Tighter escape time bound for (1+(λ,λ)) GA on Jump functions

A new arXiv preprint by Anton Eremeev and Valentin Topchii advances the runtime analysis of evolutionary algorithms by applying limit theorems from probability theory. The study focuses on the $(1+(\lambda,\lambda))$ genetic algorithm (GA) introduced by Doerr, Doerr, and Ebel in 2015, a well-known algorithm with tunable parameters: mutation rate $p$, crossover bias $c$, and intermediate population sizes $\lambda_M$ and $\lambda_C$. The benchmark used is the Jump$_k$ function family, defined on binary strings of length $n$, where the unique global optimum is at Hamming distance $k$ from a plateau of local optima. The algorithm's ability to escape this plateau is critical to its performance on multimodal problems.

The main contribution is a tightened upper bound on the escape time compared to the 2022 result by Antipov, Doerr, and Karavaev. The new bound applies to a wider range of algorithm parameters and is derived using asymptotic analysis under the condition $np \to \infty$. This mathematical approach provides sharper probabilistic guarantees, helping researchers understand how parameter choices affect the GA's ability to leave local optima. The work is published on arXiv (2607.14278) and contributes to the theoretical foundation of evolutionary computation, with implications for designing more efficient algorithms for rugged fitness landscapes.