بهینه‌سازی سبدسهام چندهدفه با استفاده از رویکرد جدید بهینه‌سازی کرم میوه
محورهای موضوعی :
مدیریت صنعتی
Amir Amini
1
,
alireza alinezhad
2
1 - Department of Industrial Engineering, Sistan And Balouchestan University
2 - Associate Professor, Department of Industrial Engineering, Faculty of Industrial and Mechanical Engineering, Qazvin branch, Islamic Azad University, Qazvin, Iran.
تاریخ دریافت : 1394/12/05
تاریخ پذیرش : 1395/04/28
تاریخ انتشار : 1395/06/04
کلید واژه:
بهینه سازی سبد سهام,
محدودیت های کلاس و عدد صحیح,
برنامه ریزی غیر خطی درجه دوم,
الگوریتم بهینه‌سازی کرم میوه,
Multi-Objective Portfolio Optimization Model,
Fruit Fly Optimization Algorithm,
Integer Constraint,
Class Constraint,
چکیده مقاله :
یکی از معروفترین مسائل بهینه سازی در حوزه مهندسی مالی مسأله بهینه سازی سبد سهام می باشد. این مسأله در ساده ترین شکل خود به انتخاب سبدی از دارایی های مختلف می پردازد در حالیکه سعی در کمینه نمودن ریسک سبد انتخابی با توجه به محدودیت های تعریف شده نظیر محدودیت بودجه و عدد صحیح دارد. بطور کلی سرمایه گذاران ترجیح می دهند به جای سرمایه گذاری در یک دارایی، در چند دارایی سرمایه گذاری نموده تا به این وسیله با تنوع بخشی به سرمایه گذاری خود ریسک غیر سیستماتیک را کاهش دهند. مدل های محاسباتی پیچیده ای برای حل این مسأله توسعه یافته اند که برای بسیاری از آن ها حل بهینه ای وجود ندارد. در این مقاله، از یک رویکرد ابتکاری و فرا ابتکاری جدید بنام الگوریتم کرم میوه برای حل مسأله‌ای چند هدفه بر مبنای مدل میانگین- واریانس مارکوییتز با محدودیت های دسته‌بندی و عدد صحیح استفاده شده است. الگوریتم بهینه‌سازی حشره میوه (FOA) یک روش جدید برای یافتن جواب بهینه سراسری بر مبنای رفتار حشره میوه در پیدا کردن غذا می‌باشد. تا کنون مطالعات اندکی روی این الگوریتم صورت گرفته است و تقریباً هیچ یک از کارهای انجام شده از این الگوریتم برای حل مسأله بهینه سازی سبد سهام استفاده ننموده اند. نتایج بدست آمده نشان دهنده عملکرد نسبی بهتر این الگوریتم نسبت به الگوریتم ژنتیک برای مجموعه داده‌های بورس تهران می‌باشد.طبقه بندی JEL: G1, P5, O3
چکیده انگلیسی:
One of the most famous optimization problems in the field of financial engineering is portfolio selection problem. In its simplest form, while trying to minimize risk in the portfolio selection according to defined constraints such as budget and integer constraints it deals with selecting a basket of various assets. Generally, investors prefer to invest in some assets rather than investing in only one asset to reduce unsystematic risk by diversifying their investment. Complex computational models have been developed to solve this problem and there is not an optimal solution for many of them. In this paper, a new and innovative approach known as fruit fly optimization algorithm (FOA) is used for multi-objective problem solving based on mean-variance Markowitz problem with class and cardinality constraints. Fruit fly optimization algorithm is a new way to find the overall optimal solution based on the behavior of the fruit fly in finding food. So far, few studies have been done on this algorithm and almost none of them used this algorithm for portfolio optimization problem. The results indicated the better comparative performance of the algorithm compared to the genetic algorithm for data set of Tehran stock exchange.JEL classification: G1, P5, O3
منابع و مأخذ:
Abidin, Z. Z., Arshad, M. R., & Ngah, U. K. (2011). A simulation based fly optimization algorithm for swarms of mini autonomous surface vehicles application. Indian J. Geo-Mar. Sci. 40(2), 250–266.
Anione, S., Loraschi, A., & Tettamanzi, A. (1993). A genetic approach to portfolio selection. Neural Network World, 6(93), 597-604.
Aryanezhad, M. B., & Hemati, M. (2008). A new genetic algorithm for solving non convex nonlinear programming problems. Applied Mathematics and Computation, 199(1), 186–194.
Chang, T.J., Meade N., Beasley, J.E., & Sharaiha, Y.M. (2000). Heuristics for cardinality constrained portfolio optimization. Computers and Operations Research, 27(13), 1271-1302.
Crama, Y., & Schyns, M. (2003). Simulated annealing for complex portfolio selection problems. European Journal of operational research, 150(3), 546-571.
Cura, T. (2009). Particle swarm optimization approach to portfolio optimization. Nonlinear Analysis: Real World Applications, 10(4), 2396-2406.
Deb, K., Pratap, A., Agarwal, S., & Meyarivan, T. A. M. T. (2002). A fast and elitist multi objective genetic algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation, 6(2), 182–197.
Dueck, G., & Winker, P. (1992). New concepts and algorithms for portfolio choice. Applied Stochastic Models and Data Analysis, 8(3), 159-178.
Fernández, A., & Gómez, S. (2007). Portfolio selection using neural networks. Computers & operations research, 34(4), 1177-1191.
Gilli, M., Këllezi, E., & Hysi, H. (2006). A data-driven optimization heuristic for downside risk minimization. Journal of Risk, 8(3), 1.
Han, J., Wang, P., & Yang, X. (2012). Tuning of PID controller based on fruit fly optimization algorithm. International Conference on Mechatronics and Automation (ICMA): 409–413.
Holland, J. H. (1975). Adaptation in natural and artificial systems: An introductory analysis with applications to biology, control, and artificial intelligence. University of Michigan Press.
Kennedy, J., & Eberhart, R. (1995). Particle Swarm Optimization. Proceedings of IEEE International Conference on Neural Networks IV, 1942–1948.
Konno, H., & Wijayanayake, A. (2001). Portfolio optimization problem under concave transaction costs and minimal transaction unit constraints. Mathematical Programming, 89(2), 233-250.
Ladyzynski, P., & Grzegorzewski, P. (2013). Particle swarm intelligence turning of fuzzy geometric proto forms for price patterns recognition and stock trading. Expert Systems with Applications, 40(7), 2391–2397.
Lee, S.M., & Chesser, D.L. (1980). Goal programming for portfolio selection. The Journal of Portfolio Management, 6(3), 22-26.
Liu, S., & Stefek, D. (1995). A genetic algorithm for the asset paring problem in portfolio optimization, in proceedings of the first international symposium on operations research and its application (ISORA), Beijing, 441–450.
Lin, S.M. (2013). Analysis of service satisfaction in web auction logistics service using a combination of fruit fly optimization algorithm and general regression neural network. Neur. Comput. Appl. 7, 459–465.
Li, C., Xu, S., Li, W., & Hu, L. (2012). A novel modified fly optimization algorithm for designing the self-tuning proportional integral derivative controller. J. Converg. Inform. Technol. 7, 69–77.
Li, H., Guo, S., Li, C., & Sun, J. (2013). A hybrid annual power load forecasting model based on generalized regression neural network with fruit fly optimization algorithm. Knowl.-Based Syst. 37, 378–387.
Markowitz Harry, M. (1952). Portfolio selection. Journal of Finance, 7(1), 77-91.
Pan, W.T. (2011). A new evolutionary computation approach: fruit fly optimization algorithm. 2011 Conference of Digital Technology and Innovation Management, Taipei.
Pan, W. T. (2012). A new fruit fly optimization algorithm: taking the financial distress model as an example. Knowledge-Based Systems, 26, 69–74.
Pan, Q. K., Sang, H. Y., Dua, J. H., & Gao, L. (2014). An improved fruit fly optimization algorithm for continuous function optimization problems. Knowledge-Based Systems, 62, 69–83.
Storn, R., & Price, K. (1997). Differential evolution–a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization, 11(4), 341–359.
Tobin, J. (1958). Liquidity preference as behavior towards risk. The Review of Economic Studies, 25(2), 65-86.
Tollo, G., & Roli, A. (2008). Meta heuristics for the portfolio selection problem. International Journal of Operations Research, 5(1), 13-35.
Trelea, I. C. (2003). The particle swarm optimization algorithm: convergence analysis and parameter selection. Information Processing Letters, 85(6), 317–325.
Wang, L., Zheng, X.L., & Wang, S.Y. (2013). A novel binary fruit fly optimization algorithm for solving the multidimensional knapsack problem. Knowl.-Based Syst., 48, 17–23.
Wang, L., Shi, Y., & Liu, S. (2015). An improved fruit fly optimization algorithm and its application to joint replenishment problems. Expert Systems with Applications (article in press).
Wang, L., Fu Q.L., Lee C.G., & Zeng Y.R. (2013). Model and algorithm of fuzzy joint replenishment problem under credibility measure on fuzzy goal. Knowledge-Based Systems, 39, 57–66.
Wang, L., Zeng, Y., & Chen, T. (2014). Back propagation neural network with adaptive differential evolution algorithm for time series forecasting. Expert Systems with Applications, 42(2), 855-863.
Yamakazi, H. & Konno, H. (1991). Mean absolute deviation portfolio optimization model and its application to Tokyo stock market. Management Science, 37, 519-531.
Yuana, X., Liua, Y., Xianga, Y., & Yan, X. (2015). Parameter identification of BIPT system using chaotic-enhanced fruit fly optimization algorithm. Applied Mathematics and Computation, 268, 1267–1281.
Yuan, X., Dai, X., Zhao, J., & He, Q. (2014). A novel multi-swarm fruit fly optimization algorithm and its application. Applied Mathematics and Computation, 233, 260–271.
Young, M.R. (1998). A mini-max portfolio selection rule with linear programming solution. Management Science, 673-683.
_||_
Abidin, Z. Z., Arshad, M. R., & Ngah, U. K. (2011). A simulation based fly optimization algorithm for swarms of mini autonomous surface vehicles application. Indian J. Geo-Mar. Sci. 40(2), 250–266.
Anione, S., Loraschi, A., & Tettamanzi, A. (1993). A genetic approach to portfolio selection. Neural Network World, 6(93), 597-604.
Aryanezhad, M. B., & Hemati, M. (2008). A new genetic algorithm for solving non convex nonlinear programming problems. Applied Mathematics and Computation, 199(1), 186–194.
Chang, T.J., Meade N., Beasley, J.E., & Sharaiha, Y.M. (2000). Heuristics for cardinality constrained portfolio optimization. Computers and Operations Research, 27(13), 1271-1302.
Crama, Y., & Schyns, M. (2003). Simulated annealing for complex portfolio selection problems. European Journal of operational research, 150(3), 546-571.
Cura, T. (2009). Particle swarm optimization approach to portfolio optimization. Nonlinear Analysis: Real World Applications, 10(4), 2396-2406.
Deb, K., Pratap, A., Agarwal, S., & Meyarivan, T. A. M. T. (2002). A fast and elitist multi objective genetic algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation, 6(2), 182–197.
Dueck, G., & Winker, P. (1992). New concepts and algorithms for portfolio choice. Applied Stochastic Models and Data Analysis, 8(3), 159-178.
Fernández, A., & Gómez, S. (2007). Portfolio selection using neural networks. Computers & operations research, 34(4), 1177-1191.
Gilli, M., Këllezi, E., & Hysi, H. (2006). A data-driven optimization heuristic for downside risk minimization. Journal of Risk, 8(3), 1.
Han, J., Wang, P., & Yang, X. (2012). Tuning of PID controller based on fruit fly optimization algorithm. International Conference on Mechatronics and Automation (ICMA): 409–413.
Holland, J. H. (1975). Adaptation in natural and artificial systems: An introductory analysis with applications to biology, control, and artificial intelligence. University of Michigan Press.
Kennedy, J., & Eberhart, R. (1995). Particle Swarm Optimization. Proceedings of IEEE International Conference on Neural Networks IV, 1942–1948.
Konno, H., & Wijayanayake, A. (2001). Portfolio optimization problem under concave transaction costs and minimal transaction unit constraints. Mathematical Programming, 89(2), 233-250.
Ladyzynski, P., & Grzegorzewski, P. (2013). Particle swarm intelligence turning of fuzzy geometric proto forms for price patterns recognition and stock trading. Expert Systems with Applications, 40(7), 2391–2397.
Lee, S.M., & Chesser, D.L. (1980). Goal programming for portfolio selection. The Journal of Portfolio Management, 6(3), 22-26.
Liu, S., & Stefek, D. (1995). A genetic algorithm for the asset paring problem in portfolio optimization, in proceedings of the first international symposium on operations research and its application (ISORA), Beijing, 441–450.
Lin, S.M. (2013). Analysis of service satisfaction in web auction logistics service using a combination of fruit fly optimization algorithm and general regression neural network. Neur. Comput. Appl. 7, 459–465.
Li, C., Xu, S., Li, W., & Hu, L. (2012). A novel modified fly optimization algorithm for designing the self-tuning proportional integral derivative controller. J. Converg. Inform. Technol. 7, 69–77.
Li, H., Guo, S., Li, C., & Sun, J. (2013). A hybrid annual power load forecasting model based on generalized regression neural network with fruit fly optimization algorithm. Knowl.-Based Syst. 37, 378–387.
Markowitz Harry, M. (1952). Portfolio selection. Journal of Finance, 7(1), 77-91.
Pan, W.T. (2011). A new evolutionary computation approach: fruit fly optimization algorithm. 2011 Conference of Digital Technology and Innovation Management, Taipei.
Pan, W. T. (2012). A new fruit fly optimization algorithm: taking the financial distress model as an example. Knowledge-Based Systems, 26, 69–74.
Pan, Q. K., Sang, H. Y., Dua, J. H., & Gao, L. (2014). An improved fruit fly optimization algorithm for continuous function optimization problems. Knowledge-Based Systems, 62, 69–83.
Storn, R., & Price, K. (1997). Differential evolution–a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization, 11(4), 341–359.
Tobin, J. (1958). Liquidity preference as behavior towards risk. The Review of Economic Studies, 25(2), 65-86.
Tollo, G., & Roli, A. (2008). Meta heuristics for the portfolio selection problem. International Journal of Operations Research, 5(1), 13-35.
Trelea, I. C. (2003). The particle swarm optimization algorithm: convergence analysis and parameter selection. Information Processing Letters, 85(6), 317–325.
Wang, L., Zheng, X.L., & Wang, S.Y. (2013). A novel binary fruit fly optimization algorithm for solving the multidimensional knapsack problem. Knowl.-Based Syst., 48, 17–23.
Wang, L., Shi, Y., & Liu, S. (2015). An improved fruit fly optimization algorithm and its application to joint replenishment problems. Expert Systems with Applications (article in press).
Wang, L., Fu Q.L., Lee C.G., & Zeng Y.R. (2013). Model and algorithm of fuzzy joint replenishment problem under credibility measure on fuzzy goal. Knowledge-Based Systems, 39, 57–66.
Wang, L., Zeng, Y., & Chen, T. (2014). Back propagation neural network with adaptive differential evolution algorithm for time series forecasting. Expert Systems with Applications, 42(2), 855-863.
Yamakazi, H. & Konno, H. (1991). Mean absolute deviation portfolio optimization model and its application to Tokyo stock market. Management Science, 37, 519-531.
Yuana, X., Liua, Y., Xianga, Y., & Yan, X. (2015). Parameter identification of BIPT system using chaotic-enhanced fruit fly optimization algorithm. Applied Mathematics and Computation, 268, 1267–1281.
Yuan, X., Dai, X., Zhao, J., & He, Q. (2014). A novel multi-swarm fruit fly optimization algorithm and its application. Applied Mathematics and Computation, 233, 260–271.
Young, M.R. (1998). A mini-max portfolio selection rule with linear programming solution. Management Science, 673-683.
