Related papers: A Tight Runtime Analysis of the $(1+(\lambda, \lam…
The $(1+(\lambda,\lambda))$ genetic algorithm, first proposed at GECCO 2013, showed a surprisingly good performance on so me optimization problems. The theoretical analysis so far was restricted to the OneMax test function, where this GA…
The $(1+(\lambda,\lambda))$ genetic algorithm is a bright example of an evolutionary algorithm which was developed based on the insights from theoretical findings. This algorithm uses crossover, and it was shown to asymptotically outperform…
It is known that the $(1+(\lambda,\lambda))$~Genetic Algorithm (GA) with self-adjusting parameter choices achieves a linear expected optimization time on OneMax if its hyper-parameters are suitably chosen. However, it is not very well…
We investigate a family of $(\mu+\lambda)$ Genetic Algorithms (GAs) which creates offspring either from mutation or by recombining two randomly chosen parents. By scaling the crossover probability, we can thus interpolate from a fully…
The $(1 + (\lambda,\lambda))$ genetic algorithm is a younger evolutionary algorithm trying to profit also from inferior solutions. Rigorous runtime analyses on unimodal fitness functions showed that it can indeed be faster than classical…
The JUMP$_k$ benchmark was the first problem for which crossover was proven to give a speed-up over mutation-only evolutionary algorithms. Jansen and Wegener (2002) proved an upper bound of $O(\text{poly}(n) + 4^k/p_c)$ for the ($\mu$+1)…
Most evolutionary algorithms (EAs) used in practice employ crossover. In contrast, only for few and mostly artificial examples a runtime advantage from crossover could be proven with mathematical means. The most convincing such result shows…
The $(1+(\lambda,\lambda))$ genetic algorithm is one of the few algorithms for which a super-constant speed-up through the use of crossover could be proven. So far, this algorithm has been used with parameters based also on intuitive…
Explaining to what extent the real power of genetic algorithms lies in the ability of crossover to recombine individuals into higher quality solutions is an important problem in evolutionary computation. In this paper we show how the…
Understanding when evolutionary algorithms are efficient or not, and how they efficiently solve problems, is one of the central research tasks in evolutionary computation. In this work, we make progress in understanding the interplay…
Population diversity is essential for avoiding premature convergence in Genetic Algorithms (GAs) and for the effective use of crossover. Yet the dynamics of how diversity emerges in populations are not well understood. We use rigorous…
Parent selection methods are widely used in evolutionary computation to accelerate the optimization process, yet their theoretical benefits are still poorly understood. In this paper, we address this gap by proposing a parent selection…
The $(1+(\lambda,\lambda))$ genetic algorithm is a recently proposed single-objective evolutionary algorithm with several interesting properties. We show that its main working principle, mutation with a high rate and crossover as repair…
We re-investigate a fundamental question: how effective is crossover in Genetic Algorithms in combining building blocks of good solutions? Although this has been discussed controversially for decades, we are still lacking a rigorous and…
We prove that the compact genetic algorithm (cGA) with hypothetical population size $\mu = \Omega(\sqrt n \log n) \cap \text{poly}(n)$ with high probability finds the optimum of any $n$-dimensional jump function with jump size $k < \frac 1…
Online algorithm selection (OAS) aims to adapt the optimization process to changes in the fitness landscape and is expected to outperform any single algorithm from a given portfolio. Although this expectation is supported by numerous…
Evolutionary algorithms (EAs) are population-based general-purpose optimization algorithms, and have been successfully applied in various real-world optimization tasks. However, previous theoretical studies often employ EAs with only a…
Despite significant progress in the theory of evolutionary algorithms, the theoretical understanding of evolutionary algorithms which use non-trivial populations remains challenging and only few rigorous results exist. Already for the most…
The compact Genetic Algorithm (cGA), parameterized by its hypothetical population size $K$, offers a low-memory alternative to evolving a large offspring population of solutions. It evolves a probability distribution, biasing it towards…
Evolutionary algorithms are known to be robust to noise in the evaluation of the fitness. In particular, larger offspring population sizes often lead to strong robustness. We analyze to what extent the $(1+(\lambda,\lambda))$ genetic…