本研究主要為應用萬用啟發式演算法(Metaheuristic)中的和弦演算法(Harmony Search;HS)來求解Chang等學者(2000)透過權重的設計,改良Markowitz(1952)的平均-變異數模型,所發展之同時考量報酬最大化與風險最小化的多目標投資組合問題。針對此問題之特性,本研究設計ㄧ混合式編碼之架構,且利用和弦演算法的和弦記憶空間、調音及隨機產生等三種機制產生新解,以達到平衡探索(Exploitation)與開發(Exploration)的作用,及有效率地產生高品質的解。根據各機制的調整,本研究共計提出十一種不同的和弦演算法架構,並利用OR-Library提供的五種全球性股市,介於1992年3月與1997年9月之間的實際數據進行測試,並與文獻中之模擬退火法(Simulated Annealing;SA)、禁忌搜尋法(Tabu Search;TS)與變動鄰域搜尋法(Variable Neighborhood Search;VNS)進行比較;和弦演算法於各例題中的表現皆優於文獻中的方法,為多目標投資組合最佳化問題提供一優異之求解方案。
This study proposes a harmony search algorithm for solving constrained portfolio optimization problems with the objective of investment return maximization and risk minimization according to Chang et al. (2000) which is based on the mean-variance model of Markowitz (1952). This study develops a hybrid encoding to deal with both continuous and combinatorial properties of the problem. The proposed algorithms employ harmony memory consideration, pitch adjustment and random search to achieve the balance between exploitation and exploration and generate high-quality new solutions effectively. The performance of the eleven proposed HS variations is tested using five global stock market indexes provided by the OR-Library from March 1992 to September 1997. The results of proposed HS algorithms are also compared with SA, TS and VNS algorithms in the literature. HS outperforms all the competing algorithms in all five test data sets, and proves to be a promising alterative in solving portfolio optimization problems.