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 Mendels foundation
of genetics and Darwins 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(2x) where the solution space is given by -1x 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 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 = 1 = 2 = =0 11 2 212 +
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
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
