Short answer 2-In Genetic Algorithms, crossover and mutation operators may resul

Question

Short answer 2-In Genetic Algorithms, crossover and mutation operators may result in invalid chromosomes. Give an example of such chromosomes when solving the Traveling Salesperson Problem.
Short answer 2-In Genetic Algorithms, crossover and mutation operators may result in invalid chromosomes. Give an example of such chromosomes when solving the Traveling Salesperson Problem.
Short answer 2-In Genetic Algorithms, crossover and mutation operators may result in invalid chromosomes. Give an example of such chromosomes when solving the Traveling Salesperson Problem.

Explanation / Answer

The idea of TSP is to find a tour of a given numbers of cities, visiting each city exactly once and returning to the starting city where the length of the tour is minimized. The first instance of the travelling salesman problem was in 1759 whose problem was to move a knight to every posituon on the chess board exactly once[6]. The main idea is to cover as many location as possible without visiting any location twice.

The TSP can be stated mathematically as follows:

Given a weighted graph G=(V,E) where the weight

between nodes is non negative number and we have to find

the tour of all nodes or cities that has a minimum total cost.

The best or optimal solution of solving Travelling salesman

problem is to evaluate all possible tours and search for the

tour which is having minimum cost. Foe example if we are

having n cities then number of possible path is n!. If n is

small we can solve the pboblem in a limited time. For

example if we have 5 cities then total 5! Path exist to

evaluate the minimum cost, it can be done in small amount

of time but if n is large it become impossible to find the

cost of every tour in polynomial time. However TSP does

not find application in many fields. Indeed many direct

application of TSP bring life to the research area and help

to direct future work like Genome Sequencing, Starlight

Interferometer Program, Scan Chain Optimization, DNA

Universal Strings, Whizzkids 96 Vehicle Routing, Touring

Airports and Designing Sonet Rings etc.

There is one more catergory of TSP i.e. multiple travelling

sales man problem(m TSP), which consists of determining

a set of routes from salesmen who all start from and turn

back to a home city. In multiple travel sales men problem

we have m salesmen located at single deport point. The

remaining cities to be visited are called intermediate nodes.

Then the m TSP consists of finding tours for all m salesmen, who all start and end at the deport, such that each intermediate node is visited exactly once and the total cost

of visiting all nodes is minimized. The cost metric can be

define in term of distance, time, etc. Multiple travelling

salesmen problem also have many application like Printing The idea of TSP is to find a tour of a given numbers of

cities, visiting each city exactly once and returning to the

starting city where the length of the tour is minimized. The

first instance of the travelling salesman problem was in

1759 whose problem was to move a knight to every

posituon on the chess board exactly once[6]. The main idea

is to cover as many location as possible without visiting

any location twice.

The TSP can be stated mathematically as follows:

Given a weighted graph G=(V,E) where the weight

between nodes is non negative number and we have to find

the tour of all nodes or cities that has a minimum total cost.

The best or optimal solution of solving Travelling salesman

problem is to evaluate all possible tours and search for the

tour which is having minimum cost. Foe example if we are

having n cities then number of possible path is n!. If n is

small we can solve the pboblem in a limited time. For

example if we have 5 cities then total 5! Path exist to

evaluate the minimum cost, it can be done in small amount

of time but if n is large it become impossible to find the

cost of every tour in polynomial time. However TSP does

not find application in many fields. Indeed many direct

application of TSP bring life to the research area and help

to direct future work like Genome Sequencing, Starlight

Interferometer Program, Scan Chain Optimization, DNA

Universal Strings, Whizzkids 96 Vehicle Routing, Touring

Airports and Designing Sonet Rings etc.

There is one more catergory of TSP i.e. multiple travelling

sales man problem(m TSP), which consists of determining

a set of routes from salesmen who all start from and turn

back to a home city. In multiple travel sales men problem

we have m salesmen located at single deport point. The

remaining cities to be visited are called intermediate nodes.

Then the m TSP consists of finding tours for all m

salesmen, who all start and end at the deport, such that each

intermediate node is visited exactly once and the total cost

of visiting all nodes is minimized. The cost metric can be

define in term of distance, time, etc. Multiple travelling

salesmen problem also have many application like Printing The idea of TSP is to find a tour of a given numbers of

cities, visiting each city exactly once and returning to the

starting city where the length of the tour is minimized. The

first instance of the travelling salesman problem was in

1759 whose problem was to move a knight to every

posituon on the chess board exactly once[6]. The main idea

is to cover as many location as possible without visiting

any location twice.

The TSP can be stated mathematically as follows:

Given a weighted graph G=(V,E) where the weight

between nodes is non negative number and we have to find

the tour of all nodes or cities that has a minimum total cost.

The best or optimal solution of solving Travelling salesman

problem is to evaluate all possible tours and search for the

tour which is having minimum cost. Foe example if we are

having n cities then number of possible path is n!. If n is

small we can solve the pboblem in a limited time. For

example if we have 5 cities then total 5! Path exist to

evaluate the minimum cost, it can be done in small amount

of time but if n is large it become impossible to find the

cost of every tour in polynomial time. However TSP does

not find application in many fields. Indeed many direct

application of TSP bring life to the research area and help

to direct future work like Genome Sequencing, Starlight

Interferometer Program, Scan Chain Optimization, DNA

Universal Strings, Whizzkids 96 Vehicle Routing, Touring

Airports and Designing Sonet Rings etc.

There is one more catergory of TSP i.e. multiple travelling

sales man problem(m TSP), which consists of determining

a set of routes from salesmen who all start from and turn

back to a home city. In multiple travel sales men problem

we have m salesmen located at single deport point. The

remaining cities to be visited are called intermediate nodes.

Then the m TSP consists of finding tours for all m

salesmen, who all start and end at the deport, such that each

intermediate node is visited exactly once and the total cost

of visiting all nodes is minimized. The cost metric can be

define in term of distance, time, etc. Multiple travelling

salesmen problem also have many application like Printing press scheduling problem, School bus routing problem,

Crew scheduling problem and Design of global navigation

satellite syatem surveying networks etc

A genetic algorithm is used to find a solution in much less

time. Although it might not find the best solution but it can

find a near perfect solution for a 100 city tour in less than a

minute. The following are some basic steps of our proposed

work.

Encoding: permutation encoding will be used to

solve TSP. We represent cities with an integer

value, and after that we initialize the population.

Distance matrix: distance matrix is an N*N

matrix of point to point distances.

Selection based on fitness function: the fitness

function will be total cost of the tour represented

by each chromosome. The lesser the sum, the fitter the solution represented by that

chromosome.

1.Generating random numbers equal to population

size.

2.Dividing random numbers into interval of two

3. According to sequence of random numbers

selecting routes from population size.

4. Best of two routes will be chosen using

tournament selection to apply Mutation.

5.Next generation of population size will be

generated.

6.Process will undergo predefined iterations.

7.After the final iteration the smallest distance size

will be displayed as result.

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