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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…
This work is focused on the application of functional-type a posteriori error estimates and corresponding indicators to a class of time-dependent problems. We consider the algorithmic part of their derivation and implementation and also…
The Minimum Spanning Tree problem (abbr. MSTP) is a well-known combinatorial optimization problem that has been extensively studied by the researchers in the field of evolutionary computing to theoretically analyze the optimization…
Evolutionary algorithms (EAs) are universal solvers inspired by principles of natural evolution. In many applications, EAs produce astonishingly good solutions. As they are able to deal with complex optimisation problems, they show great…
Upper and lower bounds are established for the survival probability $|<\psi(0)|\psi(t)>|^{2}$ of a quantum state, in terms of the energy moments $<\psi(0)|H^{n}|\psi(0)>$. Introducing a cut-off in the energy generally enables considerable…
When a problem instance is perturbed by a small modification, one would hope to find a good solution for the new instance by building on a known good solution for the previous one. Via a rigorous mathematical analysis, we show that…
In the first runtime analysis of an estimation-of-distribution algorithm (EDA) on the multi-modal jump function class, Hasen\"ohrl and Sutton (GECCO 2018) proved that the runtime of the compact genetic algorithm with suitable parameter…
In this study, we use Genetic Programming (GP) to compose new optimization benchmark functions. Optimization benchmarks have the important role of showing the differences between evolutionary algorithms, making it possible for further…
The practice of evolutionary algorithms involves the tuning of many parameters. How big should the population be? How many generations should the algorithm run? What is the (tournament selection) tournament size? What probabilities should…
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…
Consider a mathematical model of evolutionary adaptation of fitness landscape and mutation matrix as a reaction to population changes. As a basis, we use an open quasispecies model, which is modified to include explicit death flow. We…
The JUMP$_k$ benchmark was the first problem for which crossover was proven to give a speed-up over mutation-only evolutionary algorithms. Jansen and Wegener (2002) proved an upper bound of $O(\text{poly}(n) + 4^k/p_c)$ for the ($\mu$+1)…
An evolutionary search space can be smoothly transformed via a suitable change of basis; however, it can be difficult to determine an appropriate basis. In this paper, a method is proposed to select an optimum basis can be used to simplify…
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…
Despite significant empirical and theoretically supported evidence that non-static parameter choices can be strongly beneficial in evolutionary computation, the question how to best adjust parameter values plays only a marginal role 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…
Efficient computation of trajectories of switched affine systems becomes possible, if for any such hybrid system, we can manage to efficiently compute the sequence of switching times. Once the switching times have been computed, we can…
One of the easiest randomized greedy optimization algorithms is the following evolutionary algorithm which aims at maximizing a boolean function $f:\{0,1\}^n \to {\mathbb R}$. The algorithm starts with a random search point $\xi \in…
A frequently studied performance measure in online optimization is competitive analysis. It corresponds to the worst-case ratio, over all possible inputs of an algorithm, between the performance of the algorithm and the optimal offline…
Many practitioners who use the EM algorithm complain that it is sometimes slow. When does this happen, and what can be done about it? In this paper, we study the general class of bound optimization algorithms - including…