The document discusses the traveling salesman problem and genetic algorithms. The traveling salesman problem involves finding the shortest route to visit each city on a list only once and return to the origin city. Genetic algorithms provide a method to solve optimization problems like the traveling salesman problem. Genetic algorithms work by initializing a population of solutions and using operators like crossover and mutation to generate new populations, selecting the fittest solutions to reproduce until a condition is met. The genetic algorithm approach allows the traveling salesman problem to be solved effectively without prior knowledge of the problem.

1. Genetic Algorithms
Ministry of Education and Science of the Russian
Federation
Crimean Federal V.I. Vernadsky University
Taurida academy
(structural subdivision)
Author: Alexander Bidanets
3-d - year student
Bachelor course
Mathematics and informatics department
Major in: applied mathematics and informatics
Language instructor: Associate Professor Oksana Vladimirovna Yermolenko

2. Table of contents
The traveling salesman problem
What is the genetic algorithm?
Conclusion

3. What is known to be the
optimization problem?
In mathematics and computer science, an optimization problem is
the problem of finding the best solution from all feasible solutions. In optimization
problems we are looking for the largest value or the smallest value that a function
can take.

4. Traveling salesman problem
The travelling salesman problem (TSP) asks the
following question: Given a list of cities and the distances
between each pair of cities, what is the shortest possible
route that visits each city exactly once and returns to the
origin city? It is an problem in combinatorial optimization,
important in theoretical computer science.

6. What is the genetic algorithm?
Individual
(chromosome)
Any possible solution of a problem
Population Group of all individuals
Search space All possible solutions to the problem
Locus The position of a gene on the chromosome
the genes value is the number of variable slots on a chromosome;
the codes value is the number of possible values for each gene;
Now, before we start, we should understand some key terms:

7. What is the genetic algorithm?
Algorithm is started with a set of solutions (represented by chromosomes)
called population. Solutions from one population are taken and used to form a new
population. This is motivated by a hope, that the new population will be better than
the old one. Solutions which are selected to form new solutions (offspring) are
selected according to their fitness - the more suitable they are the more chances they
have to reproduce.
This is repeated until some condition is satisfied (for example number of
populations or improvement of the best solution).

8. Basic Operators of Genetic
Algorithm
•Encoding and Initialization
•Crossover (also called recombination)
•Mutation
•Selection and Fitness function
•Decoding

9. Initialization

12. Initialization
Population of solutions

13. Crossover

14. Mutation

15. Selection and

16. Relevance
• The traveling salesman problem has many different real world applications, making it a very popular problem to
solve. The problem of computer wiring can also be modeled as a TSP. We have several modules. These modules
have got a number of pins. We need to connect a subset of pins with wires in such a way that no pin hasn’t to more
than two wires attached to it and the length of the wire is minimized.
• The traveling salesman problem is a kind of testing ground for the algorithms which solved optimization problems,
because TSP is a good representative of this class problems. Therefore, the study of the genetic algorithm for the
traveling salesman problem gives a hope that genetic algorithm allows to solve other optimization problems as well.
• So, investigations of the travelling salesman problem is very important for computer science, Computer
Engineering, web, radio-electronics, business and transport industry.
• The method of genetic algorithm allows to solve the traveling salesman problem quite effectively. The relative error
of the result of this algorithm is quite little.

17. Conclusion• We has been observed how GA creates solution without having any prior knowledge about the
problem. Unlike other heuristic methods, it uses natural techniques as like crossover, mutation and
selection to make the computation easier and many times faster.
• Genetic algorithms can be used when no information is available about the gradient of the function at
the evaluated points.
• The function itself does not need to be continuous or differentiable.
• Genetic algorithms can still achieve good results even in cases in which the function has several local
minima or maxima.
• These properties of genetic algorithms have their price: unlike traditional random search, the function
is not examined at a single place, constructing a possible path to the local maximum or minimum, but
many different places are considered simultaneously.
• The function must be calculated for all elements of the population.
• GAs are useful optimization procedure
• Easy to parallelize.