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Pseudo-Boolean monotone functions are unimodal functions which are trivial to optimize for some hillclimbers, but are challenging for a surprising number of evolutionary algorithms (EAs). A general trend is that EAs are efficient if…
Expensive optimization problems (EOPs) are prevalent in real-world applications, where the evaluation of a single solution requires a significant amount of resources. In our study of surrogate-assisted evolutionary algorithms (SAEAs) in…
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…
We survey some of our recent results on inverse problems for evolution equations. The goal is to provide a unified approach to solve various types of evolution equations. The inverse problems we consider consist in determining unknown…
Evolutionary algorithms are bio-inspired algorithms that can easily adapt to changing environments. Recent results in the area of runtime analysis have pointed out that algorithms such as the (1+1)~EA and Global SEMO can efficiently…
Evolutionary algorithms have been frequently used for dynamic optimization problems. With this paper, we contribute to the theoretical understanding of this research area. We present the first computational complexity analysis of…
Real world problems always have different multiple solutions. For instance, optical engineers need to tune the recording parameters to get as many optimal solutions as possible for multiple trials in the varied-line-spacing holographic…
This paper looks in detail at how an evolutionary algorithm attempts to solve instances from the multimodal problem generator. The paper shows that in order to consistently reach the global optimum, an evolutionary algorithm requires a…
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…
The heavy-tailed mutation operator proposed in Doerr, Le, Makhmara, and Nguyen (GECCO 2017), called \emph{fast mutation} to agree with the previously used language, so far was proven to be advantageous only in mutation-based algorithms.…
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…
Runtime analysis aims at contributing to our understanding of evolutionary algorithms through mathematical analyses of their runtimes. In the context of discrete optimization problems, runtime analysis classically studies the time needed to…
Some experimental investigations have shown that evolutionary algorithms (EAs) are efficient for the minimum label spanning tree (MLST) problem. However, we know little about that in theory. As one step towards this issue, we theoretically…
Under constant selection, each trait has a fixed fitness, and small mutation rates allow populations to efficiently exploit the optimal trait. Therefore it is reasonable to expect mutation rates will evolve downwards. However, we find this…
Constrained submodular optimization problems play a key role in the area of combinatorial optimization as they capture many NP-hard optimization problems. So far, Pareto optimization approaches using multi-objective formulations have been…
It is generally accepted that populations are useful for the global exploration of multi-modal optimisation problems. Indeed, several theoretical results are available showing such advantages over single-trajectory search heuristics. In…
In real-world optimization scenarios, the problem instance that we are asked to solve may change during the optimization process, e.g., when new information becomes available or when the environmental conditions change. In such situations,…
An important question in evolutionary computation is how good solutions evolutionary algorithms can produce. This paper aims to provide an analytic analysis of solution quality in terms of the relative approximation error, which is defined…
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…
Evolutionary algorithms have been widely used for a range of stochastic optimization problems in order to address complex real-world optimization problems. We consider the knapsack problem where the profits involve uncertainties. Such a…