The 2-Opt heuristic is a very simple, easy-to-implement local search heuristic for the traveling salesman problem. While it usually provides good approximations to the optimal tour in experiments, its worst-case performance is poor. In an attempt to explain the approximation performance of 2-Opt, we analyze the smoothed approximation ratio of 2-Opt. We obtain a bound of O(log(1/σ)) for the smoothed approximation ratio of 2-Opt. As a lower bound, we prove that the worst-case lower bound of Ω(log n/log log n) for the approximation ratio holds for σ = O(1/ √ n). Our main technical novelty is that, different from existing smoothed analyses, we do not separately analyze objective values of the global and the local optimum on all inputs, but simultaneously bound them on the same input.
CITATION STYLE
Künnemann, M., & Manthey, B. (2015). Towards understanding the smoothed approximation ratio of the 2-opt heuristic. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9134, pp. 859–871). Springer Verlag. https://doi.org/10.1007/978-3-662-47672-7_70
Mendeley helps you to discover research relevant for your work.