Related papers: A General Dichotomy of Evolutionary Algorithms on …
Pseudo-Boolean monotone functions are unimodal functions which are trivial to optimize for some hillclimbers, but are challenging for a surprising number of evolutionary algorithms (EAs). A general trend is that EAs are efficient if…
For genetic algorithms using a bit-string representation of length~$n$, the general recommendation is to take $1/n$ as mutation rate. In this work, we discuss whether this is really justified for multimodal functions. Taking jump functions…
We study the $(1,\lambda)$-EA with mutation rate $c/n$ for $c\le 1$, where the population size is adaptively controlled with the $(1:s+1)$-success rule. Recently, Hevia Fajardo and Sudholt have shown that this setup with $c=1$ is efficient…
Extending previous analyses on function classes like linear functions, we analyze how the simple (1+1) evolutionary algorithm optimizes pseudo-Boolean functions that are strictly monotone. Contrary to what one would expect, not all of these…
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…
A core feature of evolutionary algorithms is their mutation operator. Recently, much attention has been devoted to the study of mutation operators with dynamic and non-uniform mutation rates. Following up on this line of work, we propose a…
The OneMax problem, alternatively known as the Hamming distance problem, is often referred to as the "drosophila of evolutionary computation (EC)", because of its high relevance in theoretical and empirical analyses of EC approaches. It is…
For every real number $c \geq 1$ and for all $\varepsilon > 0$, there is a fitness function $f : \{0,1\}^n \to \mathbb{R}$ for which the optimal mutation rate for the $(1+1)$ evolutionary algorithm on $f$, denoted $p_n$, satisfies $p_n…
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…
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…
We propose a new way to self-adjust the mutation rate in population-based evolutionary algorithms in discrete search spaces. Roughly speaking, it consists of creating half the offspring with a mutation rate that is twice the current…
We study evolutionary algorithms in a dynamic setting, where for each generation a different fitness function is chosen, and selection is performed with respect to the current fitness function. Specifically, we consider Dynamic BinVal, in…
Linear functions play a key role in the runtime analysis of evolutionary algorithms and studies have provided a wide range of new insights and techniques for analyzing evolutionary computation methods. Motivated by studies on separable…
Evolutionary algorithms (EAs) form a popular optimisation paradigm inspired by natural evolution. In recent years the field of evolutionary computation has developed a rigorous analytical theory to analyse their runtime on many illustrative…
To gain a better theoretical understanding of how evolutionary algorithms (EAs) cope with plateaus of constant fitness, we propose the $n$-dimensional Plateau$_k$ function as natural benchmark and analyze how different variants of the $(1 +…
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…
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…
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…
The heavy-tailed mutation operator proposed in Doerr, Le, Makhmara, and Nguyen (GECCO 2017), called \emph{fast mutation} to agree with the previously used language, so far was proven to be advantageous only in mutation-based algorithms.…
Dynamic linear functions on the hypercube are functions which assign to each bit a positive weight, but the weights change over time. Throughout optimization, these functions maintain the same global optimum, and never have defecting local…