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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…
Evolutionary algorithms (EAs) have found many successful real-world applications, where the optimization problems are often subject to a wide range of uncertainties. To understand the practical behaviors of EAs theoretically, there are a…
Monotone Boolean functions are a structurally important class of Boolean functions, but their restricted form imposes strong limitations on achievable nonlinearity. In this paper, we investigate whether evolutionary computation can evolve…
We consider the expected runtime of non-elitist evolutionary algorithms (EAs), when they are applied to a family of fitness functions with a plateau of second-best fitness in a Hamming ball of radius r around a unique global optimum. On one…
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…
Evolutionary algorithms (EAs) have been widely applied to multi-objective optimization due to their population-based nature. Population update, a key component in multi-objective EAs (MOEAs), is usually performed in a greedy, deterministic…
The Resource Allocation approach (RA) improves the performance of MOEA/D by maintaining a big population and updating few solutions each generation. However, most of the studies on RA generally focused on the properties of different…
We consider a model of a population with fixed size $N$, which is subjected to an unlimited supply of beneficial mutations at a constant rate $\mu_N$. Individuals with $k$ beneficial mutations have the fitness $(1+s_N)^k$. Each individual…
Hillclimbing is an essential part of any optimization algorithm. An important benchmark for hillclimbing algorithms on pseudo-Boolean functions $f: \{0,1\}^n \to \mathbb{R}$ are (strictly) montone functions, on which a surprising number of…
We investigate a family of $(\mu+\lambda)$ Genetic Algorithms (GAs) which creates offspring either from mutation or by recombining two randomly chosen parents. By scaling the crossover probability, we can thus interpolate from a fully…
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…
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…
The one-fifth rule and its generalizations are a classical parameter control mechanism in discrete domains. They have also been transferred to control the offspring population size of the $(1, \lambda)$-EA. This has been shown to work very…
In single-objective optimization, it is well known that evolutionary algorithms also without further adjustments can tolerate a certain amount of noise in the evaluation of the objective function. In contrast, this question is not at all…
Evolutionary algorithms (EAs), a large class of general purpose optimization algorithms inspired from the natural phenomena, are widely used in various industrial optimizations and often show excellent performance. This paper presents an…
Population diversity is crucial in evolutionary algorithms as it helps with global exploration and facilitates the use of crossover. Despite many runtime analyses showing advantages of population diversity, we have no clear picture of how…
Multimodal optimization requires both exploration and exploitation. Exploration identifies promising attraction basins, while exploitation finds the best solutions within these basins. The balance between exploration and exploitation can be…
Although the population size is an important parameter in evolutionary multi-objective optimization (EMO), little is known about its influence on preference-based EMO (PBEMO). The effectiveness of an unbounded external archive (UA) in PBEMO…
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…
Most research in the theory of evolutionary computation assumes that the problem at hand has a fixed problem size. This assumption does not always apply to real-world optimization challenges, where the length of an optimal solution may be…