本研究提出一個創新的混合元啟發式演算法，名為分層協作最佳化演算法（Stratified Collaboration Optimization, SCO）。SCO演算法受社會階層的概念所啟發，藉由分層的方式混合兩種不同性質的元啟發式演算法，平衡演算法於探索和利用階段的表現。本演算法採用排序機制將候選解依照性能指標（Performance Index）進行排名，排名較佳的候選解屬於較高的社會階層，由灰狼最佳化演算法（Grey Wolf Optimizer, GWO）進行搜索；反之則屬於較低的社會階層，由差分進化演算法（Differential Evolution, DE）進行搜索。在SCO中，上層具備優秀的利用能力，下層則有較為突出的探索能力，藉由社會流動機制的設計，我們試圖在探索與利用間達成平衡。在實驗的部分，第四章的實驗中我們經由二十九個測試函數（Benchmark function）評估演算法的效能與性質，並於可擴展維度函數實驗中，評估SCO與其他演算法於高維度情況下之表現；第五章則為約束型函數實驗，實驗中進一步評估演算法在受約束條件所規範的函數中，找尋最佳解的能力，這一類的問題更貼近實務上會遇到的最佳化問題，更能評估演算法面對複雜問題的能力；第六章中我們將演算法與球型複數模糊集（Sphere Complex Fuzzy Sets, SCFSs）模型結合，應用於金融時間序列預測問題上，此章節的實驗旨在驗證演算法於現實問題中的可用性，並為演算法提供潛在應用的方向。後續的章節中，本研究就實驗結果對所提出之演算法的性質進行了討論，包含混合元啟發式演算法中演算法間的協作分析，以及SCO演算法之探索與利用分析，有助於對實驗結果進行系統性的整理。;This study proposes an innovative hybrid metaheuristic algorithm called Stratified Collaboration Optimization (SCO). Inspired by the concept of social hierarchy, the SCO algorithm integrates two different types of metaheuristic algorithms in a stratified manner to balance performance during the exploration and exploitation phases. The algorithm uses a ranking mechanism to order candidate solutions based on a performance index. Higher-ranked candidates belong to a higher social stratum and are searched using the Grey Wolf Optimizer (GWO), while lower-ranked candidates belong to a lower social stratum and are searched using the Differential Evolution (DE) algorithm. In SCO, the upper group excels in exploitation capabilities, while the lower group is characterized by superior exploration abilities. This design of the social mobility mechanism aims to achieve a balance between exploration and exploitation. In the experimentation, Chapter 4 evaluates the algorithm′s performance and characteristics using 29 benchmark functions, and assesses the performance of SCO and other algorithms in high-dimensional scenarios through scalable dimension function experiments. Chapter 5 focuses on constrained function experiments, further evaluating the algorithm′s ability to find optimal solutions in functions regulated by constraints. These types of problems are more akin to practical optimization issues and better test the algorithm′s capability in handling complex problems. In Chapter 6, we combine the algorithm with the Sphere Complex Fuzzy Sets (SCFSs) model and apply it to financial time series forecasting. The experiments in this chapter aim to verify the algorithm′s applicability to real-world problems and provide potential application directions for the algorithm. In subsequent chapters, this study discusses the characteristics of the proposed algorithm based on experimental results, including an analysis of the collaboration between the algorithms and an exploration and exploitation analysis of the SCO algorithm. These discussions help to systematically organize and interpret the experimental results.
