Weighted local sharing and local clearing for multimodal optimisation

Abstract

Local sharing is a method designed for efficient multimodal optimisation that combines fitness sharing with spatially structured populations and elitist replacement. In local sharing, the bias towards sharing and the influence of spatial structure is controlled by the deme (neighbourhood) size. This introduces an undesirable trade-off; to maximise the sharing effect large deme sizes must be used, but the opposite must be true if one wishes to maximise the influence of spatial population structure. This paper introduces two modifications to the local sharing method. The first alters local sharing so that parent selection and fitness sharing operate at two different spatial levels; parent selection is performed within small demes, while the effect of fitness sharing is weighted according to the distance between individuals in the entire population structure. The second method replaces fitness sharing within demes with clearing to produce a method that we call local clearing. The proposed methods, as tested on several benchmark problems, demonstrate a level of efficiency that surpasses that of traditional fitness sharing and standard local sharing. Additionally, they offer a level of parameter robustness that surpasses other elitist niching methods, such as clearing. Through analysis of the local clearing method, we show that this parameter robustness is a result of the isolated nature of the demes in a spatially structured population being able to independently concentrate on subsets of the desired optima in a fitness landscape.