The Fitness Level Method with Tail Bounds
This work improves theoretical analysis tools for randomized search heuristics, offering more precise tail bounds for researchers in evolutionary computation and algorithm analysis.
The paper tackled the limitation of the fitness-level method's tail bounds, which previously only applied to running times at least twice the expectation, by extending it to provide sharp tail bounds including lower tails. As a result, they demonstrated the running time of randomized local search on OneMax is concentrated around n ln n - 0.1159 n.
The fitness-level method, also called the method of f-based partitions, is an intuitive and widely used technique for the running time analysis of randomized search heuristics. It was originally defined to prove upper and lower bounds on the expected running time. Recently, upper tail bounds were added to the technique; however, these tail bounds only apply to running times that are at least twice as large as the expectation. We remove this restriction and supplement the fitness-level method with sharp tail bounds, including lower tails. As an exemplary application, we prove that the running time of randomized local search on OneMax is sharply concentrated around n ln n - 0.1159 n.