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

Area of Science:

• Computational Intelligence
• Optimization Algorithms
• Swarm Intelligence

Background:

• The standard Besiege and Conquer Algorithm (BCA) faces challenges with diversity loss and premature convergence in complex optimization landscapes due to its fixed search regulation.
• Continuous optimization problems require algorithms that can maintain diversity and adapt exploration-exploitation balance.

Purpose of the Study:

• To propose and evaluate a novel Brownian motion-enhanced Besiege and Conquer Algorithm (BM-BCA) designed to overcome the limitations of the original BCA.
• To improve the search accuracy, convergence stability, and robustness of swarm-based metaheuristics for continuous optimization.

Main Methods:

• Introduced a Brownian motion-enhanced Besiege and Conquer Algorithm (BM-BCA) incorporating three key mechanisms: distance-scaled Brownian motion mutation, convergence-trend-guided BCB regulation, and hierarchical army-soldier updates.
• Evaluated BM-BCA on 29 IEEE CEC-2017 benchmark functions and three constrained engineering design problems, performing 30 independent runs for each.

Main Results:

• BM-BCA achieved superior performance compared to the original BCA and LSHADE on the CEC-2017 benchmark functions, demonstrated by Friedman mean ranks and win/tie/loss records.
• In higher dimensions (100-D), BM-BCA maintained competitiveness with significantly reduced CPU time compared to LSHADE.
• Ablation studies confirmed the effectiveness of the proposed enhancements, with BM-BCA outperforming the original BCA on 28 out of 29 functions.

Conclusions:

• The proposed BM-BCA effectively enhances diversity preservation and adaptive exploration-exploitation control in continuous optimization.
• BM-BCA demonstrates improved search accuracy, convergence stability, and robustness over the standard BCA while maintaining similar asymptotic complexity.
• The integrated framework of BM-BCA offers a promising advancement for swarm-based metaheuristics in tackling complex optimization tasks.