8 - Travelling Salesman Problems

Abstract

The traveling salesman problem (TSP) is a central problem in combinatorial optimization with many theoretical and practical applications; it also has been, and still is, at the core of numerous efforts to push the limits on the size of practically tractable optimization problems. State-of-the-art complete TSP algorithms can solve instances up to several thousand vertices in reasonable computation times (CPU hours to several CPU days), while the best SLS algorithms can find solutions whose quality is within fractions of a percent of the optimum for much larger instances with up to millions of vertices. This chapter gives a general overview of TSP applications and benchmark instances, and introduces the most basic local search algorithms for the TSP. Based on these algorithms, several SLS algorithms have been developed that have greatly improved the ability of finding high quality solutions for large instances. An overview of iterated local search algorithms, which are currently among the most successful SLS algorithms for large TSP instances, and several prominent, high-performance TSP algorithms that are based on population-based SLS methods are presented.