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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…
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…
In this article we present an Elitism Levels Traverse Mechanism that we designed to find bounds on population-based Evolutionary algorithms solving unimodal functions. We prove its efficiency theoretically and test it on OneMax function…
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…
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…
One hope when using non-elitism in evolutionary computation is that the ability to abandon the current-best solution aids leaving local optima. To improve our understanding of this mechanism, we perform a rigorous runtime analysis of a…
It is known that the $(1+(\lambda,\lambda))$~Genetic Algorithm (GA) with self-adjusting parameter choices achieves a linear expected optimization time on OneMax if its hyper-parameters are suitably chosen. However, it is not very well…
We give a detailed analysis of the cost used by the (1+1)-evolutionary algorithm. The problem has been approached in the evolutionary algorithm literature under various views, formulation and degree of rigor. Our asymptotic approximations…
A runtime analysis of the Univariate Marginal Distribution Algorithm (UMDA) is presented on the OneMax function for wide ranges of its parameters $\mu$ and $\lambda$. If $\mu\ge c\log n$ for some constant $c>0$ and…
Evolutionary algorithms (EAs) are a kind of nature-inspired general-purpose optimization algorithm, and have shown empirically good performance in solving various real-word optimization problems. During the past two decades, promising…
Most evolutionary algorithms have multiple parameters and their values drastically affect the performance. Due to the often complicated interplay of the parameters, setting these values right for a particular problem (parameter tuning) is a…
We propose a new black-box complexity model for search algorithms evaluating $\lambda$ search points in parallel. The parallel unary unbiased black-box complexity gives lower bounds on the number of function evaluations every parallel unary…
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…
Chance constrained optimization problems allow to model problems where constraints involving stochastic components should only be violated with a small probability. Evolutionary algorithms have been applied to this scenario and shown to…
Estimation of Distribution Algorithms (EDAs) are stochastic heuristics that search for optimal solutions by learning and sampling from probabilistic models. Despite their popularity in real-world applications, there is little rigorous…
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…
The Metropolis process (MP) and Simulated Annealing (SA) are stochastic local search heuristics that are often used in solving combinatorial optimization problems. Despite significant interest, there are very few theoretical results…
Run time analysis of evolutionary algorithms recently makes significant progress in linking algorithm performance to algorithm parameters. However, settings that study the impact of problem parameters are rare. The recently proposed W-model…
A fundamental question in reinforcement learning theory is: suppose the optimal value functions are linear in given features, can we learn them efficiently? This problem's counterpart in supervised learning, linear regression, can be solved…
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…