Related papers: Solving Problems with Unknown Solution Length at (…
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…
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…
We propose a new method based on discrete Fourier analysis to analyze the time evolutionary algorithms spend on plateaus. This immediately gives a concise proof of the classic estimate of the expected runtime of the $(1+1)$ evolutionary…
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…
We present a new method for proving lower bounds on the expected running time of evolutionary algorithms. It is based on fitness-level partitions and an additional condition on transition probabilities between fitness levels. The method is…
The analysis of randomized search heuristics on classes of functions is fundamental for the understanding of the underlying stochastic process and the development of suitable proof techniques. Recently, remarkable progress has been made in…
In real-world applications, many optimization problems have the time-linkage property, that is, the objective function value relies on the current solution as well as the historical solutions. Although the rigorous theoretical analysis on…
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…
Evolutionary algorithms have been frequently applied to constrained continuous optimisation problems. We carry out feature based comparisons of different types of evolutionary algorithms such as evolution strategies, differential evolution…
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…
We analyse the performance of well-known evolutionary algorithms (1+1)EA and (1+$\lambda$)EA in the prior noise model, where in each fitness evaluation the search point is altered before evaluation with probability $p$. We present refined…
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…
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…
Randomized search heuristics have been applied successfully to a plethora of problems. This success is complemented by a large body of theoretical results. Unfortunately, the vast majority of these results regard problems with binary or…
When a problem instance is perturbed by a small modification, one would hope to find a good solution for the new instance by building on a known good solution for the previous one. Via a rigorous mathematical analysis, we show that…
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…
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,…
Combinatorial optimization problems are a prominent application area of evolutionary algorithms, where the (1+1) EA is one of the most investigated. We extend this algorithm by introducing some problem knowledge with a specialized mutation…
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…
A key challenge to make effective use of evolutionary algorithms is to choose appropriate settings for their parameters. However, the appropriate parameter setting generally depends on the structure of the optimisation problem, which is…