人工蜂群演算法於投資組合最佳化問題之應用

Artificial Bee Colony Algorithms for Portfolio Optimization Problems

劉佳倩(Chia-Chien Liu)

指導教授 ： 梁韵嘉

元智大學/工程學院/工業工程與管理學系/碩士(2011年)

摘要

由於現今全球經濟成長趨緩，微薄的薪資與定期存款之利息無法因應通貨膨脹所造成的影響，因此投資理財已成為大眾關注之重要焦點。人工蜂群演算法（Artificial Bee Colony；ABC）為近年來於最佳化領域中受到關注的萬用啟發式演算法之一，其為模擬自然界中蜜蜂覓食行為之原理所發展的一種群體智慧演算法（Swarm Intelligence）。因此，本研究使用人工蜂群演算法求解投資組合最佳化問題（Portfolio Optimization Problem），為投資者提供有效之投資組合，作為投資參考之依據。本研究以Markowitz之平均數-變異數模型（Mean-Variance Portfolio Model；M-V模型）為基礎，針對不同屬性之投資者分別考慮下方標準差（Downside Standard Deviation；DSD）與上方標準差（Upside Standard Deviation；USD）適當修正投資組合模型，以人工蜂群演算法以不同資料期間及不同規模大小之例題求解各不同模型，並與變動鄰域搜尋法（Variable Neighborhood Search；VNS）、模擬退火演算法（Simulated Annealing；SA）及禁忌搜尋演算法（Tabu Search；TS）進行比較。結果顯示人工蜂群演算法具有較佳之績效，尤其以考慮柏拉圖選取策略之ABC II表現最佳，也成功驗證本研究提出之人工蜂群演算法適用於求解投資組合最佳化問題，並提供不同屬性之投資者作為投資參考之依據。

關鍵字

人工蜂群演算法 ； 投資組合最佳化問題 ； 平均數-變異數模型

並列摘要

As global economy of today is slowdown and meager salary and interest of term deposit can’t adjust to the impact of inflation, financial investment has become an important focus of public concern. Artificial Bee Colony (ABC), one of metaheuristic algorithms, has attracted lots of attention in optimization field in recent years. ABC, employing the idea of swarm intelligence, simulates the principle of bee foraging behavior in the nature. Thus, this study adopts ABC to solve Portfolio Optimization Problem, and to provide effective portfolio as a reference basis of investment for investors. This study, based on Markowitz’s famous Mean-Variance Portfolio Model (M-V Model), aims at considering Downside Standard Deviation (DSD) and Upside Standard Deviation (USD) respectively and modifying the M-V model to fit the demands of different types of investors. Several well-known stock market indexes over different periods of time are tested to verify the modified models and the performance of the proposed ABC algorithms. The results are also compared with the ones obtained by Variable Neighborhood Search (VNS), Simulated Annealing (SA) and Tabu Search (TS) algorithms in the literatures. The results show that ABC performs better in terms of diversity, convergence, and effectiveness, particularly in ABC II when a Pareto front selection strategy is considered. Thus, ABC in this study is suitable for solving Portfolio Optimization Problem, and is able to provide valuable portfolio for investors with different attributes.

並列關鍵字

Artificial Bee Colony ； Portfolio Optimization Problem ； Mean-Variance Portfolio Model

參考文獻

Armananzas, R. and Lozano, J. A. (2005). "A multiobjective approach to the portfolio optimization problem," Proceedings of the IEEE Congress on Evolutionary Computation, Vol. 2, pp. 1388–1395.

Chang, T. J., Meade, N., Beasley, J. E. and Sharaiha, Y. M. (2000). "Heuristics for cardinality constrained portfolio optimization," Computers and Operations Research, Vol. 27, pp. 1271–1302.

Chang, T. J., Yang, S. C. and Chang. K. J. (2009). "Portfolio optimization problems in different risk measures using genetic algorithm," Expert Systems with Applications, Vol. 37(7), pp. 10529–10537.

Chen, Y. and Zhu, H. (2010). "PSO heuristics algorithm for portfolio optimization," Advances in Swarm Intelligence, Vol. 6145, pp. 183–190.

Chyu, C. C. and Chang, W. S. (2010). "A pareto evolutionary algorithm approach to bi-objective unrelated parallel machine scheduling problems," The International Journal of Applied Management and Technology, Vol. 49, pp. 697–708.