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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)
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 define a collection of language classes which are TxtEx-learnable (learnable in the limit from positive data). The learners map any data input to an element of a fixed lattice, and keep the least upper bound of all lattice elements thus obtained as the current hypothesis. Each element of the lattice is a grammar for a language, and the learner climbs the(More)
Ant Colony Optimization (ACO) is a powerful metaheuristic for solving combinatorial optimization problems. With this paper we contribute to the theoretical understanding of this kind of algorithm by investigating the classical minimum cut problem. An ACO algorithm similar to the one that was proved successful for the minimum spanning tree problem is(More)
We consider stochastic versions of OneMax and LeadingOnes and analyze the performance of evolutionary algorithms with and without populations on these problems. It is known that the (1+1) EA on OneMax performs well in the presence of very small noise, but poorly for higher noise levels. We extend these results to LeadingOnes and to many different noise(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)