME
Gene 1 Gene 2 Gene 3 Gene 4 Gene 5
10101 11101 10000 01100 00001

7. 3. Fitness:
 Value of objective funtion for its phenotype.
 Indicates goodness of solution.
 Also indicates how close the solution is to optimal
one.
4. Populations:
 Collection of individuals.
Two aspects of population are considered:
1) Initial population generation
2) Population size

8. SIMPLE GA
Reproduction operator:
Used to perform mutations and recombinations over
solutions of the problem.
Steps:
1. Start with randomly generated population.
2. Calculate fitness of each chromosome.
3. Repeat the following steps until n offsprings have
been created.
 Select a pair of parent chromosomes from the
current population.

9.  With probability Pc crossover the pair at a
randomly chosen point to form two offsprings.
 Mutate the two offsprings at each locus with
probability Pm.
4. Replace the current population with the new
population.
5. Goto step 2.

10. GENERAL GA
STAR
T
Initial
Population
Selection
Mutationn
Crossover
Termin
ate ?
No
Yes
Best Individuals
Output
STOP

11. Operators
1. Encoding: process of representing individual
genes.
Encoding
Binary Octal
Hexa
decim
al
Perm
utatio
n
Value Tree
Chromo. 1
110100011
Chromo. 2
0111111
Chromo.1
03467216
Chromo. 2
15723314
Chromo.1
9CE7
Chromo. 2
3DBA
Chromo.1
15326479
8
Chromo. 2
86794123
5
Chromo.1
1.245 5.346
Chromo. 2
ABCHJDEK
SJ

12. 2. Selection:
Process of choosing two parents from the population
for
crossing.
Techniques:
1. Roulette Wheel Selection:
 Sum the total expected value of the individuals in
the population. Let it be T.
 Repeat N times:
1. Choose a random integer “r” between 0 and T.
2. Loop through the individuals in the population
summing the expected values, until the sum is
greater than or equal to “r”. The individual whose
expected value puts the sum over this limit is the
one selected.

13. 2. Random Selection:
Selects a parent from the population.
3. Rank Selection:
 Ranks the population and every chromosome
receives
Fitness from the ranking.
 Worst has fitness 1 and best has N.
4. Tournament Selection:
Provides selective pressure strategy by holding a
tournament competition between Nu individuals.

14. 5. Boltzmann Selection:
A continuously varying temperature controls the rate
of
selection according to a preset schedule. The temp.
is high
which means that selection pressure is low. Temp. is
gradually lowered which gradually increases the
selection
pressure thereby allowing GA to converge to the
best
part of search space.
6. Stochastic Universal Sampling:
Provides zero bias and minimum spread. The
individuals
are mapped to contiguous segement of a line, such

15. 3. Crossover(Recombination):
Process of taking two parent solutions and producing a
child.
1. Single-Point Crossover:
Parent 1 10110010 Child 1 10110111
Parent 2 10101111 Child 2 10101010
2. Two-Point Crossover:
Parent 1 10110010 Child 1 10101111
Parent 2 10101111 Child 2 10110010
3. Multipoint Crossover(N-Point Crossover):
Even number of cross sites where cross-sites are selected
around circle.
Odd number of cross sites where different cross-sites is
assumed at string beginning.

16. 4. Uniform Crossover:
Parent 1 10110011
Parent 2 00011010
Mask 11010110
Child 1 10011010
Child 2 00110011
5. Crossover with Reduced Surrogate:
Restrict location of crossover points.
6. Shuffle Crossover:
Similar to single crossover but before exchange
variables are shuffled.

17. 7. Three-Parent Crossover:
Parent 1 10110011
Parent 2 00011010
Parent 3 11010110
Child 1 10010010
8. Precedence Preservative Crossover:
Operator passes on precedence relations of
operation given in two parental permutation to one
offsprings at the same rate, while no new
precendence relations are introduced.
9. Ordered Crossover:
Parent 1 42 13 65 Child 1 42 31 65
Parent 2 23 14 56 Child 2 23 41 56

18. 10. Partially Matched Crossover:
 Two chromosomes are aligned.
 Two crossing sites are selected uniformly at
random along the strings, defining a matching
section.
 The matching section is used to effect a cross
through position-by-position exchange operation.
 Alleles are moved to their new positions in the
offspring.
11. Crossover Probability:
Is a parameter to describe how often crossover will
be
performed. If there is no crossover, offsprings are
exact
copies of parents. Offsprings are made from parts of

19. 4. Mutation:
 Recovering the lost genetic material as well as
randomly distribute genetic information.
Mutation
Flipping Interchanging Reversing
Mutation
Prob.
Parent 1011
0101
Mutation
Chromo.
1000
1001
Child 0011
1100
Paren
t
10110101
Child 11110001
Paren
t
10110101
Child 10110110

20. Stopping Condition for GA
1. Maximum Generation
2. Elapsed Time
3. No change in Fitness
4. Stall generation
5. Stall time limit

21. Stopping Techniques
 Best Individual
 Worst Individual
 Sum of Fitness
 Median Fitness

22. Problem
Q. Maximize the function
f(x)=x^2
String
No.
Initial
Popula
tion
X
value
Fitnes
s
F(x)
Prob. %
Prob.
Expect
ed
count
Actual
Count
1 01100 12 144 0.1247 12.47 0.4987 1
2 11001 25 625 0.5411 54.11 2.1645 2
3 00101 5 25 0.0216 2.16 0.0866 0
4 10011 19 361 0.3126 31.26 1.2502 1
sum 1155 1.000 100 4.00 4
averag
e
288.75 0.25 25 1.00 1
Max. 625 0.5411 54.11 2.16 2
Selection:

23. String
No.
Mating
Pool
Crossove
r point
Offspring
after
crossover
X value Fitness
value
1 01100 4 01101 13 169
2 11001 4 11000 24 576
3 11001 2 11011 27 729
4 10011 2 10001 17 289
Sum 1763
Average 440.75
maximum 729
Crossover

24. Mutation
String
No.
Offsprin
g after
crossove
r
Mutation
Chromo.
For
flipping
Offspring
after
mutation
X value Fitness
value
1 01101 10000 11101 29 841
2 11000 00000 11000 24 576
3 11011 00000 11011 27 729
4 10001 00100 10101 20 400
Sum 2546
Average 636.5
maximum 841

25. Thank You