.

1. Evolutionary
Algorithms
Dr Iman Ardekani

2.  Nature, science and engineering
 Optimization problem
 Evolutionary algorithms
 Genetic algorithms
 An example
Content
By Iman Ardekani

3.  In the procedure of exploring the natural laws in
science for fabricating useful products in
engineering, we often face two problems:
1. Learning Problem
2. Optimization Problem
Nature, Science and Engineering
By Iman Ardekani

4.  Learning Problem
 Processing and classification of data in order to create
information and knowledge.
Nature, Science and Engineering
Data Information Knowledge
Learning Problem
By Iman Ardekani

5.  Optimization Problem
 Using data in order to find an optimal solution, e.g. the
best decision or parameters of an optimal controller.
Nature, Science and Engineering
Knowledge Best Solution
Optimization Problem
By Iman Ardekani

6.  Optimization problem has a long history. When Euclid founded
Geometry (as a knowledge), he tried to solve the first
optimization problems. Examples are:
1. What is the shortest path between two points?
2. How to break a stick to make a rectangle with maximum
area?
Optimization Problem
By Iman Ardekani

7. 
Optimization Problem
By Iman Ardekani

8.  An example for optimization problem (combinatorial):
How to place 8 queens on a chess board so that no queens
attack each other.
 How to differentiate with respect to a Queen ?
Optimization Problem
By Iman Ardekani

9.  An example for optimization problem (multi-objective):
How to minimize costs and maximize benefits.
 There is no answer here.
Optimization Problem
By Iman Ardekani

10. 
Optimization Problem
By Iman Ardekani

11.  There are many different EA algorithms, the basic
of which can be explained through Genetic
Algorithms.
 They are all random-based solution space
searching meta-heuristic algorithms.
Evolutionary Algorithms
By Iman Ardekani

12.  Mendel (1822-1884) – Philosopher and scientist
cultivated and tested about 29,000 plants between 1856 and
1863 to verify his laws of heritance. Mendel's work was rejected
at first, and was not widely accepted until after he died.
 Darwin (1809-1882) – Scientist
developed his evolution theory, stating that evolution is the
change in the inherited characteristics of biological populations
over successive generations.
Evolutionary Algorithms
Evolutionary algorithms are based on the basic principles of Mendel’s
foundation of genetics and Darwin’s theory of evolution .
By Iman Ardekani

13.  John Holland – Professor of psychology and Professor of
electrical engineering at the University of Michigan
The main idea of genetic algorithm is that every individual of a
species can be characterized by its abilities that help it to cope
with its environment in terms of survival and reproduction.
Genetic Algorithm
By Iman Ardekani

14.  A genetic algorithm is a search heuristic algorithm that mimics
the process of natural evolution. It has 5 phases:
Genetic Algorithm
1. Population
Generation
2. Fitness
Evaluation
4. Crossover
5. Mutation 3. Selection
By Iman Ardekani

15. Phase 1: Population Generation
 Individuals
1. Individuals = a sample from the solution space (each individual
is a solution)
2. Generation = a group of individuals
Genetic Algorithm
individual 1 individual 2 …. individual N
Population | Popsize = N
By Iman Ardekani

16. Phase 1: Population Generation
 Population Generation Rules
1. The first generation is produced randomly.
2. Next generations are produced through breeding.
Genetic Algorithm
Generation
1
Generation
2
Generation
3
By Iman Ardekani

17. Phase 1: Population Generation
 Chromosomes and Fitness
Each individual has two properties:
a) Its location (chromosome composed of genes)
b) Its quality (fitness value)
Genetic Algorithm
individual n
Chromosome
Fitness
By Iman Ardekani

18. Phase 2: Fitness Evaluation
 Fitness value of an individual is usually the value of the cost-
function (to be optimized) with respect to the locations (genes)
of the individual.
Genetic Algorithm
X1: Gene 1
...
X2: Gene 2
XL: Gene 2
chromosome
F(x1,x2,…,xL) Fitness value
By Iman Ardekani

19. Phase 3: Selection
 After evaluating the fitness of all individuals, we use a selection
process to generate a mating pool.
 Each individual may be selected several times.
 Even low quality individuals have chance to be selected.
 Individuals in the mating pool are called parents.
Genetic Algorithm
By Iman Ardekani

20. Phase 3: Selection
 Selection Rule:
1. Higher quality = more chance of being selected into the mating pool
Example:
Genetic Algorithm
Individual Fitness Relative
1 90 45%
2 60 30%
3 20 10%
4 30 15%
Mating pool
individual 1
individual 4
individual 1
individual 2
By Iman Ardekani

21. Phase 4: Crossover
 Two parents might be selected randomly from the mating pool
to generate two offspring.
Genetic Algorithm
Mating pool
individual 1
individual 4
individual 1
individual 2
Random
selection
individual 1
individual 4
Offspring 1
Offspring 2
Crossover
By Iman Ardekani

22. Phase 4: Crossover
 Crossover Rule:
1. Genes of each offspring is a certain combination of the genes
of its parents.
Genetic Algorithm
X1: Gene 1
X2: Gene 2
X4: Gene 4
Parent 1
chromosome
X3: Gene 3
Y1: Gene 1
Y2: Gene 2
Parent 2
chromosome
Y4: Gene 4
Y3: Gene 3
Offspring 1
chromosome
X1: Gene 1
X2: Gene 2
Y4: Gene 4
Y3: Gene 3
By Iman Ardekani

23.  Phase 5: Mutation
 There is a very low chance for (small) changes in the genes of
the offspring; however, it should be considered.
 Mutation = Small changes in the genes of an offspring
Genetic Algorithm
X1: Gene 1
X2: Gene 2
Y4: Gene 4
Offspring 1
chromosome
Y3: Gene 3
X1: Gene 1
X2: Gene 2
Z : Gene 3
By Iman Ardekani

24.  Phase 5: Mutation
 After considering the chance for mutation, the next generation
will be formed of new offspring.
Genetic Algorithm
Current
Generation
Next
Generation
Fitness
evaluation
Selection
Crossover
Mutation
By Iman Ardekani

25.  Evolution of a walking creature:
Genetic Algorithm
By Iman Ardekani

26.  The problem is finding the maximal point of f(x):
f(x)=2+xsin(2x)
where the solution space is given by
-1x 2
Example
-1 -0.5 0 0.5 1 1.5 2
0
1
2
3
4
By Iman Ardekani

27.  Defining chromosomes and genes
−1𝑥 2
1. We can divide the solution space into 212 sections.
2. In this case, each solution value can be represented by a 12-bit
binary number.
3. This 12-bit representation can be considered as Chromosome
4. Each bit can be considered as a gene.
By Iman Ardekani

28.  Defining chromosomes and genes
𝑥 𝑚𝑖𝑛 = −1
𝑥 𝑚𝑖𝑛 = 2
𝑥 = 𝑥 𝑚𝑎𝑥 − 𝑥 𝑚𝑖𝑛
𝑖=0
11
𝑎𝑖2𝑖
212
+ 𝑥 𝑚𝑖𝑛
Example: 0.9534 can be represented by
1 0 1 0 0 1 1 0 1 0 1 1
By Iman Ardekani

29.  Initial population generation
Example
By Iman Ardekani

30.  Steps to follow:
1. 10 random value for x (individuals) leads to 10 chromosomes.
2. The fitness value of each individual can be found as y=f(x).
3. The relative fitness can be then obtained accordingly.
4. Based on the relative fitness values, a selection wheel can be
created.
5. A mating pool can be created by using the selection wheel.
6. Two individual can be selected from the mating pool as
parents.
Example
By Iman Ardekani

31.  Steps to follow:
7. A random number is generated. If the random number is
higher than a certain level (crossover probability), the
crossover will happen.
8. Otherwise, two other parents will be selected and step 7 will
be repeated.
Example
1 0 1 0 0 1 1 0 1 0 1 1
0 0 1 0 0 1 0 0 1 0 0 1
Parent 1
Parent 2
By Iman Ardekani

32.  Steps to follow:
7. A random number is generated. If the random number is
higher than a certain level (crossover probability), the
crossover will happen.
8. Otherwise, two other parents will be selected and step 7 will
be repeated.
Example
1 0 1 0 0 1 1 0 1 0 1 1
0 0 1 0 0 1 0 0 1 0 0 1
Parent 1
Parent 2
By Iman Ardekani

33.  Steps to follow:
9. Crossover process
Example
1 0 1 0 0 1 1 0 1 0 1 1
0 0 1 0 0 1 0 0 1 0 0 1
Parent 1
Parent 2
1 0 1 0 0 1
1 0 1 0 1 10 0 1 0 0 1
0 0 1 0 0 1Child 1
Child 2
By Iman Ardekani

34.  Steps to follow:
10. For each gene of each child, a random number will be
generated. If the number is higher than a certain value
(mutation probability – very low) then the value of the gene
will be changed. Otherwise, the gene remains untouched.
Example
1 0 1 0 0 1 0 0 1 0 0 1Child 1
1 0 1 0 0 0 0 0 1 0 0 1Child 1
mutation
By Iman Ardekani

35.  Steps to follow:
11. The two children (after considering the mutation probability)
will be add to the next generation.
12. Step 7 will be repeated until the size of the new generation
becomes equal to the Popsize.
13. Step 2 will be repeated for the new generation.
Example
By Iman Ardekani

36.  10th generation
Example
By Iman Ardekani

37.  50th generation
Example
By Iman Ardekani

38. Questions?
End
By Iman Ardekani