Identifying and exploiting the scale of a search space in particle swarm optimization

Multi-modal optimization involves two distinct tasks: identifying promising attraction basins and finding the local optima in these basins. Unfortunately, the second task can interfere with the first task if they are performed simultaneously. Specifically, the promise of an attraction basin is often estimated by the fitness of a single sample solution, so an attraction basin represented by a random sample solution can appear to be less promising than an attraction basin represented by its local optimum. The goal of thresheld convergence is to prevent these biased comparisons by disallowing local search while global search is still in progress. Ideally, thresheld convergence achieves this goal by using a distance threshold that is correlated to the size of the attraction basins in the search space. In this paper, a clustering-based method is developed to identify the scale of the search space which thresheld convergence can then exploit. The proposed method employed in the context of a multi-start particle swarm optimization algorithm has led to large improvements across a broad range of multi-modal problems.