+1-415-670-9189
info@expertsmind.com
Create an initial population of p chromosomes
Course:- Engineering Mathematics
Reference No.:- EM132138066




Assignment Help
Expertsmind Rated 4.9 / 5 based on 47215 reviews.
Review Site
Assignment Help >> Engineering Mathematics

(1) This problem concerns of the proof of the NP-completeness of 300L

a) Convert the formula F into a 300L graph
b) Find a solution for the 300L instance of F and verify that it is a solution for F

F = (Z1 V Z2) ^ (z1 V z2 V z3 V z4)

(2)

The Traveling Salesman Problem (TSP) is one which has commanded much attention in Artificial Intelligence because it is so easy to describe and so difficult to solve. The problem can simply be stated as: if a traveling salesman vvishes to visit exactly once each of a list m cities (where the cost of traveling from city i to city j is co) and then return to the home city, what is the least costly route the traveling salesman can take.

The importance of the TSP is that it is representative of a larger class of problems known as combinatorial optimization problems. The TSP problem belongs in the class of combinatorial optimization problems known as NIP-hard. Today. no one has found a polynomial-time algorithm for the TSP.

A Simple Genetic Algorithm

A simple genetic algorithm can be defined in the following 9 steps:

Step 1: create an initial population of P chromosomes (generation 0)

Step 2: evaluate the fitness of each chromosome

Step 3: Select P parents from the current population via proportional selection (i.e.. the selection probability is proportional to the fitness).

Step 4: choose at random a pair of parents for mating. Exchange bit strings with a crossover operation to create two offspring (e.g., one-point crossover)

Step 5: process each offprint by the mutation operation, and insert the resulting offspring in the new population

Step 6: repeat steps 4 and 5 until all parents are selected and mated (P offspring are created)

Step 7: replace the old population of chromosomes in the new population Step 8: evaluate the fitness of each chromosome in the new population

Step 9: go back to step 3 if the number of generations is less than some upper bound. Otherwise, the final result is the best chromosome created during the search.

Selection Probability:

The parent chromosomes are selected for mating via proportional selection. also known as roulette wheel selection'. It is defined as follows:
'1) Sum up the fitness values of all chromosomes in the population
2) Generate a random number between 0 and the sum of the fitness values
3) Select the first chromosome whose fitness value added to the sum of the fitness values of the previous chromosomes is greater than or equal to the random number

Initial population
In addition to the crossover and mutation operators you will also evaluate the impact of the GAs with the following initial populations:
- Randomly generated population
- Nearest neighbor insertion
Crossover and mutation operators
Write a program that solves the TSP using Genetic Algorithms. Explain and implement the following crossover & mutation operators:
- Uniform order-based crossover
- Cycle Crossover (CX)
- Reciprocal exchange mutation
- Scramble Mutation

Output:
1. Solution
2. Implementation of Genetic algorithms with the above mentioned crossover and mutation operations
3. A basic evaluation that should describe the following two basic configurations:

Configuration

initial Solution

Crossover

Mutation

Selection

1

Random

Uniform
Crossover

Reciprocal
Exchange

Random
Selection

2

Random

Cycle
Crossover

Scramble
Mutation

Random
Selection

Population size = 100 Mutation rate = 0.1

Extensive evaluation of the GA, i.e., initial population, crossover & mutation operators. Extensively evaluate the following combination of operations investigate the impact of varying the population, size, explore different mutation rates, and evaluate the impact of your GA with and without elite survival.

Configuration

Initial
Solution

Crossover

Mutation

Selection

3

Random

Uniform
Crossover

Reciprocal
Exchange

Roulette Wheel

4

Random

Cycle
Crossover

Reciprocal
Exchange

Roulette Wheel

5

Random

Cycle
Crossover

Scramble
Mutation

Roulette Wheel

6

Random

Uniform
Crossover

Scramble
Mutation

Best and
Second best
candidates

Provide a comprehensive description of the algorithms and an extensive evaluation of the results. It should describe the experimental design, what experiments are and what they are intended to show.

Use tables and figures where appropriate.

Assess the overall performance of your optimization algorithms for solving the travelling salesman problem. Typically, to evaluate the performance of your algorithm for a single configuration you would run your algorithm multiple times (at least 5 times in this project with at least 1000 iterations per execution) and record the best fitness for all runs. You can then report the mean and median fitness across all runs. Your results should show that you have considered the suggested operators (e.g., crossover, mutation and selection).

(nb: problem instances will be provided) Deliverable:
- Source code in python
- Any instructions for executing source
- A sample file that describes the test run on the program
- Descriptions and documentation

Answered:-

Verified Expert

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 and returns to the origin city?" It is an NP-hard problem in combinatorial optimization, important in operations research and theoretical computer science



Put your comment
 
View Conversion
Minimize
  1. user image
    urv2138066

    Very happy with this assignment It has met my requirements. I would highly recommend this service. Five out of five. The quality, timeliness and price of ExpertsMind cannot be matched. Thanks for understanding my task and to do it in a very well manner. It is really good to approach the experts like this one. he prepared very well after clearing the doubts.



Ask Question & Get Answers from Experts
Browse some more (Engineering Mathematics) Materials
Formulate a linear programming model that can be used to determine the optimal production schedule for the presses to meet the contract requirements that yields the maximum
Target Inc. has a project costing $40,000 and cash flows of $8,000, $15,600, and $22,700 for Years 1 to 3, respectively. Based on the profitability index rule, should the pr
For the container of Fig use Bernoulli's equation to derive a formula for the distance X where the free jet leaving horizontally will strike the floor, as a function of h an
Solve the problem-Using the lexicographic tie-breaking procedure. Find conditions on the parameters a, b, c, d, e, f, g, h, i, and j such that the following statements are tr
Apply the graph obtained in part (c) to estimate visually the Fahrenheit temperature corresponding to a Celsius temperature of 28o. Then calculate that temperature exactly by
An airlines corporation is considering the purchase of jet passenger planes so as to increase their passenger service. The type A plane costs $450 million each, the type B c
Need LP tutorial help involving optimization and the use of Solver. Solve the following modifications of the Tatham Capital Budgeting model (solve each part independently of t
Use rbf function in R to create your RBF model. Try cluster numbers 5 to 25. Use your hold-out validation set to figure out the best number of clusters. Report the best numb