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Identifying and exploiting the scale of a search space in differential evolution

Optimisation in multimodal landscapes involves two distinct tasks: identifying promising regions and location of the (local) optimum within each region. Progress towards the second task can interfere with the first by providing a misleading estimate of a region's value. Thresheld convergence is a generally applicable “meta”-heuristic designed to control an algorithm's rate of convergence and hence which mode of search it is using at a given time. Previous applications of thresheld convergence in differential evolution (DE) have shown considerable promise, but the question of which threshold values to use for a given (unknown) function landscape remains open. This work explores the use of clustering-based method to infer the distances between local optima in order to set a series of decreasing thresholds in a multi-start DE algorithm. Results indicate that on those problems where normal DE converges, the proposed strategy can lead to sizable improvements.