Based on binary evolution operator-enhanced black-kite algorithm with natural replacement for engineering numerical optimization problems.

This study proposes an enhanced Black-kite Algorithm (BKA), termed SMNBKA-ICMIC, to improve optimization performance. The algorithm introduces four key improvements: ICMIC-based initialization to enhance population diversity, integration of the Simulated Binary Crossover (SBX) operator to strengthen exploration, a refined position-update formula of migration to mitigate premature convergence, and a novel natural replacement mechanism to balance global and local search. The SMNBKA-ICMIC demonstrates exceptional performance in benchmark functions from CEC 2017, 2020, and 2022, securing the top rank from best value in these tests. Additionally, the algorithm demonstrates superior performance across a diverse set of representative benchmarks. It achieves the top of best value in 9 out of 10 complex engineering optimization problems—chosen for their relevance to real-world design and control challenges—and exhibits remarkable effectiveness in the canonical multi-knapsack problem, a standard test for combinatorial optimization. These results validate SMNBKA-ICMIC as a state-of-the-art metaheuristic, ensuring robust convergence and practical utility for complex numerical optimization.