Some measurements on the effects of the curse of dimensionality

Abstract

The existence of the curse of dimensionality is well known, and its general effects are well acknowledged. However, perhaps due to this colloquial understanding, specific measurements on the curse of dimensionality and its effects are not as extensive. In continuous domains, the volume of the search space grows exponentially with dimensionality. Conversely, the number of function evaluations budgeted to explore this search space usually grows only linearly. New experiments show that particle swarm optimization and differential evolution have super-linear growth in convergence time as dimensionality grows. When restricted by a linear growth in allotted function evaluations, this super-linear growth in convergence time leads to a decrease in the allowed population size.