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Experience shows that typical evolutionary algorithms can cope well with stochastic disturbances such as noisy function evaluations. In this first mathematical runtime analysis of the $(1+\lambda)$ and $(1,\lambda)$ evolutionary algorithms…
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…
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…
We present two adaptive schemes for dynamically choosing the number of parallel instances in parallel evolutionary algorithms. This includes the choice of the offspring population size in a (1+$\lambda$) EA as a special case. Our schemes…
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…
We argue that proven exponential upper bounds on runtimes, an established area in classic algorithms, are interesting also in heuristic search and we prove several such results. We show that any of the algorithms randomized local search,…
The interplay between mutation and selection plays a fundamental role in the behaviour of evolutionary algorithms (EAs). However, this interplay is still not completely understood. This paper presents a rigorous runtime analysis of a…
Unlike traditional evolutionary algorithms which produce offspring via genetic operators, Estimation of Distribution Algorithms (EDAs) sample solutions from probabilistic models which are learned from selected individuals. It is hoped that…
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…
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…
While evolutionary algorithms are known to be very successful for a broad range of applications, the algorithm designer is often left with many algorithmic choices, for example, the size of the population, the mutation rates, and the…
Choosing the right selection rate is a long standing issue in evolutionary computation. In the continuous unconstrained case, we prove mathematically that a single parent $\mu=1$ leads to a sub-optimal simple regret in the case of the…
The one-fifth rule and its generalizations are a classical parameter control mechanism in discrete domains. They have also been transferred to control the offspring population size of the $(1, \lambda)$-EA. This has been shown to work very…
Self-adjustment of parameters can significantly improve the performance of evolutionary algorithms. A notable example is the $(1+(\lambda,\lambda))$ genetic algorithm, where the adaptation of the population size helps to achieve the linear…
Understanding how evolutionary algorithms perform on constrained problems has gained increasing attention in recent years. In this paper, we study how evolutionary algorithms optimize constrained versions of the classical LeadingOnes…
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…
Theory of evolutionary computation (EC) aims at providing mathematically founded statements about the performance of evolutionary algorithms (EAs). The predominant topic in this research domain is runtime analysis, which studies the time it…
We analyse the impact of the selective pressure for the global optimisation capabilities of steady-state EAs. For the standard bimodal benchmark function \twomax we rigorously prove that using uniform parent selection leads to exponential…
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…
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…