The document provides information about optimization algorithms and genetic algorithms. It discusses that genetic algorithms are modeled after biological evolution and use processes like selection of fittest individuals, crossover to produce offspring for the next generation, and mutation. The key phases of a genetic algorithm are described as initializing a population, calculating fitness scores, selecting parents for reproduction, performing crossover on parents to create offspring, and applying occasional mutation. Genetic algorithms are suited for optimization problems as they can find good solutions efficiently.

1. Name : TAHAN M K H
School : University of
Jinan
Major : Computer
Science and Technology
Stay Hard!

2. Optimization
 It is an act, process, or methodology of making
something (such as a design, system, or decision)
as fully perfect, functional, or effective as possible.
 It helps to find the inputs that gives the best outputs.
 Requires an optimization algorithm.
 Common applications: Minimal cost, maximal profit,
minimal error etc.

3. Optimization Algorithm
 An optimization algorithm is a process
of searching a set of solutions in the
state space to maximize or minimize the
objective function of a specific problem.
 It is a procedure which is executed iteratively
by comparing various solutions till an optimum
or a satisfactory solution is found.

4. Types of Optimization Algorithm

5. Difference Between Single Solution based and Population based search
 Single-solution algorithms perform local search process by employing a single candidate solution trying to
improve this solution in its neighborhood.
 In contrast, population-based algorithms guide the search process by maintaining multiple solutions located in
different points of search space.
 However, the main drawback of single-solution algorithms is that the global optimum may not reach and it may
get stuck in local optimum. On the other hand, population-based algorithms with several starting points that
maintain the diversity of the solutions globally in the search space and results are of better exploration during
the search process

6. Genetic Algorithm
Genetic algorithms are modeled after the biological evolutionary processes that use natural selection to select the
best species to survive. They are heuristics based and low cost to compute. This algorithm reflects the process of
natural selection where the fittest individuals are selected for reproduction in order to produce offspring of the next
generation.
Genetic algorithms are well suited to deploy in resource constrained tactical environments because they are fast,
use low resources and their degree of computation accuracy is just enough to meet mission computation objectives
in many cases.

7. The Notion of Natural Selection
 The process of natural selection starts with the selection of fittest individuals from a population.
 They produce offspring which inherit the characteristics of the parents and will be added to the next generation.
 If parents have better fitness, their offspring will be better than parents and have a better chance at surviving.
 This process keeps on iterating and at the end, a generation with the fittest individuals will be found.
 This notion can be applied for a search problem. We consider a set of solutions for a problem and select the set
of best ones out of them.

8. N dimensional linear space
Linear algebra is a branch in mathematics that deals with objects and operations in what is called -dimensional space. We
already familiar with 1, 2 and 3-dimensional spaces from elementary algebra. The only objects are points which can be
represented by a single numerical values.
2-dimensional space is a flat plane and consists of primitive objects such as points and lines.
3-dimensional space consists of points, lines, and planes.

9. N dimensional linear space
Higher dimensional spaces ( N > 3 ) are more difficult to visualize. While 2D and 3D spaces seem readily applicable to every
day life, higher dimensional spaces seem far more abstract.
Consider a textbook. In 3D space we describe the textbook with width, height, and depth. These three variables are
geometric properties of the textbook. However, not all variables need to have a geometric meaning. We can make the
description of the textbook richer by adding additional variables such as color, copyright year, author name, and page count.
Since we have added 4 more variables to the description, we call this a 7-dimensional space ( N = 7 ).

10. Phases Considered in a Genetic Algorithm
Initial population
01 Fitness function
Selection Crossover
02
03 04
05 Mutation

11. Phases in a Genetic Algorithm

12. Initial Population
 The process begins with a set of individuals
which is called a Population. Each individual
is a solution to the problem we want to solve.
 An individual is characterized by a set of para-
meters (variables) known as Genes. Genes are
joined into a string to form a Chromosome
(solution).
 In a genetic algorithm, the set of genes of an
individual is represented using a string, in terms
of an alphabet. Usually, binary values are used
(string of 1s and 0s). We can say that we encode the
genes in a chromosome.

13. Fitness Function
The fitness function determines how fit an individual is (the ability of an individual to compete with other
individuals). It gives a fitness score to each individual. The probability that an individual will be selected for
reproduction is based on its fitness score.

14. Selection
 The idea of selection phase is to select the fittest individuals and let them pass their genes to the next
generation.
 Two pairs of individuals (parents) are selected based on their fitness scores. Individuals with high fitness have
more chance to be selected for reproduction.

15. Crossover
 Crossover is the most significant phase in a genetic algorithm.
For each pair of parents to be mated, a crossover point is chosen
at random from within the genes.
 Offspring are created by exchanging the genes of parents
among themselves until the crossover point is reached.
 The new offspring are added to the population.

16. Crossover
A( , )
( , )
C( , ）
( , )
H
G
F( + ∆ , − ∆ )
E( , − ∆ )

17. Mutation
In certain new offspring formed, some of their genes can be subjected to a mutation with a low random probability.
This implies that some of the bits in the bit string can be flipped.
The algorithm terminates if the population has converged (does not produce offspring which are significantly
different from the previous generation). Then it is said that the genetic algorithm has provided a set of solutions to
our problem.

18. Mutation
A( , )
( , )
C( , ）
( , )
H
G
F( + ∆ , − ∆ )
E( , − ∆ )

19. Conclusions
 N-dimensional linear space
 Difference between crossover and mutation phase.
 The significance / geometrical meaning of Crossover phase.
 Float Method

20. Thanks
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