Travelling Salesman Problem

The Travelling Salesman Problem (TSP) is a well-known combinatorial optimization problem in which a salesman must visit a set of cities exactly once and return to the starting city, with the goal of minimizing the total travel distance or cost. Represented as a weighted graph, each city is a node and each route between cities is an edge with an associated weight (distance or cost). TSP is classified as an NP-hard problem, meaning that as the number of cities increases, finding the exact optimal solution becomes computationally expensive. Due to its complexity, TSP is often solved using approximation algorithms and heuristics such as Genetic Algorithms, Simulated Annealing, Ant Colony Optimization, or Dynamic Programming for smaller instances. TSP has wide applications in logistics, manufacturing, circuit design, and route planning.

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