Unbiased Black-Box Complexities of Jump Functions

We analyze the unbiased black-box complexity of jump functions with small, medium, and large sizes of the fitness plateau surrounding the optimal solution. Among other results, we show that when the jump size is $(1/2 - \varepsilon)n$, that is, only a small constant fraction of the fitness values is visible, then the unbiased black-box complexities for arities $3$ and higher are of the same order as those for the simple \textsc{OneMax} function. Even for the extreme jump function, in which all but the two fitness values $n/2$ and $n$ are blanked out, polynomial-time mutation-based (i.e., unary unbiased) black-box optimization algorithms exist. This is quite surprising given that for the extreme jump function almost the whole search space (all but a $\Theta(n^{-1/2})$ fraction) is a plateau of constant fitness. To prove these results, we introduce new tools for the analysis of unbiased black-box complexities, for example, selecting the new parent individual not by comparing the fitnesses of the competing search points, but also by taking into account the (empirical) expected fitnesses of their offspring.Comment: This paper is based on results presented in the conference versions [GECCO 2011] and [GECCO 2014

Bounding Bloat in Genetic Programming

While many optimization problems work with a fixed number of decision variables and thus a fixed-length representation of possible solutions, genetic programming (GP) works on variable-length representations. A naturally occurring problem is that of bloat (unnecessary growth of solutions) slowing down optimization. Theoretical analyses could so far not bound bloat and required explicit assumptions on the magnitude of bloat. In this paper we analyze bloat in mutation-based genetic programming for the two test functions ORDER and MAJORITY. We overcome previous assumptions on the magnitude of bloat and give matching or close-to-matching upper and lower bounds for the expected optimization time. In particular, we show that the (1+1) GP takes (i) $\Theta(T_{init} + n \log n)$ iterations with bloat control on ORDER as well as MAJORITY; and (ii) $O(T_{init} \log T_{init} + n (\log n)^3)$ and $\Omega(T_{init} + n \log n)$ (and $\Omega(T_{init} \log T_{init})$ for $n=1$) iterations without bloat control on MAJORITY.Comment: An extended abstract has been published at GECCO 201

Simple Max-Min Ant Systems and the Optimization of Linear Pseudo-Boolean Functions

With this paper, we contribute to the understanding of ant colony optimization (ACO) algorithms by formally analyzing their runtime behavior. We study simple MAX-MIN ant systems on the class of linear pseudo-Boolean functions defined on binary strings of length 'n'. Our investigations point out how the progress according to function values is stored in pheromone. We provide a general upper bound of O((n^3 \log n)/ \rho) for two ACO variants on all linear functions, where (\rho) determines the pheromone update strength. Furthermore, we show improved bounds for two well-known linear pseudo-Boolean functions called OneMax and BinVal and give additional insights using an experimental study.Comment: 19 pages, 2 figure

Intuitive Analyses via Drift Theory

Humans are bad with probabilities, and the analysis of randomized algorithms offers many pitfalls for the human mind. Drift theory is an intuitive tool for reasoning about random processes. It allows turning expected stepwise changes into expected first-hitting times. While drift theory is used extensively by the community studying randomized search heuristics, it has seen hardly any applications outside of this field, in spite of many research questions which can be formulated as first-hitting times. We state the most useful drift theorems and demonstrate their use for various randomized processes, including approximating vertex cover, the coupon collector process, a random sorting algorithm, and the Moran process. Finally, we consider processes without expected stepwise change and give a lemma based on drift theory applicable in such scenarios without drift. We use this tool for the analysis of the gambler's ruin process, for a coloring algorithm, for an algorithm for 2-SAT, and for a version of the Moran process without bias

Vom Mythos der Allmacht: die Darstellung der Staatssicherheit im DDR-Spielfilm der 1960er Jahre

"The article deals with stylising State Security, by the examples of the DEFA spy films 'Reserviert für den Tod' (Spared for Death, 1963), 'For Eyes only - Streng Geheim' (For Eyes only - Strictly Confidential, 1963) and 'Schwarzer Samt' (Black Velvet, 1964). The author analyses by way of which narratives and stylistic means the MfS was presented in the early 1960s. Topically, these films reproduce all those threat scenarios employed by the SED propaganda to justify the building of the Wall. At the same time State Security acts as an almighty secret service always ready for the defence which is not used to control the population but rather protects it from imminent danger." (author's abstract