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Motivated by Leinster-Cobbold measures of biodiversity, the notion of the spread of a finite metric space is introduced. This is related to Leinster’s magnitude of a metric space. Spread is generalized to infinite metric spaces equipped with a measure and is calculated for spheres and straight lines. For Riemannian manifolds the spread is related to the volume and total scalar curvature. A notion of scale-dependent dimension is introduced and seen for approximations to certain fractals to be numerically close to the Minkowski dimension of the original fractals.

Improved ant colony optimization (ACO) algorithms for continuous-domain optimization have been widely applied in recent years, but these improved methods have a weak perception of environmental information changes and only rely on the residues of the pheromones in the path to guide colony evolution. In this paper, we propose an ant colony algorithm based on the reinforcement learning model (RLACO). RLACO can acquire more environmental information by calculating the diversity of the ant colony, and, uses the diversity and other basic information of the ant colony to establish a reinforcement learning model. At different stages of evolution, the algorithm chooses an optimal strategy that can maximize the reward to improve the global search ability and convergence speed of the colony. The experimental results on CEC 2017 test functions show that the proposed algorithm is superior to other algorithms for continuous-domain optimization in convergence speed, accuracy and global search ability.