Apart from few exceptions, the mathematical runtime analysis of evolutionary algorithms is mostly concerned with expected runtimes. In this work, we argue that stochastic domination is a notion that should be used more frequently in this area. Stochastic domination allows to formulate much more informative performance guarantees than the expectation alone, it allows to decouple the algorithm an...

We study the problem of maximizing the overlap of two convex polytopes under translation in R for some constant d ≥ 3. Let n be the number of bounding hyperplanes of the polytopes. We present an algorithm that, for any ε > 0, finds an overlap at least the optimum minus ε and reports the translation realizing it. The running time is O(n d/2 +1 log n) with probability at least 1 − n−O(1), which c...

Fitness sharing is a popular diversity mechanism implementing the idea that similar individuals in the population have to share resources and thus, share their fitnesses. Previous runtime analyses of fitness sharing studied a variant where selection was based on populations instead of individuals. We use runtime analysis to highlight the benefits and dangers of the original fitness sharing mech...

Nowadays, dust phenomenon is one of the important challenges in warm and dry areas. Forecasting the phenomenon before its occurrence helps to take precautionary steps to prevent its consequences. Fuzzy expert systems capabilities have been taken into account to assist and cope with the uncertainty associated to complex environments such as dust forecasting problem. This paper presents novel hyb...

In the year 2000 the dominant method for solving matrix eigen-value problems is still the QR algorithm. This paper discusses the family of GR algorithms, with emphasis on the QR algorithm. Included are historical remarks, an outline of what GR algorithms are and why they work, and descriptions of the latest, highly parallelizable, versions of the QR algorithm. Now that we know how to paralleliz...