A Multi-Strategy Black-Winged Kite Algorithm with Bi-Stage Balanced Selection and Equilibrium-Enhanced Attack for Numerical and Engineering Optimization

The Black-winged Kite Algorithm (BKA) is a bio-inspired meta-heuristic that emulates the raptor’s migratory and hunting behaviors. Despite its high adaptability, minimal parameter tuning, and competitive accuracy, the BKA tends to stagnate prematurely and exhibits slow tail convergence on complex landscapes. To address these drawbacks, we propose a Multi-Strategy Black-Winged Kite Algorithm (MSBKA) that incorporates three synergistic enhancements. First, a bi-stage fitness and distance balanced selection (BFS) is introduced to dynamically calibrate the trade-off between exploration and exploitation while supplying diverse leaders that preserve population diversity. Second, a hybrid equilibrium strategy (HES) grafts the search operator of the Equilibrium Optimizer into the attack phase, endowing the swarm with multi-directional momentum for escaping local optima and refining global convergence accuracy. Finally, a leader-based boundary control (LBS) repairs out-of-bound individuals by repositioning them around the incumbent best, eliminating redundant evaluations and accelerating overall convergence. We evaluated the proposed framework through ablation studies and comparative trials against seven recently introduced meta-heuristic variants, including ESLPSO, GLS-MPA, AFDBARO, EOSMA, ALSHADE, TERIME, and EMTLBO. These experiments were conducted on the CEC 2017 and CEC 2022 test suites. The MSBKA achieved the best average rank of 1.810 on CEC 2017 and 2.250 on CEC 2022. In addition, the algorithm was applied to three constrained engineering design problems, demonstrating its practical utility. Overall, the experimental results demonstrate that the MSBKA exhibits competitive global exploration and local exploitation capabilities, together with stable convergence behavior on the tested benchmark problems, indicating its potential applicability to real-world engineering optimization.