Historical knowledge-based MBO for global optimization problems and its application to clustering optimization

Monarch butterfly optimization (MBO), which is a simple and widely used algorithm, has some limitations, such as utilizing the obtained experiential knowledge about the search space inefficiently, the lack of exploration, and being rotational variance. This paper proposes a new variation of MBO, which is called knowledge-based MBO (KMBO), to address these limitations. KMBO is proposed by introducing new operators that are linearized and can utilize the population's experimental knowledge. Furthermore, KMBO adopts the re-initialization operator to enhance the exploration ability and increase the diversity of the population. To verify KMBO’s performance, it is tested on 23 well-known optimization benchmark functions and compared with MBO and five other state-of-the-art evolutionary algorithms. Experimental results confirm the superior performance of our proposed algorithm compared with MBO in terms of solution accuracy and convergence speed. Also, results demonstrate that KMBO performs better than or provides competitive performance with the other six algorithms. In addition, the real-world application of KMBO on clustering optimization is presented. The results prove that KMBO is applicable to solve real-world problems and achieve superior results.