Chaos-BBO: Chaos balanced butterfly optimizer with dynamic continuum chaotic strategies and its applications

To address the real-world constrained engineering optimization problem (CEOP) and the breast cancer classification task using a high-performance heuristic approach, a novel Chaos balanced butterfly optimizer, named Chaos-BBO, was proposed with chaos regulation strategies for the smell dynamic parameter \(C_1\) and balance dynamic parameter \(C_2\). The basic BBO algorithm was inspired by the smell and light perception of the special butterfly. Notably, this article collected twelve continuum chaotic mappings with one-dimensional, which has some differences from the common ten chaos mappings. we collected twelve continuum chaotic mapping functions to expand their application scope in the swarm intelligent (SI) algorithm, and their chaotic properties were also depicted in detail. Twenty-three CEC and nine CEC2022 benchmark functions were applied to evaluate the performance of the designed Chaos-BBO, which was compared to FA, GWO algorithm, BOA, HHO algorithm, SMA, JS algorithm, AO algorithm, AHA, and HBA expert for the basic BBO algorithm. Then, Friedman rank and Wilcoxon rank-sum (WRS) tests were utilized to analyze the statistical properties and rankings of the comparison methods. Finally, the proposed Chaos-BBO was utilized to address eight CEOPs and the breast cancer classification task. The results of the numerical optimization and application tasks demonstrated the superiority of the designed Chaos-BBO approach.