KING: An efficient optimization approach

Abstract

Real-world engineering optimization problems are often highly challenging due to narrow feasible regions, numerous local optima, and intricate constraints. Metaheuristic algorithms (MAs) have shown promise in addressing these issues owing to their global search capability, flexibility, and adaptability. However, a critical challenge with MAs is effectively balancing the global search (exploration) and local search (exploitation) phases, which significantly influences the efficiency and precision of convergence. Many MAs require problem-specific adjustments to control convergence behavior, thereby increasing computational cost and implementation effort. Moreover, existing improvements are often tailored to specific problems, lacking comprehensive validation in terms of generality, robustness, and scalability. To overcome these limitations, this paper proposes a novel high-performance optimization algorithm with enhanced adaptability, named the Three Kingdoms Optimization Algorithm (KING), inspired by historical dynamics of the Three Kingdoms period in China. We establish an analogy between key components of MAs—such as population initialization, exploration, and exploitation—and four historical phases: the ascent of the might, joint confrontation, three-legged tripod, and whole country united. KING incorporates a new reinforcement convergence mechanism to systematically guide the search process while maintaining an effective balance between exploration and exploitation, enabling rapid and efficient convergence. Additionally, a dynamic, tolerance-based constraint-handling technique is introduced to strengthen its capability in solving complex constrained problems. The performance of KING is extensively evaluated on the IEEE CEC 2017 and IEEE CEC 2022 benchmark test suites, comparing it with classical algorithms, high-performance variants, and state-of-the-art methods across problems of varying scales. Experimental results demonstrate that KING outperforms the compared algorithms in convergence speed, solution accuracy, and stability. Its superiority is further validated through applications to four real-world engineering problems. The proposed algorithm proves to be an effective and reliable tool for engineering optimization. Its source code will be made publicly available at https://aliasgharheidari.com/KING.html and other websites.