Abstract:
This paper illustrates the importance of independent, component-wise stochastic scaling values, from both a theoretical and empirical perspective. It is shown that a swarm employing scalar stochasticity is unable to express every point in the search space if the problem dimensionality is sufficiently large in comparison to the swarm size. The theoretical result is emphasized by an empirical experiment, comparing the performance of a scalar swarm on benchmarks with reachable and unreachable optima. It is shown that a swarm using scalar stochasticity performs significantly worse when the optimum is not in the span of its initial positions. Lastly, it is demonstrated that a scalar swarm performs significantly worse than a swarm with component-wise stochasticity on a large range of benchmark functions, even when the problem dimensionality allows the scalar swarm to reach the optima.
