Sample based crowding method for multimodal optimization in continuous domain

We proposed a selection scheme called sample-based crowding, which is aimed to improve the performance of genetic algorithms for multimodal optimization in ill-scaled and locally multimodal domains. These domains can be problematic for conventional approaches, but are commonly found in real-world optimization problems. The principle of crowding is to apply a tournament selection to a parent-child pair with a high similarity. In the sample-based crowding, we determine such pairs based on a statistical comparison of the fitness values, which are sampled from the region between the pairs. Further, we take into account the ranks of the parents among the sampled values in the selection process, to determine their indispensability. These measurements are scale-invariant, which enables the proposed method to search a domain without presuming the distance between the optima or the scaling and the correlation of the variables. The proposed approach is evaluated in two benchmark problems with an ill-scaled and a locally multimodal landscape. The proposed method has a substantial advantage in terms of comprehensiveness compared to the conventional approaches, despite the additional cost of evaluations.