Geometric Approaches to Solving the Traveling Salesman Problem

The Traveling Salesman Problem (TSP) is a classic combinatorial optimization problem that seeks to find the shortest possible route that visits a set of given cities exactly once and returns to the starting city. Despite its simple formulation, the TSP is known to be NP-hard, making it computationally challenging to find an optimal solution, particularly for large problem instances. geometric approaches to solving the TSP, leveraging insights from computational geometry and convex optimization. We begin by formulating the TSP as a graph optimization problem, where cities are represented as nodes and edges represent possible routes between cities. We then investigate geometric algorithms and techniques for efficiently computing approximate solutions to the TSP, aiming to find routes that are close to optimal in terms of length.