Related papers: Tight Runtime Bounds for Static Unary Unbiased Evo…
The analysis of randomized search heuristics on classes of functions is fundamental for the understanding of the underlying stochastic process and the development of suitable proof techniques. Recently, remarkable progress has been made in…
We show that, for any c>0, the (1+1) evolutionary algorithm using an arbitrary mutation rate p_n = c/n finds the optimum of a linear objective function over bit strings of length n in expected time Theta(n log n). Previously, this was only…
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…
This paper extends the runtime analysis of non-elitist evolutionary algorithms (EAs) with fitness-proportionate selection from the simple OneMax function to the linear functions. Not only does our analysis cover a larger class of fitness…
The most common representation in evolutionary computation are bit strings. This is ideal to model binary decision variables, but less useful for variables taking more values. With very little theoretical work existing on how to use…
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 the last decade remarkable progress has been made in development of suitable proof techniques for analysing randomised search heuristics. The theoretical investigation of these algorithms on classes of functions is essential to the…
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…
The one-fifth success rule is one of the best-known and most widely accepted techniques to control the parameters of evolutionary algorithms. While it is often applied in the literal sense, a common interpretation sees the one-fifth success…
Extending previous analyses on function classes like linear functions, we analyze how the simple (1+1) evolutionary algorithm optimizes pseudo-Boolean functions that are strictly monotone. Contrary to what one would expect, not all of these…
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…
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…
In this work, we introduce multiplicative drift analysis as a suitable way to analyze the runtime of randomized search heuristics such as evolutionary algorithms. We give a multiplicative version of the classical drift theorem. This allows…
To gain a better theoretical understanding of how evolutionary algorithms (EAs) cope with plateaus of constant fitness, we propose the $n$-dimensional Plateau$_k$ function as natural benchmark and analyze how different variants of the $(1 +…
We propose a new way to self-adjust the mutation rate in population-based evolutionary algorithms in discrete search spaces. Roughly speaking, it consists of creating half the offspring with a mutation rate that is twice the current…
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 this paper we revisit the question how hard it can be for the $(1+1)$ Evolutionary Algorithm to optimize monotone pseudo-Boolean functions. By introducing a more pessimistic stochastic process, the partially-ordered evolutionary…
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…
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…
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…