Traveling Salesperson Problem

The Traveling Salesperson Problem (TSP) seeks the shortest route visiting all points exactly once and returning to the origin, a classic optimization challenge with broad applications. Current research focuses on improving heuristic and metaheuristic algorithms, such as Lin-Kernighan-Helsgaun (LKH) and genetic algorithms, often incorporating techniques like test-time augmentation and novel crossover operators to enhance solution quality and efficiency. Deep reinforcement learning, particularly using graph neural networks and attention mechanisms, is also emerging as a powerful approach, especially for variations like the Traveling Purchaser Problem and precedence-constrained TSP. These advancements offer significant potential for optimizing logistics, supply chain management, and other real-world routing problems.