1. Genetic Algorithms

2. Introduction To Genetic Algorithms (GAs)

3. What Are Genetic Algorithms (GAs)?
Genetic Algorithms are search and optimization techniques based on Darwin’s Principle of Natural Selection.
What exactly are Genetic Algorithms?
As the name suggests, Genetic Algorithms or Gas borrow their basic working principle from natural genetics.
Genetic Algorithms are search and optimization methods based on Darwin’s principle of Natural Selection.

4. Characteristics of GA
Parallel-search procedures that can be implemented on parallel processing machines for speeding operations
Applies to both continuous and discrete optimization problems
Stochastic in nature and less likely to get caught in local minima
Facilitates both structure and parameter identification

5. Darwin’s Principle Of Natural Selection
IF there are organisms that reproduce, and
IF offsprings inherit traits from their parents, and
IF there is variability of traits, and
IF the environment cannot support all members of a growing population,
THEN those members of the population with less-adaptive traits (determined by the environment) will die out, and
THEN those members with more-adaptive traits (determined by the environment) will thrive
The result is the evolution of species.

6. Working of GA
GA encodes each point in a parameter space into a binary bit called chromosome
Each point is associated with a fitness function
Gene pool is a population of all such points
In each generation GA constructs a new population using genetic operators
Crossover
Mutation

7. Components of GA Encoding schemes Crossover operators
Mutation operators

8. Encoding schemes
Transforms points in parameter space into string representations
Eg (11,6,9) is represented as
Encoding schemes provide a way of translating problem-specific knowledge directly into GA framework
After this the fitness function is evaluated
Next selection is based on the fittest survivor

9. Fitness evaluation

10. How is it different from other optimization and search procedures?
Works with a coding of the parameter set, not the parameters themselves
Search for a population of point and not a single point
Use objective function information and not derivatives or other auxiliary knowledge

11. How GA is used and different from other optimization techniques?
The first step in GA is to code the parameter x as a finite length string
Example 1 can be code as string of 5 bits with an output f=f(s) , where s=string of bits
Successive populations are generated using the GA
For effective check GA requires only objective functions associated with individual strings

12. Simple genetic algorithm
Reproduction:- individual strings are copied according to their objective fn: values f(FITNESS FUNCTION)
Crossover:- Members of the newly reproduced strings are mated at random. Each pair of strings undergoes crossing overs.
Mutation:-supplements reproduction and crossover and acts as an insurance policy against premature loss of important notions

13. Basic Idea Of Principle Of Natural Selection
“Select The Best, Discard The Rest”
Darwin’s principle of Natural Selection can be stated very simply as “ select the best and discard the rest”.
Let us consider an example. Consider a population of animals of a particular species in a jungle. This population of animals has some animals which are stronger than the others and have characteristics that help them survive better in that environment as compared to the others. Now, the resources, like food,water,etc in the jungle are limited. So, these animals have to compete with one another for these resources. Ultimately, only the strongest, or fittest individuals survive and the rest perish. In other words, in this “struggle for existence” , nature selects the best, and discards the rest.
Now, these surviving animals mate amongst themselves and propagate their favorable characteristics from one generation to another.
What is mating? At the genetic level it can be seen as the crossover of 2 chrmosomes, one from each parent. They exchange some genetic matter and give rise to the new chromosome of the child that has both the parents’ features.Thus the favorable characteristics of the parents that helped them survive in that environment are propagated from one generation to the next till the species becomes best adapted to it’s environment. This is called evolution.

14. Example 1 Maximize f(x) =x2 on the integer scale from 0-31
1000
f(x) 31 x

15. Example 1 No: String Fitness % of total 1 01101 169 14.2 2 11000 576
49.2 3
01000 64
5.5 4
10011
361
30.9
Total
1170
100

16. Roulette wheel with slots sized according to fitness

17. Crossover
A1=
A2=
A1’=
A2’=

18. Simple GA by Hand(Reproduction)
No:
String x
f(x) x2
pselect
fi/Ʃf
Expected count
n.pselect
Actual count
(Roulette Wheel0 1
01101 13
169
.14
.58 2
11000 24
576
.49
1.97 3
01000 08 64
.06
0.24 4
10011 19
361
0.31
1.24
Sum
1170
1.00
4.0
Average
293
0.25
1.0
Maximum

19. Crossover
Mating Pool after Reproduction(Cross Site shown)
Mate
Crossover
New population x
F(x)
0110|1 2 4 12
144
1100|0 1 25
625
11|000 27
729
10|011 3 16
256
Sum
1754
Average
439
Maximum
Probability of mutation in this test is With 20 transferred bit positions we should expect 20*0.001=0.02

20. Grist for the search mill
How does the directed search guide help improvement?
Seeking similarities among strings in population
Causal relationships between similarities and high fitness
SCHEMATA

21. Evolution in the real world
Each cell of a living thing contains chromosomes - strings of DNA
Each chromosome contains a set of genes - blocks of DNA
Each gene determines some aspect of the organism (like eye colour)
A collection of genes is sometimes called a genotype
A collection of aspects (like eye colour) is sometimes called a phenotype
Reproduction involves recombination of genes from parents and then small amounts of mutation (errors) in copying
The fitness of an organism is how much it can reproduce before it dies
Evolution based on “survival of the fittest”

22. Basic Idea Of Principle Of Natural Selection
“Select The Best, Discard The Rest”
Darwin’s principle of Natural Selection can be stated very simply as “ select the best and discard the rest”.
Let us consider an example. Consider a population of animals of a particular species in a jungle. This population of animals has some animals which are stronger than the others and have characteristics that help them survive better in that environment as compared to the others. Now, the resources, like food,water,etc in the jungle are limited. So, these animals have to compete with one another for these resources. Ultimately, only the strongest, or fittest individuals survive and the rest perish. In other words, in this “struggle for existence” , nature selects the best, and discards the rest.
Now, these surviving animals mate amongst themselves and propagate their favorable characteristics from one generation to another.
What is mating? At the genetic level it can be seen as the crossover of 2 chrmosomes, one from each parent. They exchange some genetic matter and give rise to the new chromosome of the child that has both the parents’ features.Thus the favorable characteristics of the parents that helped them survive in that environment are propagated from one generation to the next till the species becomes best adapted to it’s environment. This is called evolution.

23. Algorithm } Generate Initial Population do
Calculate the Fitness of each member {
Select Parents from current population
Perform Crossover add offspring to the new population
Merge new population into the current
population
Mutate current population till result
is obtained }
Algorithm

24. Population population Chromosomes could be:
Bit strings ( )
Real numbers ( )
Permutations of element (E11 E3 E7 ... E1 E15)
Lists of rules (R1 R2 R3 ... R22 R23)
... any data structure ...

25. Algorithm } Generate Initial Population do
Calculate the Fitness of each member {
Select Parents from current population
Perform Crossover add offspring to the new population
Merge new population into the current
population
Mutate current population till result
is obtained }
Algorithm

26. Algorithm } Generate Initial Population do
Calculate the Fitness of each member {
Select Parents from current population
Perform Crossover add offspring to the new population
Merge new population into the current
population
Mutate current population till result
is obtained }
Algorithm

27. Fitness Function
A fitness function quantifies the optimality of a solution so that that particular solution may be ranked against all the other solutions.
A fitness value is assigned to each solution depending on how close it actually is to solving the problem.
Ideal fitness function correlates closely to goal + quickly computable.

28. Algorithm } Generate Initial Population do
Calculate the Fitness of each member {
Select Parents from current population
Perform Crossover add offspring to the new population
Merge new population into the current
population
Mutate current population till result
is obtained }
Algorithm

29. Algorithm } Generate Initial Population do
Calculate the Fitness of each member {
Select Parents from current population
Perform Crossover add offspring to the new population
Merge new population into the current
population
Mutate current population till result
is obtained }
Algorithm

30. Crossover Mimics biological recombination
Some portion of genetic material is swapped between chromosomes
Typically the swapping produces an offspring

31. CROSSOVER
( )
( )
( )
( )

32. Algorithm } Generate Initial Population do
Calculate the Fitness of each member {
Select Parents from current population
Perform Crossover add offspring to the new population
Merge new population into the current
population
Mutate current population till result
is obtained }
Algorithm

33. Algorithm } Generate Initial Population do
Calculate the Fitness of each member {
Select Parents from current population
Perform Crossover add offspring to the new population
Merge new population into the current
population
Mutate current population till result
is obtained }
Algorithm

34. Mutation
Selects a random locus – gene location – with some probability and alters the allele at that locus
The intuitive mechanism for the preservation of variety in the population

35. Mutation: Local Modification
Before: ( )
After: ( )
Before: ( )
After: ( )

36. The Problem The Traveling Salesman Problem is defined as: Given:
1) A set of cities
2) Symmetric distance matrix that indicates the cost of travel from each city to every other city.
Goal:
1) Find the shortest circular tour, visiting every city exactly once.
2) Minimize the total travel cost, which includes the cost of traveling from the last city back to the first city’.

37. Traveling Salesperson Problem

38. Encoding Represent every city with an integer .
Consider 6 Indian cities –
Mumbai, Nagpur , Calcutta, Delhi, Bangalore and Pune assign a number to each.
Mumbai
Nagpur
Calcutta
Delhi
Bangalore
Pune

39. Encoding
Thus a path would be represented as a sequence of integers from 1 to 6.
The path [ ] represents a path from
Mumbai to Nagpur - Nagpur to Calcutta - Calcutta to Delhi - Delhi to Bangalore - Bangalore to Pune and pune to Mumbai.

40. Fitness Function
The fitness function will be the total cost of the tour represented by each chromosome.
This can be calculated as the sum of the distances traversed in each travel segment.
The Lesser The Sum, The Fitter The Solution Represented By That Chromosome.

41. Distance/Cost Matrix For TSP1 2 3 4 5 6
863
1987
1407
998
163
1124
1012
1049
620
1461
1881
1844
2061
1437
841

42. Fitness Function (contd.)
So, for a chromosome [ ], the total cost of travel or fitness will be calculated as shown below
Fitness =
= kms.
Since our objective is to Minimize the distance, the lesser the total distance, the fitter the solution.

43. Initial Population for TSP
(5,3,4,6,2)
(2,4,6,3,5)
(4,3,6,5,2)
(2,3,4,6,5)
(4,3,6,2,5)
(3,4,5,2,6)
(3,5,4,6,2)
(4,5,3,6,2)
(5,4,2,3,6)
(4,6,3,2,5)
(3,4,2,6,5)
(3,6,5,1,4)

44. Select Parents (5,3,4,6,2) (2,4,6,3,5) (4,3,6,5,2) (2,3,4,6,5)
(4,3,6,2,5)
(3,4,5,2,6)
(3,5,4,6,2)
(4,5,3,6,2)
(5,4,2,3,6)
(4,6,3,2,5)
(3,4,2,6,5)
(3,6,5,1,4)
Try to pick the better ones.

45. Create Off-Spring – 1 point
(5,3,4,6,2)
(2,4,6,3,5)
(4,3,6,5,2)
(2,3,4,6,5)
(4,3,6,2,5)
(3,4,5,2,6)
(3,5,4,6,2)
(4,5,3,6,2)
(5,4,2,3,6)
(4,6,3,2,5)
(3,4,2,6,5)
(3,6,5,1,4)
(3,4,5,6,2)

46. Create More Offspring (5,3,4,6,2) (2,4,6,3,5) (4,3,6,5,2) (2,3,4,6,5)
(4,3,6,2,5)
(3,4,5,2,6)
(3,5,4,6,2)
(4,5,3,6,2)
(5,4,2,3,6)
(4,6,3,2,5)
(3,4,2,6,5)
(3,6,5,1,4)
(3,4,5,6,2)
(5,4,2,6,3)

47. Mutate
(5,3,4,6,2)
(2,4,6,3,5)
(4,3,6,5,2)
(2,3,4,6,5)
(4,3,6,2,5)
(3,4,5,2,6)
(3,5,4,6,2)
(4,5,3,6,2)
(5,4,2,3,6)
(4,6,3,2,5)
(3,4,2,6,5)
(3,6,5,1,4)
(3,4,5,6,2)
(5,4,2,6,3)

48. Mutate
(5,3,4,6,2)
(2,4,6,3,5)
(4,3,6,5,2)
(2,3,4,6,5)
(2,3,6,4,5)
(3,4,5,2,6)
(3,5,4,6,2)
(4,5,3,6,2)
(5,4,2,3,6)
(4,6,3,2,5)
(3,4,2,6,5)
(3,6,5,1,4)
(3,4,5,6,2)
(5,4,2,6,3)

49. Eliminate
(5,3,4,6,2)
(2,4,6,3,5)
(4,3,6,5,2)
(2,3,4,6,5)
(2,3,6,4,5)
(3,4,5,2,6)
(3,5,4,6,2)
(4,5,3,6,2)
(5,4,2,3,6)
(4,6,3,2,5)
(3,4,2,6,5)
(3,6,5,1,4)
(3,4,5,6,2)
(5,4,2,6,3)
Tend to kill off the worst ones.

50. Integrate
(5,3,4,6,2)
(2,4,6,3,5)
(5,4,2,6,3)
(3,4,5,6,2)
(2,3,6,4,5)
(3,4,5,2,6)
(3,5,4,6,2)
(4,5,3,6,2)
(5,4,2,3,6)
(4,6,3,2,5)
(3,4,2,6,5)
(3,6,5,1,4)

51. Restart
(5,3,4,6,2)
(2,4,6,3,5)
(5,4,2,6,3)
(3,4,5,6,2)
(2,3,6,4,5)
(3,4,5,2,6)
(3,5,4,6,2)
(4,5,3,6,2)
(5,4,2,3,6)
(4,6,3,2,5)
(3,4,2,6,5)
(3,6,5,1,4)

52. When to Use a GA
Alternate solutions are too slow or overly complicated
Need an exploratory tool to examine new approaches
Problem is similar to one that has already been successfully solved by using a GA
Want to hybridize with an existing solution
Benefits of the GA technology meet key problem requirements

53. SUMMARY
Genetic Algorithms (GAs) implement optimization strategies based on simulation of the natural law of evolution of a species by natural selection
The basic GA Operators are:
Encoding
Recombination
Crossover
Mutation
GAs have been applied to a variety of function optimization problems, and have been shown to be highly effective in searching a large, poorly defined search space

54. THANK YOU