Related papers: The $(1+(\lambda,\lambda))$ Genetic Algorithm for …
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…
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…
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…
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…
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…
While the theoretical analysis of evolutionary algorithms (EAs) has made significant progress for pseudo-Boolean optimization problems in the last 25 years, only sporadic theoretical results exist on how EAs solve permutation-based…
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,…
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…
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…
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…
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…
Genetic algorithms are heuristic optimization techniques inspired by Darwinian evolution, which are characterized by successfully finding robust solutions for optimization problems. Here, we propose a subroutine-based quantum genetic…
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…
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…
A genetic algorithm (GA) is a search-based optimization technique based on the principles of Genetics and Natural Selection. We present an algorithm which enhances the classical GA with input from quantum annealers. As in a classical GA,…
It is an ongoing debate whether and how comma selection in evolutionary algorithms helps to escape local optima. We propose a new benchmark function to investigate the benefits of comma selection: OneMax with randomly planted local optima,…
Genetic algorithms are highly effective optimization techniques for many computationally challenging problems, including combinatorial optimization tasks like portfolio optimization. Quantum computing has also shown potential in addressing…
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…
We study unbiased $(1+1)$ evolutionary algorithms on linear functions with an unknown number $n$ of bits with non-zero weight. Static algorithms achieve an optimal runtime of $O(n (\ln n)^{2+\epsilon})$, however, it remained unclear whether…
Genetic algorithms are heuristic optimization techniques inspired by Darwinian evolution. Quantum computation is a new computational paradigm which exploits quantum resources to speed up information processing tasks. Therefore, it is…