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The first rigorous theoretical analysis (Horoba, Sudholt (GECCO 2010)) of an ant colony optimizer for the stochastic shortest path problem suggests that ant system experience significant difficulties when the input data is prone to noise. In this work, we propose a slightly different ant optimizer to deal with noise. We prove that under mild conditions, it(More)
We study the behavior of a Max-Min Ant System (MMAS) on the stochastic single-destination shortest path (SDSP) problem. Two previous papers already analyzed this setting for two slightly different MMAS algorithms, where the pheromone update fitness-independently rewards edges of the best-so-far solution. The first paper showed that, when the best-so-far(More)
The benefit of sexual recombination is one of the most fundamental questions both in population genetics and evolutionary computation. It is widely believed that recombination helps solving difficult optimization problems. We present the first result, which rigorously proves that it is beneficial to use sexual recombination in an uncertain environment with(More)
Understanding the impact of crossover on performance is a major problem in the theory of genetic algorithms (GAs). We present new insight on working principles of crossover by analyzing the performance of crossover-based GAs on the simple functions OneMax and Jump. First, we assess the potential speedup by crossover when combined with a fitness-invariant(More)
We extend the work of Lehre and Witt (GECCO 2010) on the unbiased black-box model by considering higher arity variation operators. In particular, we show that already for binary operators the black-box complexity of LeadingOnes drops from &#920;(<i>n</i><sup>2</sup>) for unary operators to <i>O</i>(<i>n</i> log <i>n</i>). For OneMax, the &#937;(<i>n</i> log(More)
The all-pairs shortest path problem is the first non-artificial problem for which it was shown that adding crossover can significantly speed up a mutation-only evolutionary algorithm. Recently, the analysis of this algorithm was refined and it was shown to have an expected optimization time (w. r. t. the number of fitness evaluations) of Θ(n 3.25 (log n)(More)
Bioinspired algorithms, such as evolutionary algorithms and ant colony optimization, are widely used for different combinatorial optimization problems. These algorithms rely heavily on the use of randomness and are hard to understand from a theoretical point of view. This paper contributes to the theoretical analysis of ant colony optimization and studies(More)
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 <i>n</i>. Our investigations point out how the progress according to function values is stored in(More)