Selecting strategies in particle swarm optimization by sampling-based landscape modality detection using inner products

In population-based optimization algorithms (POAs) such as particle swarm optimization (PSO), if landscape modality of an objective function can be identified, strategies of the POAs can be selected properly. We have proposed a method that estimates the landscape modality by sampling some points along a line and counting the number of changes in the objective values from increasing to decreasing and vice versa. In the method, the range of sampling on the line cannot be decided when the width of the search points in a dimension is zero. In this study, we propose to determine the range using inner products and also we propose to select a proper strategy according to the landscape modality: The gbest model is selected in unimodal landscape and the lbest model is selected in multimodal landscape. Also, a simple parameter selection for unimodal landscape is introduced. The advantage of the proposed method is shown by solving various problems including unimodal and multimodal problems and by comparing the results of the proposed method with those of the gbest and lbest model of PSO.