Related papers: Sharp Bounds on the Runtime of the (1+1) EA via Dr…
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…
This paper explores the use of the standard approach for proving runtime bounds in discrete domains---often referred to as drift analysis---in the context of optimization on a continuous domain. Using this framework we analyze the (1+1)…
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…
Unlike traditional evolutionary algorithms which produce offspring via genetic operators, Estimation of Distribution Algorithms (EDAs) sample solutions from probabilistic models which are learned from selected individuals. It is hoped that…
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…
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…
Drift analysis has become a powerful tool to prove bounds on the runtime of randomized search heuristics. It allows, for example, fairly simple proofs for the classical problem how the (1+1) Evolutionary Algorithm (EA) optimizes an…
Despite significant progress in the theory of evolutionary algorithms, the theoretical understanding of evolutionary algorithms which use non-trivial populations remains challenging and only few rigorous results exist. Already for the most…
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…
While most theoretical run time analyses of discrete randomized search heuristics provide bounds on the expected number of evaluations to find the global optimum, we consider the anytime performance of evolutionary and…
In a seminal paper in 2013, Witt showed that the (1+1) Evolutionary Algorithm with standard bit mutation needs time $(1+o(1))n \ln n/p_1$ to find the optimum of any linear function, as long as the probability $p_1$ to flip exactly one bit…
Drift analysis is one of the state-of-the-art techniques for the runtime analysis of randomized search heuristics (RSHs) such as evolutionary algorithms (EAs), simulated annealing etc. The vast majority of existing drift theorems yield…
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…
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…
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…
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 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…
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…
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 +…
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…