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The OneMax problem, alternatively known as the Hamming distance problem, is often referred to as the "drosophila of evolutionary computation (EC)", because of its high relevance in theoretical and empirical analyses of EC approaches. It is…
In many real-world optimization problems, the objective function evaluation is subject to noise, and we cannot obtain the exact objective value. Evolutionary algorithms (EAs), a type of general-purpose randomized optimization algorithm,…
The $(1+(\lambda,\lambda))$ genetic algorithm, first proposed at GECCO 2013, showed a surprisingly good performance on so me optimization problems. The theoretical analysis so far was restricted to the OneMax test function, where this GA…
A key property underlying the success of evolutionary algorithms (EAs) is their global search behavior, which allows the algorithms to `jump' from a current state to other parts of the search space, thereby avoiding to get stuck in local…
Multi-objective evolutionary algorithms (MOEAs) have become essential tools for solving multi-objective optimization problems (MOPs), making their running time analysis crucial for assessing algorithmic efficiency and guiding practical…
For every real number $c \geq 1$ and for all $\varepsilon > 0$, there is a fitness function $f : \{0,1\}^n \to \mathbb{R}$ for which the optimal mutation rate for the $(1+1)$ evolutionary algorithm on $f$, denoted $p_n$, satisfies $p_n…
Recent theoretical research has shown that self-adjusting and self-adaptive mechanisms can provably outperform static settings in evolutionary algorithms for binary search spaces. However, the vast majority of these studies focuses on…
We analyse the performance of well-known evolutionary algorithms (1+1)EA and (1+$\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…
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…
Recently, the runtime analysis of multi-valued estimation-of-distribution algorithms in the framework of Ben Jedidia et al. (TCS 2024) has made significant advancements. However, almost all existing analyses are limited to multi-valued…
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…
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…
The generalized egg dropping problem is a classic challenge in sequential decision-making. Standard dynamic programming evaluates the minimax minimum number of tests in $\mathcal{O}(K \cdot N^2)$ time. A known approach formulates the…
The NP-complete Permutation Pattern Matching problem asks whether a $k$-permutation $P$ is contained in a $n$-permutation $T$ as a pattern. This is the case if there exists an order-preserving embedding of $P$ into $T$. In this paper, we…
Traditionally, robust statistics has focused on designing estimators tolerant to a minority of contaminated data. Robust list-decodable learning focuses on the more challenging regime where only a minority $\frac 1 k$ fraction of 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…
Understanding how crossover works is still one of the big challenges in evolutionary computation research, and making our understanding precise and proven by mathematical means might be an even bigger one. As one of few examples where…
The running-time analysis of evolutionary combinatorial optimization is a fundamental topic in evolutionary computation. However, theoretical results regarding the $(\mu+\lambda)$ evolutionary algorithm (EA) for combinatorial optimization…
The goal of this paper is to understand how exponential-time approximation algorithms can be obtained from existing polynomial-time approximation algorithms, existing parameterized exact algorithms, and existing parameterized approximation…
Finding the best configuration of algorithms' hyperparameters for a given optimization problem is an important task in evolutionary computation. We compare in this work the results of four different hyperparameter tuning approaches for a…