Solving the traveling salesman problem using a hybrid approach
Import required libraries: numpy, torch, matplotlib, and scipy.

load_data(filename): Loads the TSP instance from a TSPLIB file, calculates the distance matrix between cities, and converts it into a PyTorch tensor.

Generator and Discriminator: These are the neural network classes for the generator and discriminator used in the GAN.

train_gan(): Trains the GAN using the generator and discriminator networks, optimizers, dataloader, and device.

Genetic Algorithm related functions:

initialize_population(): Initializes the population for the GA.
selection(): Selects parents for the GA using roulette wheel selection.
crossover(): Performs crossover between parents to generate offspring.
mutation(): Applies mutation to the offspring population.
evaluate_fitness(): Evaluates the fitness of the candidate solutions in the population.
run_ga(): Runs the GA to improve candidate solutions.
evaluate_population(): Evaluates the population by calculating the fitness scores of each individual.

In the main section:

Set parameters for the hybrid approach.
Load and preprocess TSP instances from the TSPLIB dataset.
Create the generator, discriminator, and optimizers.
Create a dataloader.
Train the GAN on TSP instances and generate a pool of candidate solutions.
Initialize the population for the GA using candidate solutions from the GAN.
Improve candidate solutions using the GA.
Plot the improvement of the solution over time.
Plot the final solution.
Check if the solution was improved by the GA.
Plot the candidate solutions generated by the GAN.