Adaptive Brownian motion and convergence-trend-driven strategies for enhancing the Besiege and Conquer algorithm

The Besiege and Conquer Algorithm (BCA) is a swarm-based metaheuristic for continuous optimization, but its fixed BCB-controlled search regulation can cause rapid diversity loss and premature convergence on complex landscapes. To address these limitations, this paper proposes a Brownian motion-enhanced Besiege and Conquer Algorithm (BM-BCA). BM-BCA redesigns the search process of BCA through three coordinated mechanisms: a distance-scaled Brownian motion mutation for diversity preservation, a convergence-trend-guided BCB regulation strategy for adaptive exploration-exploitation control, and a hierarchical army-soldier update mechanism for local candidate refinement. The proposed algorithm is evaluated on 29 IEEE CEC-2017 benchmark functions and three constrained engineering design problems, with 30 independent runs conducted for each benchmark function. On the 50-dimensional CEC-2017 suite, BM-BCA obtains the best Friedman mean rank of 2.03 and achieves wins/ties/losses of 24/4/1 against the original BCA and 20/5/4 against LSHADE. In the 100-dimensional setting, BM-BCA remains competitive while requiring an average CPU time of 1.613 s, substantially lower than LSHADE (11.485 s). The ablation study further shows that BM-BCA outperforms the original BCA on 28 out of 29 functions, confirming the effectiveness of the proposed improvement framework. These results demonstrate that BM-BCA improves the search accuracy, convergence stability, and robustness of BCA while preserving the same asymptotic complexity order.