Seonglae ChoTraveling salesman problem
Finding minimal cost Hamiltonian cycle. Optimal solution is only found by Brute-force Search(exponential).
The weight between two cities can be
- Ticket cost (asymmetric)
- Travel time (asymmetric)
- Euclidean distance (symmetric)
TSP Algorithm Notion
Travelling salesman problem
The travelling salesman problem (TSP) asks the following question: "Given a list of cities and the distances between each pair of cities, what is the shortest possible route that visits each city exactly once and returns to the origin city?" It is an NP-hard problem in combinatorial optimization, important in theoretical computer science and operations research.
https://en.wikipedia.org/wiki/Travelling_salesman_problem
Researchers Approach New Speed Limit for Seminal Problem | Quanta Magazine
Integer linear programming can help find the answer to a variety of real-world problems. Now researchers have found a much faster way to do it.
https://www.quantamagazine.org/researchers-approach-new-speed-limit-for-seminal-problem-20240129/
