Related papers: Optimal Mutation Rates for the $(1+\lambda)$ EA on…
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 propose and analyze a self-adaptive version of the $(1,\lambda)$ evolutionary algorithm in which the current mutation rate is part of the individual and thus also subject to mutation. A rigorous runtime analysis on the OneMax benchmark…
We analyze the performance of the 2-rate $(1+\lambda)$ Evolutionary Algorithm (EA) with self-adjusting mutation rate control, its 3-rate counterpart, and a $(1+\lambda)$~EA variant using multiplicative update rules on the OneMax problem. We…
Most evolutionary algorithms have parameters, which allow a great flexibility in controlling their behavior and adapting them to new problems. To achieve the best performance, it is often needed to control some of the parameters during…
Most research in the theory of evolutionary computation assumes that the problem at hand has a fixed problem size. This assumption does not always apply to real-world optimization challenges, where the length of an optimal solution may be…
It may seem very intuitive that for the maximization of the OneMax problem $\OM(x):=\sum_{i=1}^n{x_i}$ the best that an elitist unary unbiased search algorithm can do is to store a best so far solution, and to modify it with the operator…
This paper extends the runtime analysis of non-elitist evolutionary algorithms (EAs) with fitness-proportionate selection from the simple OneMax function to the linear functions. Not only does our analysis cover a larger class of fitness…
It is known that the evolutionary algorithm $(1+1)$-EA with mutation rate $c/n$ optimises every monotone function efficiently if $c<1$, and needs exponential time on some monotone functions (HotTopic functions) if $c\geq 2.2$. We study the…
Evolutionary algorithms (EAs) are general-purpose optimisers that come with several parameters like the sizes of parent and offspring populations or the mutation rate. It is well known that the performance of EAs may depend drastically on…
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…
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…
Evolutionary Algorithms (EAs) and other randomized search heuristics are often considered as unbiased algorithms that are invariant with respect to different transformations of the underlying search space. However, if a certain amount of…
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…
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…
Many real-world applications have the time-linkage property, and the only theoretical analysis is recently given by Zheng, et al. (TEVC 2021) on their proposed time-linkage OneMax problem, OneMax$_{(0,1^n)}$. However, only two elitist…
It is well known that evolutionary algorithms (EAs) achieve peak performance only when their parameters are suitably tuned to the given problem. Even more, it is known that the best parameter values can change during the optimization…
For every mutation rate $p \in (0, 1)$, and for all $\varepsilon > 0$, there is a fitness function $f : \{0,1\}^n \to \mathbb{R}$ with a unique maximum for which the optimal mutation rate for the $(1+1)$ evolutionary algorithm on $f$ is in…
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…
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 most common representation in evolutionary computation are bit strings. This is ideal to model binary decision variables, but less useful for variables taking more values. With very little theoretical work existing on how to use…