On the Invariance of Ant Colony Optimization

@article{Birattari2007OnTI,
  title={On the Invariance of Ant Colony Optimization},
  author={M. Birattari and Paola Pellegrini and Marco Dorigo},
  journal={IEEE Transactions on Evolutionary Computation},
  year={2007},
  volume={11},
  pages={732-742}
}
Ant colony optimization (ACO) is a promising metaheuristic and a great amount of research has been devoted to its empirical and theoretical analysis. Recently, with the introduction of the hypercube framework, Blum and Dorigo have explicitly raised the issue of the invariance of ACO algorithms to transformation of units. They state (Blum and Dorigo, 2004) that the performance of ACO depends on the scale of the problem instance under analysis. In this paper, we show that the ACO internal state… 
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TLDR
This paper proposes a new framework for implementing ant colony optimization algorithms called the hyper-cube framework, which limits the pheromone values to the interval [0,1], and proves that in the ant system, the ancestor of all ant colony optimized algorithms, the average quality of the solutions produced increases in expectation over time when applied to unconstrained problems.
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In this paper some examples of combinatorial optimization problems to which ant colony optimization can be applied in an invariant fashion are described.
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