1. Genetic Algorithm (GA)
Presented By: Sakeena Javaid
Supervised By: Dr. Nadeem Javaid
Research Domain: Energy Management in Smart Grid
Department of Computer Science
Comsats Institute of Information Technology,
44000, Islamabad, Pakistan.

2. Introduction GAs were developed
By John Holland, David E. Goldberg and his students
At the University of Michigan
This is in line with the Darwinian Theory [1]
“Survival of the Fittest”  
Fittest: ability to adapt to the environment
More individuals are produced each generation that can survive
Phenotypic variation exists among individuals and the variation is heritable
Those individuals with heritable traits better suited to the environment will survive
Darwin’s Quotation
"Variation
is a feature of natural populations and every population produces more progeny than its environment can manage. The consequences of this overproduction is that those individuals with the best genetic fitness for the environment will produce offspring that can more successfully compete in that environment. Thus the subsequent generation will have a higher representation of these offspring and the population will have evolved."
[1] Darwin's Theory of Evolution by Natural Selection. Available online: (last accessed on 2 Feb 2017)

3. Why GA?
Exhaustive search (where every possible combination is checked)
accurate result
time consuming
inefficient when the numbers of variables are large
optimizers tend to :
limit the number of variables they use
limit the number of values these variables can take
The genetic algorithm (does not try every possible combination)
Optimal solution by selecting variables intelligently
Far more variables can be utilized
All values of a variable can be checked
Simultaneous searching
Less likely to become stuck in "local minima"
Less time
Efficient
Solving Difficult Problems
There is a large set of problems, which are NP-Hard

4. Why GA is applied? At least three situations where GA is applied [2]
GA work with the coding of the parameters
Randomly generates population
GAs use objective function information (without any derivative or auxiliary information)
GAs use probabilistic transition rules (instead of deterministic transition rules)
GAs search from population of points instead of using single point
[2] Golberg, D. E. (1989). Genetic algorithms in search, optimization, and machine learning. Addion Wesley. Reading.

5. Basic Terminologies of GA
Representation
Binary strings
Crossover
N-point or uniform
Mutation (probability)
Bitwise bit-flipping
Parent selection
Fitness-Proportionate
Survivor selection
children replace parents
Speciality
Emphasis on crossover

6. What is GA (1/2)? A search based algorithm based on the concepts of:
natural selection and genetics [3]
To find true or approximate solutions
Particular class of evolutionary algorithms
Use techniques inspired by evolutionary biology
Inheritance
Mutation
Selection
Crossover ( Recombination)
[3] Genetic Algorithm. Available online: (last accessed 2 Feb 2017)

7. Figure 1: Solution Representation
What is GA (2/2)?
Solutions are represented in binary as strings
0s and 1s, however,
Other encodings are also possible
Implemented as a computer simulation
Using abstract representations called
Chromosomes, genotypes, phenotypes
Candidate solutions (called individuals),
Starts from a population
Randomly generated individuals
In each generation, fitness of every individual is evaluated
Multiple individuals are selected (based on their fitness)
The new population is used in next iteration
Figure 1: Solution Representation

8. GA Requirements A typical genetic algorithm requires two things
The solution domain (set search space)
A fitness function to evaluate the solution
A standard representation of the solution is as an array of bits
Chromosomes could be
Bit strings ( )
Real numbers ( )
Permutations of element (E11 E3 E7 ... E1 E15)
Lists of rules (R1 R2 R3 ... R22 R23)
Program elements (genetic programming)

9. GA Steps (1/13) Complete cycle consists of some steps
Initialization
Selection
Reproduction
Survival Selection
Termination
Termination is based on the specified criteria
Figure 2: GA Steps

10. GA Steps (2/13) Initialization
Two primary methods to initialize a population in a GA
Random Initialization
Populate the initial population with completely random solutions.
Random population is created with a group of individuals (the search space)
Population size depends on the nature of the problem (typically contains several hundreds or thousands of possible solutions)
Heuristic initialization
Populate the initial population using a known heuristic for the problem.
Starts with the couple of good solutions.

11. GA Steps (3/13) Selection Fitness Proportionate
Every individual can become a parent with a probability
Which is proportional to its fitness
Fitter individuals have a higher chance of mating
Propagating their features to the next generation
Two popular fitness proportionate techniques
Roulette Wheel Selection
Tournament Selection

12. GA Steps (4/13) B A C Roulette Wheel Selection
Main idea: better individuals get higher chance
Chances proportional to fitness
Implementation: roulette wheel technique
Assign to each individual a part of the roulette wheel
Spin the wheel n times to select n individuals A C
1/6 = 17%
3/6 = 50% B
2/6 = 33%
fitness(A) = 3
fitness(B) = 1
fitness(C) = 2

13. GA Steps (5/13) Tournament Selection Binary tournament
Two individuals are randomly chosen
The fitter of the two is selected as a
parent
Probabilistic binary tournament
Two individuals are randomly chosen;
with a chance p, 0.5<p<1,
The fitter of the two is selected as
a parent
Larger tournaments
n individuals are randomly chosen
The fittest one is selected as a parent

14. GA Steps (6/13) Fitness Function
A fitness function simply defined is a function
Which takes the solution as input
Produces the suitability of the solution as the output
In some cases, the fitness and the objective function may be same
Premature convergence
Fitness too large
Relatively superfit individuals dominate population
Population converges to a local maximum
Too much exploitation; too few exploration
Slow finishing
Fitness too small
No selection pressure
After many generations, average fitness has converged, but no global maximum is found; not sufficient difference between best and average fitness
Too few exploitation; too much exploration

15. GA Steps (7/13) Crossover and Mutation
Crossover (also called recombination), and/or mutation
Exploration: Discovering promising areas in the search space, i.e. gaining information on the problem
Exploitation: Optimising within a promising area, i.e. using information
Crossover is explorative
It makes a big jump to an area somewhere “in between” two (parent) areas
Mutation is exploitative
Creating random small diversions, thereby staying near (in the area of ) the parent

16. GA Steps (8/13) Crossover Operator
Generating offspring from two selected parents
Single point crossover
Two point crossover (Multi point crossover)
Uniform crossover
Choose a random point on the two parents
Split parents at this crossover point
Create children by exchanging tails
Pc typically in range (0.6, 0.9)
Crossover is a generalization of one point crossover
Wherein alternating segments are swapped
To get new off-springs

17. GA Steps (9/13) Uniform crossover Mutation
We don’t divide the chromosome into segments
We treat each gene separately
We essentially flip a coin for each chromosome
To decide whether or not it’ll be offspring
We can also bias the coin to one parent
Mutation
Is used to maintain and introduce diversity
Is usually applied with a low probability
Bit Flip Mutation
Random Resetting
Swap Mutation
Scramble Mutation
Inversion Mutation

18. GA Steps (10/13) Bit flip mutation Random Resetting Swap Mutation
We select one or more random bits and flip them
Used for binary encoded GAs
Random Resetting
Extension of the bit flip for the integer representation
A random value from the set of permissible values is
assigned to a randomly chosen gene
Swap Mutation
We select two positions on the chromosome at random
Interchange the values

19. GA Steps (11/13) Scramble Mutation Inversion Mutation
Popular with permutation representations
Entire chromosome, a subset of genes is chosen
Their values are scrambled or shuffled randomly
Inversion Mutation
Select a subset of genes like in scramble mutation
Instead of shuffling the subset
invert the entire string in the subset

20. GA Steps (12/13) approaches Most of methods above used for parent
selection
Survivor Selection Policy
Which individuals are to be kicked out
Which are to be kept in the next generation
Survivor selection can be divided into two
approaches
Age-Based Selection
e.g. SGA
In SSGA can implement as “delete-random”
(not recommended) or as first-in-first-out
(a.k.a. delete-oldest)

21. GA Steps (13/13) Fitness-Based Selection Elitism Termination Criteria
Using one of the methods above
Elitism
Always keep at least one copy
of the fittest solution
Termination Criteria
No improvement in the population
Absolute number of generations
Objective function value has reached
a certain pre-defined value

22. Algorithm Algorithm Randomly generate population
Evaluate fitness of population
While (termination criteria is reached) do
Parent selection
Crossover with probability pc
Mutation with probability pm
Decode and fitness calculation
Survivor selection
Find best
Return best

23. GA Example 1 (1/3) Example x2 example: selection
Population of four strings
Initial population is generated
Simple ‘x’ value is calculated
Fitness is evaluated
For the specified criteria x2

24. Example 1 (2/3) Example 1 x2 example: Crossover Number of strings
1-bit crossover is chosen
For finding the suitable offspring
Crossover point is selected
Offspring after crossover
Simple ‘x’ value is calculated
Fitness value (x2) is determined

25. Example 1 (3/3) Example 1 x2 example: Mutation
To maintain the population diversity
1-bit mutation is applied
Four strings are taken
X value is calculated
Fitness function is evaluated

26. Example 2 Example 2 f(x) = {MAX(x2): 0 <= x <= 32 }
Encode Solution
Use 5 bits (1 or 0)
Generate initial population
Evaluate each solution against objective
Create next generation of solutions
Probability of “being a parent” depends on the fitness
Ways for parents to create next generation
Reproduction
Crossover (Cut and paste portions of one string to another)
Mutation (Randomly flip a bit) A 1 B C D
Sol.
String
Fitness
% of Total A
01101
169
14.4 B
11000
576
49.2 C
01000 64
5.5 D
10011
361
30.9

27. Example 3 Example 3 Works by constructing a table listing
which edges are present in the two parents
if an edge is common to both, mark with a +
e.g. [ ] and
[ ]

28. Example 4 Edge Selection Pick an initial element at random
put it in the offspring
Set the variable current element entry
Remove all references to current element
from the table
Examine list for current element:
If there is a common edge,
pick that to be next element
Otherwise pick the entry in the list,
which itself has the shortest list
Ties are split at random
In the case of reaching an empty list:
Examine the other end of the offspring
is for extension
Otherwise a new element is chosen at
random

29. Applications Other Applications Optimization Parallelization
Most commonly used in optimization problems
To maximize or minimize a given objective function value under a given set of constraints
Parallelization
Good parallel capabilities, and prove to be very effective means in solving certain problems, and also provide a good area for research
Image Processing
Used for various digital image processing (DIP) tasks as well like dense pixel matching
Scheduling applications
GAs are used to solve various scheduling problems
Particularly the time tabling problem

30. Thanks
Questions and Answers