Modified Black-Winged Kite Optimization Algorithm with Three-Phase Attacking Strategy and Lévy–Cauchy Migration Behavior to Solve Mathematical Problems

The Black-winged Kite Algorithm (BKA) is a novel heuristic optimization algorithm proposed in 2024, which has demonstrated superior optimization performance on most CEC benchmark functions and several engineering problems. To further enhance its convergence accuracy and solution quality, this paper proposes a Modified Black-winged Kite Algorithm (MBKA). First, a three-phase attacking strategy is designed to replace the original BKA's attacking mechanism, thereby enhancing population diversity and improving solution quality. Additionally, a Lévy-Cauchy migration strategy is incorporated to achieve a more effective balance between exploration and exploitation. The effectiveness of MBKA is assessed through extensive experiments on 18 classical benchmark functions, the CEC-2017 and CEC-2022 test suites, and two real-world engineering optimization problems. The results indicate that MBKA consistently outperforms the original BKA and several state-of-the-art algorithms in both convergence accuracy and convergence speed across most test cases.