Travelling Salesman Problem-Genetic Algiorthm with Crossover and Mutation

This code implements a genetic algorithm to solve the travelling salesman problem for a given graph. The algorithm works as follows:

• First, a population of random genomes is initialized, where each genome is a random path in the graph.

• Then, the fitness of each genome is calculated as the total distance travelled on the path.

• The genetic algorithm is then applied to the population for a number of generations.

• In each generation, the fittest individuals are selected using tournament selection.

• Then, crossover is applied to the selected individuals to create new offspring.

• Finally, mutation is applied to the offspring with a given mutation rate.

• The new offspring replace the weakest individuals in the population.

• This process is repeated for a number of generations until a stopping criterion is reached (in this case, a maximum number of generations is defined).

• The fittest individual in the final population is returned as the solution to the travelling salesman problem.

The code defines several functions to implement the genetic algorithm, including:

• fitness(): a function to calculate the fitness of a given genome (i.e. the total distance travelled on the path).

• select_population(): a function to select a random sample of individuals from a given population.

• tournament_selection(): a function to select the fittest individuals from a given population using tournament selection.

• ordered_crossover(): a function to apply ordered crossover to two parent genomes and generate new offspring.

• mutation(): a function to apply mutation to a given genome.

• total_population_score(): a function to calculate the total score of a given population (i.e. the sum of all the fitness scores of the individuals in the population).

• generate_path(): a function to generate a random path in the graph.

• initialize_population(): a function to initialize a random population of given size.

_{The code is tailored to solve the travelling salesman problem for a specific graph defined in the code. The graph has six cities labelled "PISKLM" and the distances between the cities are defined by a 6x6 adjacency matrix. However, it is easy to make your own changes by inititalizing a different graph and changing the relevant parameters. You can also change the genetic parameters to see how they affect the convergence to a solution.}