Create a function that solves the Traveling Salesman Problem using a genetic algorithm
Challenge in Detail
Create a function that solves the Traveling Salesman Problem using a genetic algorithm.
The function should take a list of cities and their coordinates as input and return the shortest possible route, visiting each city exactly once and returning to the starting city.
The genetic algorithm should involve selection, crossover, and mutation operations to evolve a population of candidate solutions.
TSP — Traveling Salesman Problem
The Traveling Salesman Problem (TSP) is a classic problem in optimization and combinatorial optimization. The problem can be stated simply as follows:
Given a list of cities and the distances between each pair of cities, find the shortest possible route that visits each city exactly once and returns to the original city.
Key Characteristics of TSP:
- Cyclic Tour: The solution should be a cyclic tour, meaning you start and end at the same city.
- Visit Each City Once: Each city should be visited exactly once.
- Optimal Solution: The total distance of the tour should be as short as possible.
Why is TSP Important?
The TSP is a foundational problem for many reasons:
- NP-Hard Problem: The TSP is known to be NP-hard, meaning that as the number of cities increases, the time required to find the optimal solution can grow exponentially. This makes it computationally infeasible to solve exactly for large numbers of cities.
- Applicability: Despite its simple description, many real-world problems can be modeled or approximated by the TSP, such as vehicle routing, computer chip design, and DNA sequencing.