This repository contains Python code to approximate a solution for the Traveling Salesman Problem (TSP) using a genetic algorithm. The genetic algorithm is a heuristic optimization method inspired by the process of natural selection.
The Traveling Salesman Problem (TSP) is a classic optimization problem in which a salesman must visit a set of cities exactly once and return to the starting city, minimizing the total distance traveled. It is an NP-hard problem with applications in logistics, operations research, and computer science.
The Python code in this repository implements a genetic algorithm to solve the Traveling Salesman Problem (TSP). Here's an overview of how the code works:
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Genetic Algorithm: The core of the solution is a genetic algorithm, a heuristic optimization technique inspired by the process of natural selection. In the context of the TSP, the algorithm evolves a population of candidate solutions (routes) over multiple generations, gradually improving the fitness (total distance traveled) of the best solutions.
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Representation of Solutions: Each candidate solution is represented as a permutation of cities. For example, if there are N cities, a solution might be represented as [0, 1, 2, ..., N-1], where each number represents the index of a city to be visited.
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Fitness Function: The fitness of each solution is calculated as the total distance traveled along the route. The fitness function computes the sum of distances between consecutive cities in the route, considering the Euclidean distance between their coordinates.
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Selection, Crossover, and Mutation: The genetic algorithm uses selection, crossover, and mutation operators to evolve the population of solutions. Selection chooses the fittest individuals to be parents for the next generation, crossover combines pairs of parents to create offspring, and mutation introduces small changes to individual solutions to explore new areas of the search space.
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Visualization: The code includes visualization of the TSP solution using matplotlib. The visualization shows the cities as blue dots and the optimal route as a black line connecting them. This visualization helps in understanding the behavior of the genetic algorithm and visually inspecting the quality of the solutions.
The genetic algorithm iterates until a termination condition is met, such as reaching a maximum number of generations or no significant improvement in the best solution over several generations.