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

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

2010-07-27

arxiv.org/abs/1007.4707v1

Computer Science

Neural and Evolutionary Computing

19 pages, 2 figures

Scientific paper

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.

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