Three Kingdoms Optimization Algorithm: An Efficient Optimization Approach

Abstract: Real-world engineering optimization problems frequently exhibit narrow feasible regions, multiple local optima, and complex equality/inequality constraints that pose significant resolution challenges. Metaheuristic algorithms (MAs) demonstrate inherent advantages in addressing such problems through their global search capabilities, operational flexibility, and adaptive mechanisms. However, the critical balance between exploration and exploitation phases in MAs substantially influences optimization efficiency and precision, necessitating algorithmic modifications to regulate convergence behavior when applied to engineering optimization scenarios. This requirement significantly escalates implementation costs. Furthermore, existing problem-specific algorithmic enhancements lack comprehensive evaluations of generality and robustness, with questionable adaptability across varying dimensionalities. Therefore, it is imperative to design a high-performance optimization algorithm with superior adaptability. Inspired by historical evolutionary patterns from the Three Kingdoms period, this paper proposes the Three Kingdoms Optimization Algorithm (KING). We establish conceptual analogies between fundamental components of MAs—population initialization, global exploration, local exploitation, and convergence enhancement strategies—and four historical phases: the ascent of the might, joint confrontation, three-legged tripod, and whole country united. KING introduces an innovative reinforcement convergence mechanism that systematically guides algorithmic convergence while maintaining equilibrium between exploration and exploitation, thereby enabling efficient and rapid convergence. Furthermore, KING incorporates dynamic equality tolerance-based constraint-handling techniques to strengthen its adaptability for complex constrained optimization problems. Algorithmic performance across diverse problem scales has been rigorously validated through comprehensive comparisons with classical algorithms, high-performance variants, and state-of-art methods using IEEE CEC 2017 and IEEE CEC 2022 benchmark function test suites across multiple dimensions. Empirical results demonstrate KING's superior performance in convergence speed, solution accuracy, and stability. Furthermore, KING exhibits significant advantages over comparative algorithms when applied to four practical engineering optimization problems. Thus, KING can serve as an effective optimization tool for addressing engineering optimization issues. The source codes of KING will be publicly available over related websites.

Three Kingdoms Optimization Algorithm (KING): KING is an innovative optimization algorithm inspired by historical evolutionary patterns from the Three Kingdoms period. It uses a combination of global exploration and local exploitation strategies to effectively tackle complex optimization problems. The following provides a detailed overview of the fundamental components and processes involved in KING.

Conceptual Foundation: KING mimics the historical evolutionary patterns from the Three Kingdoms period, establishing analogies between fundamental components of metaheuristic algorithms and four historical phases. The algorithm's design reflects the strategic balance and dynamic interactions of historical events, enabling effective exploration and exploitation of the solution space.

Algorithm Structure: The KING algorithm consists of several distinct phases, each contributing to the optimization process:

Reinforcement Convergence Mechanism: KING introduces an innovative reinforcement convergence mechanism that systematically guides algorithmic convergence while maintaining equilibrium between exploration and exploitation, thereby enabling efficient and rapid convergence.

Constraint-Handling Techniques: KING incorporates dynamic equality tolerance-based constraint-handling techniques to strengthen its adaptability for complex constrained optimization problems.

Historical Phase Analogies: The algorithm establishes conceptual analogies between fundamental components of metaheuristic algorithms and four historical phases from the Three Kingdoms period.

Summary of KING Stages: To summarize, KING incorporates several key mechanisms inspired by the Three Kingdoms historical patterns:

The KING algorithm starts with an initialized population and iteratively applies exploration, exploitation, and convergence enhancement strategies to optimize solutions for complex engineering problems.