Lens imaging opposition-based learning for differential evolution with cauchy perturbation

Opposition-based learning (OBL) is an effective optimization strategy that enhances the performance of various global optimization algorithms. Among these algorithms, differential evolution (DE) based on OBL has received the attention of many researchers. However, OBL is a strategy with relative symmetry between the target point and the opposite point, which does not contribute significantly to the population in the later stage of the algorithm, and tends to disregard more meaningful points around the opposite points. Therefore, we propose a novel opposition-based differential evolution based on the principle of convex lens (LensOBLDE), which utilizes the distance relationship between the target point and the focal length of the lens, and dynamically adjusts the search radius by controlling the parameters, thus further improving the search ability. In addition, to avoid the algorithm from falling into a local optimum, a small-scale and low-probability cauchy perturbation strategy is applied to the elite individuals in the population, which ensures the exploration and exploitation of the algorithm. Finally, LensOBLDE evaluates the performance of several advanced algorithms on the CEC2017 benchmark suite and conducts a statistical test to evaluate the difference between algorithms. The results indicate that LensOBLDE outperforms several algorithms with a significant difference between them. This verifies the effectiveness of the strategies newly added in this study.