Measuring the curse of dimensionality and its effects on particle swarm optimization and differential evolution

The existence of the curse of dimensionality is well known, and its general effects are well acknowledged. However, and 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. The divergence of these growth rates has important effects on the parameters used in particle swarm optimization and differential evolution as dimensionality increases. New experiments focus on the effects of population size and key changes to the search characteristics of these popular metaheuristics when population size is less than the dimensionality of the search space. Results show how design guidelines developed for low-dimensional implementations can become unsuitable for high-dimensional search spaces.