Constrained portfolio selection model at considering risk-adjusted measure by using the Genetic Network Programming
Subject Areas : Design of Experimentiman bavarsad salehpoor 1 , saber mola alizade zavardehi 2
1 - Industrial Engineering Department, Amirkabir University of Technology, P.O. Box 15875-4413, Tehran, Iran
2 - Department of Industrial Engineering, Masjed-Soleiman Branch Islamic Azad University Masjed-Soleiman, Iran
Keywords: Portfolio optimization, GNP, Iran Stock Exchange, efficient Boundary Points,
Abstract :
This article present a new Decision making method of Stock portfolio optimization issues in different risk Sizes by Using Evolutionary computing mode which is mentioned genetic network programming (GNP).Then; its Ability compared to the Ability of the mean–variance model in efficient Boundary Points of Optimal constraints. Based on mean–variance Method by Markowitz we collected Three Risk Levels; mean absolute deviation (MAD), semi variance (SV) and variance with skewness (VWS). It is showed that these stock portfolio optimization issues with four risk sizes able to solve genetic network programming. The Sustainability of this proposed model is verified by 50 Iranian factories mentioned on the Stock Exchange. Finally, genetic network programming (GNP) compared with genetic algorithm (GA) both with and without cardinality constraint. Results demonstrated that GNP has a more efficient frontier than GA.
References:
Ackora-Prah, J., Gyamerah, S. A., Andam, P. S., & Gyamfi, D. (2014). Pattern Search for Portfolio Selection. Applied Mathematical Sciences, 8(143), 7137-7147.
Aguilar-Rivera, R., Valenzuela-Rendón, M., & Rodríguez-Ortiz, J. (2015). Genetic algorithms and Darwinian approaches in financial applications: A survey. Expert Systems with Applications, 42(21), 7684-7697.
Ahmad, G., Hasan, F., Shahid, M., Imran, M., & Alam, M. (2023). A Cardinality-Constrained Portfolio Selection Model Using Golden Eagle Optimizer in Stock Markets. Paper presented at the 2023 4th International Conference on Data Analytics for Business and Industry (ICDABI).
Ahmadi, A., & Davari-Ardakani, H. (2017). A multistage stochastic programming framework for cardinality constrained portfolio optimization. Numerical Algebra, Control & Optimization, 7(3), 359-377.
Anagnostopoulos, K., & Mamanis, G. (2011). The mean–variance cardinality constrained portfolio optimization problem: An experimental evaluation of five multiobjective evolutionary algorithms. Expert Systems with Applications, 38(11), 14208-14217.
Anagnostopoulos, K. P., & Mamanis, G. (2011a). The mean–variance cardinality constrained portfolio optimization problem: An experimental evaluation of five multiobjective evolutionary algorithms. Expert Systems with Applications, 38(11), 14208-14217.
Anagnostopoulos, K. P., & Mamanis, G. (2011b). Multiobjective evolutionary algorithms for complex portfolio optimization problems. Computational Management Science, 8(3), 259-279.
Atiya, A. F. (2001). Bankruptcy prediction for credit risk using neural networks: A survey and new results. IEEE Transactions on neural networks, 12(4), 929-935.
Bacanin, N., & Tuba, M. (2014). Firefly algorithm for cardinality constrained mean-variance portfolio optimization problem with entropy diversity constraint. The Scientific World Journal, 2014.
Bastiani, S. S., Cruz-Reyes, L., Fernandez, E., Gómez, C., & Rivera, G. (2015). An ant colony algorithm for solving the selection portfolio problem, using a quality-assessment model for portfolios of projects expressed by a priority ranking Design of Intelligent Systems Based on Fuzzy Logic, Neural Networks and Nature-Inspired Optimization (pp. 357-373): Springer.
Baykasoğlu, A., Yunusoglu, M. G., & Özsoydan, F. B. (2015). A GRASP based solution approach to solve cardinality constrained portfolio optimization problems. Computers & Industrial Engineering, 90, 339-351.
Birbil, Ş. İ., & Fang, S.-C. (2003). An electromagnetism-like mechanism for global optimization. Journal of Global Optimization, 25(3), 263-282.
Branda, M., Bucher, M., Červinka, M., & Schwartz, A. (2018). Convergence of a Scholtes-type regularization method for cardinality-constrained optimization problems with an application in sparse robust portfolio optimization. Computational Optimization and Applications, 70(2), 503-530.
Branke, J., Scheckenbach, B., Stein, M., Deb, K., & Schmeck, H. (2009). Portfolio optimization with an envelope-based multi-objective evolutionary algorithm. European Journal of Operational Research, 199(3), 684-693.
Busetti, F. (2006). Heuristic approaches to realistic portfolio optimisation. WIT Transactions on Modelling and Simulation, 43.
Canela, M. A., & Collazo, E. P. (2007). Portfolio selection with skewness in emerging market industries. Emerging Markets Review, 8(3), 230-250.
Černý, V. (1985). Thermodynamical approach to the traveling salesman problem: An efficient simulation algorithm. Journal of optimization theory and applications, 45(1), 41-51.
Cesarone, F., Scozzari, A., & Tardella, F. (2013). A new method for mean-variance portfolio optimization with cardinality constraints. Annals of Operations Research, 205(1), 213-234.
Chang, T.-J., Meade, N., Beasley, J. E., & Sharaiha, Y. M. (2000). Heuristics for cardinality constrained portfolio optimisation. Computers & Operations Research, 27(13), 1271-1302.
Chang, T.-J., Yang, S.-C., & Chang, K.-J. (2009). Portfolio optimization problems in different risk measures using genetic algorithm. Expert Systems with Applications, 36(7), 10529-10537.
Chen, A. H., Liang, Y.-C., & Liu, C.-C. (2012). An artificial bee colony algorithm for the cardinality-constrained portfolio optimization problems. Paper presented at the Evolutionary Computation (CEC), 2012 IEEE Congress on.
Chen, A. H., Liang, Y.-C., & Liu, C.-C. (2013). Portfolio optimization using improved artificial bee colony approach. Paper presented at the Computational Intelligence for Financial Engineering & Economics (CIFEr), 2013 IEEE Conference on.
Chen, B., Lin, Y., Zeng, W., Xu, H., & Zhang, D. (2017). The mean-variance cardinality constrained portfolio optimization problem using a local search-based multi-objective evolutionary algorithm. Applied Intelligence, 47(2), 505-525.
Chen, J.-S., Hou, J.-L., Wu, S.-M., & Chang-Chien, Y.-W. (2009). Constructing investment strategy portfolios by combination genetic algorithms. Expert Systems with Applications, 36(2), 3824-3828.
Chen, W. (2015). Artificial bee colony algorithm for constrained possibilistic portfolio optimization problem. Physica A: Statistical Mechanics and its Applications, 429, 125-139.
Chen, W., Li, D., & Liu, Y.-J. (2018). A novel hybrid ICA-FA algorithm for multi-period uncertain portfolio optimization model based on multiple criteria. IEEE Transactions on Fuzzy Systems.
Chen, W., Li, D., Lu, S., & Liu, W. (2018). Multi-period mean–semivariance portfolio optimization based on uncertain measure. Soft Computing, 1-17.
Chen, W., Wang, Y., Gupta, P., & Mehlawat, M. K. (2018). A novel hybrid heuristic algorithm for a new uncertain mean-variance-skewness portfolio selection model with real constraints. Applied Intelligence, 1-23.
Chen, W., & Xu, W. A Hybrid Multiobjective Bat Algorithm for Fuzzy Portfolio Optimization with Real-World Constraints. International Journal of Fuzzy Systems, 1-17.
Chen, Y., Mabu, S., & Hirasawa, K. (2010). A model of portfolio optimization using time adapting genetic network programming. Computers & Operations Research, 37(10), 1697-1707.
Chen, Y., Mabu, S., Hirasawa, K., & Hu, J. (2007). Trading rules on stock markets using genetic network programming with sarsa learning. Paper presented at the Proceedings of the 9th annual conference on Genetic and evolutionary computation.
Chiam, S., Tan, K., & Al Mamum, A. (2008). Evolutionary multi-objective portfolio optimization in practical context. International Journal of Automation and Computing, 5(1), 67-80.
Chiam, S. C., Al Mamun, A., & Low, Y. (2007). A realistic approach to evolutionary multiobjective portfolio optimization. Paper presented at the Evolutionary Computation, 2007. CEC 2007. IEEE Congress on.
Cui, T., Cheng, S., & Bai, R. (2014). A combinatorial algorithm for the cardinality constrained portfolio optimization problem. Paper presented at the Evolutionary Computation (CEC), 2014 IEEE Congress on.
Cui, X., Zheng, X., Zhu, S., & Sun, X. (2013). Convex relaxations and MIQCQP reformulations for a class of cardinality-constrained portfolio selection problems. Journal of Global Optimization, 56(4), 1409-1423.
Cura, T. (2009). Particle swarm optimization approach to portfolio optimization. Nonlinear analysis: Real world applications, 10(4), 2396-2406.
Deng, G.-F., & Lin, W.-T. (2010). Ant colony optimization for Markowitz mean-variance portfolio model. Paper presented at the International Conference on Swarm, Evolutionary, and Memetic Computing.
Deng, G.-F., Lin, W.-T., & Lo, C.-C. (2012). Markowitz-based portfolio selection with cardinality constraints using improved particle swarm optimization. Expert Systems with Applications, 39(4), 4558-4566.
Dropsy, V. (2011). Do macroeconomic factors help in predicting international equity risk premia?: Testing the out-of-sample accuracy of linear and nonlinear forecasts. Journal of Applied Business Research (JABR), 12(3), 120-132.
Eguchi, T., Hirasawa, K., Hu, J., & Ota, N. (2006). A study of evolutionary multiagent models based on symbiosis. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 36(1), 179-193.
Ertenlice, O., & Kalayci, C. B. (2018). A survey of swarm intelligence for portfolio optimization: Algorithms and applications. Swarm and evolutionary computation, 39, 36-52.
Esfahanipour, A., & Mousavi, S. (2011). A genetic programming model to generate risk-adjusted technical trading rules in stock markets. Expert Systems with Applications, 38(7), 8438-8445.
Feng, Y., Zhang, B., & Peng, J. (2023). Mean-risk model for uncertain portfolio selection with background risk and realistic constraints. Journal of Industrial & Management Optimization, 19(7).
Fernández, A., & Gómez, S. (2007). Portfolio selection using neural networks. Computers & Operations Research, 34(4), 1177-1191.
Fieldsend, J. E., Matatko, J., & Peng, M. (2004). Cardinality constrained portfolio optimisation. Paper presented at the International Conference on Intelligent Data Engineering and Automated Learning.
Fogarasi, N., & Levendovszky, J. (2013). Sparse, mean reverting portfolio selection using simulated annealing. Algorithmic Finance, 2(3-4), 197-211.
Frajtova-Michalikova, K., Spuchľakova, E., & Misankova, M. (2015). Portfolio Optimization. Procedia Economics and Finance, 26, 1102-1107.
Golberg, D. E. (1989). Genetic algorithms in search, optimization, and machine learning. Addion wesley, 1989, 102.
Golmakani, H. R., & Alishah, E. J. (2008). Portfolio selection using an artificial immune system. Paper presented at the Information Reuse and Integration, 2008. IRI 2008. IEEE International Conference on.
Golmakani, H. R., & Fazel, M. (2011). Constrained portfolio selection using particle swarm optimization. Expert Systems with Applications, 38(7), 8327-8335.
Guijarro, F. (2018). A similarity measure for the cardinality constrained frontier in the mean–variance optimization model. Journal of the Operational Research Society, 69(6), 928-945.
Gunjan, A., & Bhattacharyya, S. (2023). A brief review of portfolio optimization techniques. Artificial Intelligence Review, 56(5), 3847-3886. doi:10.1007/s10462-022-10273-7
Hajnoori, A., Amiri, M., & Alimi, A. (2013). Forecasting stock price using grey-fuzzy technique and portfolio optimization by invasive weed optimization algorithm. Decision Science Letters, 2(3), 175-184.
Hardoroudi, N. D., Keshvari, A., Kallio, M., & Korhonen, P. (2017). Solving cardinality constrained mean-variance portfolio problems via MILP. Annals of Operations Research, 254(1-2), 47-59.
Hirasawa, K., Eguchi, T., Zhou, J., Yu, L., Hu, J., & Markon, S. (2008). A double-deck elevator group supervisory control system using genetic network programming. IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews), 38(4), 535-550.
Hirasawa, K., Okubo, M., Katagiri, H., Hu, J., & Murata, J. (2001). Comparison between genetic network programming (GNP) and genetic programming (GP). Paper presented at the Evolutionary Computation, 2001. Proceedings of the 2001 Congress on.
Holland, J. H. (1975). Adaptation in natural and artificial systems: an introductory analysis with applications to biology, control, and artificial intelligence: U Michigan Press.
Huang, H.-H., & Wang, C.-P. (2013). Portfolio selection and portfolio frontier with background risk. The North American Journal of Economics and Finance, 26, 177-196.
Huang, X. (2008). Portfolio selection with a new definition of risk. European Journal of Operational Research, 186(1), 351-357.
Jaaman, S. H. H., Lam, W. H., & Isa, Z. (2011). Different Downside Risk Approaches in Portfolio Optimisation. Journal of Quality Measurement and Analysis JQMA, 7(1), 77-84.
Jalota, H., & Thakur, M. (2018). Genetic algorithm designed for solving portfolio optimization problems subjected to cardinality constraint. International Journal of System Assurance Engineering and Management, 9(1), 294-305.
Jawad, M., Naz, M., & Muqaddus, H. (2024). A multi-criteria decision-making approach for portfolio selection by using an automatic spherical fuzzy AHP algorithm. Journal of the Operational Research Society, 75(1), 85-98.
Jia, J., & Dyer, J. S. (1996). A standard measure of risk and risk-value models. Management Science, 42(12), 1691-1705.
Jiang, C., Ma, Y., & An, Y. (2016). Portfolio selection with a systematic skewness constraint. The North American Journal of Economics and Finance, 37, 393-405.
Jimbo, H. C., Ngongo, I. S., Andjiga, N. G., Suzuki, T., & Onana, C. A. (2017). Portfolio Optimization under Cardinality Constraints: A Comparative Study. Open Journal of Statistics, 7(04), 731.
Jin, Y., Qu, R., & Atkin, J. Constrained portfolio optimisation: the state-of-the-art Markowitz models. In: The 2016 International Conference on Operations Research and Enterprise Systems, 23-25 February 2016, Rome, Italy.
Kalayci, C. B., Ertenlice, O., Akyer, H., & Aygoren, H. (2017). An artificial bee colony algorithm with feasibility enforcement and infeasibility toleration procedures for cardinality constrained portfolio optimization. Expert Systems with Applications, 85, 61-75.
Kalayci, C. B., Ertenlice, O., Akyer, H., & Aygoren, H. (2017). A review on the current applications of genetic algorithms in mean-variance portfolio optimization Ortalama-varyans portföy optimizasyonunda genetik algoritma uygulamaları üzerine bir literatür araştırması.
KAMILI, H., & RIFFI, M. E. (2015). PORTFOLIO SELECTION USING THE CAT SWARM OPTIMIZATION. Journal of Theoretical & Applied Information Technology, 74(3).
Kandakoglu, M., Walther, G., & Ben Amor, S. (2024). The use of multi-criteria decision-making methods in project portfolio selection: a literature review and future research directions. Annals of Operations Research, 332(1), 807-830.
Kao, Y., & Cheng, H.-T. (2013). Bacterial foraging optimization approach to portfolio optimization. Computational Economics, 42(4), 453-470.
Katagiri, H., Hirasawa, K., Hu, J., Murata, J., & Kosaka, M. (2002). Network structure oriented evolutionary model: Genetic network programming. Transactions of the Society of Instrument and Control Engineers, 38(5), 485-494.
Kennedy, J., & Eberhart, R. (1942). Particle Swarm Optimization: IEEE International Conference on Neural Networks, 1995. Perth: IEEE, 19951.
Kessaci, Y. (2017). A multi-objective continuous genetic algorithm for financial portfolio optimization problem. Paper presented at the Proceedings of the Genetic and Evolutionary Computation Conference Companion.
Kirkpatrick, S., Gelatt, C. D., & Vecchi, M. P. (1983). Optimization by simulated annealing. Science, 220(4598), 671-680.
Konno, H., & Yamamoto, R. (2005). A mean-variance-skewness model: algorithm and applications. International Journal of Theoretical and Applied Finance, 8(04), 409-423.
Konno, H., & Yamazaki, H. (1991). Mean-absolute deviation portfolio optimization model and its applications to Tokyo stock market. Management science, 37(5), 519-531.
Koza, J. R. (1992). Genetic programming: on the programming of computers by means of natural selection (Vol. 1): MIT press.
Lam, M. (2004). Neural network techniques for financial performance prediction: integrating fundamental and technical analysis. Decision support systems, 37(4), 567-581.
Le Thi, H. A., Moeini, M., & Dinh, T. P. (2009). Portfolio selection under downside risk measures and cardinality constraints based on DC programming and DCA. Computational Management Science, 6(4), 459-475.
Liagkouras, K., & Metaxiotis, K. (2014). A new probe guided mutation operator and its application for solving the cardinality constrained portfolio optimization problem. Expert Systems with Applications, 41(14), 6274-6290.
Liagkouras, K., & Metaxiotis, K. (2016). A new efficiently encoded multiobjective algorithm for the solution of the cardinality constrained portfolio optimization problem. Annals of Operations Research, 1-39.
Liagkouras, K., & Metaxiotis, K. (2018). Handling the complexities of the multi-constrained portfolio optimization problem with the support of a novel MOEA. Journal of the Operational Research Society, 1-19.
Lim, K. (2024). Covariance Matrix Analysis for Optimal Portfolio Selection. Available at SSRN 4874008.
Lin, C.-C., & Liu, Y.-T. (2008). Genetic algorithms for portfolio selection problems with minimum transaction lots. European Journal of Operational Research, 185(1), 393-404.
Lin, D., Wang, S., & Yan, H. (2001). A multiobjective genetic algorithm for portfolio selection problem.
Lin, S.-Y., Horng, S.-J., Kao, T.-W., Huang, D.-K., Fahn, C.-S., Lai, J.-L., . . . Kuo, I.-H. (2010). An efficient bi-objective personnel assignment algorithm based on a hybrid particle swarm optimization model. Expert Systems with Applications, 37(12), 7825-7830.
Liu, S.-T. (2011). The mean-absolute deviation portfolio selection problem with interval-valued returns. Journal of computational and applied mathematics, 235(14), 4149-4157.
Lwin, K., & Qu, R. (2013). A hybrid algorithm for constrained portfolio selection problems. Applied Intelligence, 39(2), 251-266.
Lwin, K., Qu, R., & Kendall, G. (2014). A learning-guided multi-objective evolutionary algorithm for constrained portfolio optimization. Applied Soft Computing, 24, 757-772.
Ma, X., Gao, Y., & Wang, B. (2012). Portfolio optimization with cardinality constraints based on hybrid differential evolution. AASRI Procedia, 1, 311-317.
Mabu, S., Hirasawa, K., & Hu, J. (2004). Genetic network programming with reinforcement learning and its performance evaluation. Paper presented at the Genetic and Evolutionary Computation Conference.
Mabu, S., Hirasawa, K., & Hu, J. (2007). A graph-based evolutionary algorithm: genetic network programming (GNP) and its extension using reinforcement learning. Evolutionary Computation, 15(3), 369-398.
Mabu, S., Hirasawa, K., Hu, J., & Murata, J. (2002). Online learning of genetic network programming (gnp). Paper presented at the CEC.
Macedo, L. L., Godinho, P., & Alves, M. J. (2017). Mean-semivariance portfolio optimization with multiobjective evolutionary algorithms and technical analysis rules. Expert Systems with Applications, 79, 33-43.
Maringer, D., & Kellerer, H. (2003). Optimization of cardinality constrained portfolios with a hybrid local search algorithm. Or Spectrum, 25(4), 481-495.
Markowitz, H. (1952). Portfolio selection. The journal of finance, 7(1), 77-91.
Mishra, S. K., Panda, G., & Majhi, B. (2016). Prediction based mean-variance model for constrained portfolio assets selection using multiobjective evolutionary algorithms. Swarm and evolutionary computation, 28, 117-130.
Mishra, S. K., Panda, G., & Majhi, R. (2014). Constrained portfolio asset selection using multiobjective bacteria foraging optimization. Operational Research, 14(1), 113-145.
Monge, J. F. (2017). Cardinality constrained portfolio selection via factor models. arXiv preprint arXiv:1708.02424.
Moral-Escudero, R., Ruiz-Torrubiano, R., & Suárez, A. (2006). Selection of optimal investment portfolios with cardinality constraints. Paper presented at the Evolutionary Computation, 2006. CEC 2006. IEEE Congress on.
Mozafari, M., Jolai, F., & Tafazzoli, S. (2011). A new IPSO-SA approach for cardinality constrained portfolio optimization. International Journal of Industrial Engineering Computations, 2(2), 249-262.
Murray, W., & Shek, H. (2012). A local relaxation method for the cardinality constrained portfolio optimization problem. Computational Optimization and Applications, 53(3), 681-709.
Mutunge, P., & Haugland, D. (2018). Minimizing the tracking error of cardinality constrained portfolios. Computers & Operations Research, 90, 33-41.
Ni, Q., Yin, X., Tian, K., & Zhai, Y. (2017). Particle swarm optimization with dynamic random population topology strategies for a generalized portfolio selection problem. Natural Computing, 16(1), 31-44.
Oh, K. J., Kim, T. Y., Min, S.-H., & Lee, H. Y. (2006). Portfolio algorithm based on portfolio beta using genetic algorithm. Expert Systems with Applications, 30(3), 527-534.
Ruiz-Torrubiano, R., & Suárez, A. (2010). Hybrid approaches and dimensionality reduction for portfolio selection with cardinality constraints. IEEE Computational Intelligence Magazine, 5(2), 92-107.
Sabar, N. R., Turky, A., Leenders, M., & Song, A. (2018). Multi-population Genetic Algorithm for Cardinality Constrained Portfolio Selection Problems. Paper presented at the International Conference on Computational Science.
Saborido, R., Ruiz, A. B., Bermúdez, J. D., Vercher, E., & Luque, M. (2016). Evolutionary multi-objective optimization algorithms for fuzzy portfolio selection. Applied Soft Computing, 39, 48-63.
Sadigh, A. N., Mokhtari, H., Iranpoor, M., & Ghomi, S. (2012). Cardinality constrained portfolio optimization using a hybrid approach based on particle swarm optimization and Hopfield neural network. Advanced Science Letters, 17(1), 11-20.
Sadjadi, S. J., Gharakhani, M., & Safari, E. (2012). Robust optimization framework for cardinality constrained portfolio problem. Applied Soft Computing, 12(1), 91-99.
Samuelson, P. (1958). The fundamental approximation theorem of portfolio analysis in terms of means variances and higher moments. Review of Economic Studies, 25, 65-86.
Shaw, D. X., Liu, S., & Kopman, L. (2008). Lagrangian relaxation procedure for cardinality-constrained portfolio optimization. Optimisation Methods & Software, 23(3), 411-420.
Skolpadungket, P., Dahal, K., & Harnpornchai, N. (2007). Portfolio optimization using multi-obj ective genetic algorithms. Paper presented at the Evolutionary Computation, 2007. CEC 2007. IEEE Congress on.
Soleimani, H., Golmakani, H. R., & Salimi, M. H. (2009). Markowitz-based portfolio selection with minimum transaction lots, cardinality constraints and regarding sector capitalization using genetic algorithm. Expert Systems with Applications, 36(3), 5058-5063.
Streichert, F., & Tanaka-Yamawaki, M. (2006). The effect of local search on the constrained portfolio selection problem. Paper presented at the Evolutionary Computation, 2006. CEC 2006. IEEE Congress on.
Suthiwong, D., & Sodanil, M. (2016). Cardinality-constrained portfolio optimization using an improved quick artificial bee colony algorithm. Paper presented at the Computer Science and Engineering Conference (ICSEC), 2016 International.
Thakur, M., Meghwani, S. S., & Jalota, H. (2014). A modified real coded genetic algorithm for constrained optimization. Applied Mathematics and Computation, 235, 292-317.
Thomaidis, N. S. (2010). Active portfolio management from a fuzzy multi-objective programming perspective. Paper presented at the European Conference on the Applications of Evolutionary Computation.
Tian, F., Li, D. J., Fu, Q., Zhu, Z. F., Fu, Y. C., Wang, X. K., & Sun, C. Q. (2006). Construction of introgression lines carrying wild rice (Oryza rufipogon Griff.) segments in cultivated rice (Oryza sativa L.) background and characterization of introgressed segments associated with yield-related traits. Theoretical and Applied Genetics, 112(3), 570-580.
Tuba, M., & Bacanin, N. (2014). Artificial bee colony algorithm hybridized with firefly algorithm for cardinality constrained mean-variance portfolio selection problem. Applied Mathematics & Information Sciences, 8(6), 2831.
Vercher, E., & Bermúdez, J. D. (2015). Portfolio optimization using a credibility mean-absolute semi-deviation model. Expert Systems with Applications, 42(20), 7121-7131.
Wang, X., Wang, B., Li, T., Li, H., & Watada, J. (2023). Multi-criteria fuzzy portfolio selection based on three-way decisions and cumulative prospect theory. Applied Soft Computing, 134, 110033.
Wang, Z., Liu, S., & Kong, X. (2012). Artificial bee colony algorithm for portfolio optimization problems. International Journal of Advancements in Computing Technology, 4(4), 8-16.
Woodside-Oriakhi, M., Lucas, C., & Beasley, J. E. (2011). Heuristic algorithms for the cardinality constrained efficient frontier. European Journal of Operational Research, 213(3), 538-550.
Yang, S.-C., Lin, T.-L., Chang, T.-J., & Chang, K.-J. (2011). A semi-variance portfolio selection model for military investment assets. Expert Systems with Applications, 38(3), 2292-2301.
Yin, X., Ni, Q., & Zhai, Y. (2015). A novel PSO for portfolio optimization based on heterogeneous multiple population strategy. Paper presented at the Evolutionary Computation (CEC), 2015 IEEE Congress on.
Yu, J., Ge, J., Heuveling, J., Schneider, E., & Yang, M. (2015). Structural basis for substrate specificity of an amino acid ABC transporter. Proceedings of the National Academy of Sciences, 201415037.
Yu, L., Wang, S., & Lai, K. K. (2008). Neural network-based mean–variance–skewness model for portfolio selection. Computers & Operations Research, 35(1), 34-46.
Yuen, S. Y., Chow, C. K., Zhang, X., & Lou, Y. (2016). Which algorithm should I choose: an evolutionary algorithm portfolio approach. Applied Soft Computing, 40, 654-673.
Zhang, P. (2015). Multi-period possibilistic mean semivariance portfolio selection with cardinality constraints and its algorithm. Journal of Mathematical Modelling and Algorithms in Operations Research, 14(2), 239-253.
Zhang, P. (2016). An interval mean–average absolute deviation model for multiperiod portfolio selection with risk control and cardinality constraints. Soft Computing, 20(3), 1203-1212.
Zhang, P. (2018). Chance-constrained multiperiod mean absolute deviation uncertain portfolio selection. Journal of Industrial & Management Optimization, 14208-14217.
Zhang, P., & Li, B. (2017). The Admissible Multiperiod Mean Variance Portfolio Selection Problem with Cardinality Constraints. Industrial Engineering & Management Systems, 16(1), 118-128.
Zhang, P., & Zhang, W.-G. (2014). Multiperiod mean absolute deviation fuzzy portfolio selection model with risk control and cardinality constraints. Fuzzy Sets and Systems, 255, 74-91.
Zhou, Z., Jin, Q., Xiao, H., Wu, Q., & Liu, W. (2018). Estimation of cardinality constrained portfolio efficiency via segmented DEA. Omega, 76, 28-37.
Zhou, Z., Liu, X., Xiao, H., Wu, S., & Liu, Y. A DEA-based MOEA/D algorithm for portfolio optimization. Cluster Computing, 1-10.
Ackora-Prah, J., Gyamerah, S. A., Andam, P. S., & Gyamfi, D. (2014). Pattern Search for Portfolio Selection. Applied Mathematical Sciences, 8(143), 7137-7147.
Aguilar-Rivera, R., Valenzuela-Rendón, M., & Rodríguez-Ortiz, J. (2015). Genetic algorithms and Darwinian approaches in financial applications: A survey. Expert Systems with Applications, 42(21), 7684-7697.
Ahmad, G., Hasan, F., Shahid, M., Imran, M., & Alam, M. (2023). A Cardinality-Constrained Portfolio Selection Model Using Golden Eagle Optimizer in Stock Markets. Paper presented at the 2023 4th International Conference on Data Analytics for Business and Industry (ICDABI).
Ahmadi, A., & Davari-Ardakani, H. (2017). A multistage stochastic programming framework for cardinality constrained portfolio optimization. Numerical Algebra, Control & Optimization, 7(3), 359-377.
Anagnostopoulos, K., & Mamanis, G. (2011). The mean–variance cardinality constrained portfolio optimization problem: An experimental evaluation of five multiobjective evolutionary algorithms. Expert Systems with Applications, 38(11), 14208-14217.
Anagnostopoulos, K. P., & Mamanis, G. (2011a). The mean–variance cardinality constrained portfolio optimization problem: An experimental evaluation of five multiobjective evolutionary algorithms. Expert Systems with Applications, 38(11), 14208-14217.
Anagnostopoulos, K. P., & Mamanis, G. (2011b). Multiobjective evolutionary algorithms for complex portfolio optimization problems. Computational Management Science, 8(3), 259-279.
Atiya, A. F. (2001). Bankruptcy prediction for credit risk using neural networks: A survey and new results. IEEE Transactions on neural networks, 12(4), 929-935.
Bacanin, N., & Tuba, M. (2014). Firefly algorithm for cardinality constrained mean-variance portfolio optimization problem with entropy diversity constraint. The Scientific World Journal, 2014.
Bastiani, S. S., Cruz-Reyes, L., Fernandez, E., Gómez, C., & Rivera, G. (2015). An ant colony algorithm for solving the selection portfolio problem, using a quality-assessment model for portfolios of projects expressed by a priority ranking Design of Intelligent Systems Based on Fuzzy Logic, Neural Networks and Nature-Inspired Optimization (pp. 357-373): Springer.
Baykasoğlu, A., Yunusoglu, M. G., & Özsoydan, F. B. (2015). A GRASP based solution approach to solve cardinality constrained portfolio optimization problems. Computers & Industrial Engineering, 90, 339-351.
Birbil, Ş. İ., & Fang, S.-C. (2003). An electromagnetism-like mechanism for global optimization. Journal of Global Optimization, 25(3), 263-282.
Branda, M., Bucher, M., Červinka, M., & Schwartz, A. (2018). Convergence of a Scholtes-type regularization method for cardinality-constrained optimization problems with an application in sparse robust portfolio optimization. Computational Optimization and Applications, 70(2), 503-530.
Branke, J., Scheckenbach, B., Stein, M., Deb, K., & Schmeck, H. (2009). Portfolio optimization with an envelope-based multi-objective evolutionary algorithm. European Journal of Operational Research, 199(3), 684-693.
Busetti, F. (2006). Heuristic approaches to realistic portfolio optimisation. WIT Transactions on Modelling and Simulation, 43.
Canela, M. A., & Collazo, E. P. (2007). Portfolio selection with skewness in emerging market industries. Emerging Markets Review, 8(3), 230-250.
Černý, V. (1985). Thermodynamical approach to the traveling salesman problem: An efficient simulation algorithm. Journal of optimization theory and applications, 45(1), 41-51.
Cesarone, F., Scozzari, A., & Tardella, F. (2013). A new method for mean-variance portfolio optimization with cardinality constraints. Annals of Operations Research, 205(1), 213-234.
Chang, T.-J., Meade, N., Beasley, J. E., & Sharaiha, Y. M. (2000). Heuristics for cardinality constrained portfolio optimisation. Computers & Operations Research, 27(13), 1271-1302.
Chang, T.-J., Yang, S.-C., & Chang, K.-J. (2009). Portfolio optimization problems in different risk measures using genetic algorithm. Expert Systems with Applications, 36(7), 10529-10537.
Chen, A. H., Liang, Y.-C., & Liu, C.-C. (2012). An artificial bee colony algorithm for the cardinality-constrained portfolio optimization problems. Paper presented at the Evolutionary Computation (CEC), 2012 IEEE Congress on.
Chen, A. H., Liang, Y.-C., & Liu, C.-C. (2013). Portfolio optimization using improved artificial bee colony approach. Paper presented at the Computational Intelligence for Financial Engineering & Economics (CIFEr), 2013 IEEE Conference on.
Chen, B., Lin, Y., Zeng, W., Xu, H., & Zhang, D. (2017). The mean-variance cardinality constrained portfolio optimization problem using a local search-based multi-objective evolutionary algorithm. Applied Intelligence, 47(2), 505-525.
Chen, J.-S., Hou, J.-L., Wu, S.-M., & Chang-Chien, Y.-W. (2009). Constructing investment strategy portfolios by combination genetic algorithms. Expert Systems with Applications, 36(2), 3824-3828.
Chen, W. (2015). Artificial bee colony algorithm for constrained possibilistic portfolio optimization problem. Physica A: Statistical Mechanics and its Applications, 429, 125-139.
Chen, W., Li, D., & Liu, Y.-J. (2018). A novel hybrid ICA-FA algorithm for multi-period uncertain portfolio optimization model based on multiple criteria. IEEE Transactions on Fuzzy Systems.
Chen, W., Li, D., Lu, S., & Liu, W. (2018). Multi-period mean–semivariance portfolio optimization based on uncertain measure. Soft Computing, 1-17.
Chen, W., Wang, Y., Gupta, P., & Mehlawat, M. K. (2018). A novel hybrid heuristic algorithm for a new uncertain mean-variance-skewness portfolio selection model with real constraints. Applied Intelligence, 1-23.
Chen, W., & Xu, W. A Hybrid Multiobjective Bat Algorithm for Fuzzy Portfolio Optimization with Real-World Constraints. International Journal of Fuzzy Systems, 1-17.
Chen, Y., Mabu, S., & Hirasawa, K. (2010). A model of portfolio optimization using time adapting genetic network programming. Computers & Operations Research, 37(10), 1697-1707.
Chen, Y., Mabu, S., Hirasawa, K., & Hu, J. (2007). Trading rules on stock markets using genetic network programming with sarsa learning. Paper presented at the Proceedings of the 9th annual conference on Genetic and evolutionary computation.
Chiam, S., Tan, K., & Al Mamum, A. (2008). Evolutionary multi-objective portfolio optimization in practical context. International Journal of Automation and Computing, 5(1), 67-80.
Chiam, S. C., Al Mamun, A., & Low, Y. (2007). A realistic approach to evolutionary multiobjective portfolio optimization. Paper presented at the Evolutionary Computation, 2007. CEC 2007. IEEE Congress on.
Cui, T., Cheng, S., & Bai, R. (2014). A combinatorial algorithm for the cardinality constrained portfolio optimization problem. Paper presented at the Evolutionary Computation (CEC), 2014 IEEE Congress on.
Cui, X., Zheng, X., Zhu, S., & Sun, X. (2013). Convex relaxations and MIQCQP reformulations for a class of cardinality-constrained portfolio selection problems. Journal of Global Optimization, 56(4), 1409-1423.
Cura, T. (2009). Particle swarm optimization approach to portfolio optimization. Nonlinear analysis: Real world applications, 10(4), 2396-2406.
Deng, G.-F., & Lin, W.-T. (2010). Ant colony optimization for Markowitz mean-variance portfolio model. Paper presented at the International Conference on Swarm, Evolutionary, and Memetic Computing.
Deng, G.-F., Lin, W.-T., & Lo, C.-C. (2012). Markowitz-based portfolio selection with cardinality constraints using improved particle swarm optimization. Expert Systems with Applications, 39(4), 4558-4566.
Dropsy, V. (2011). Do macroeconomic factors help in predicting international equity risk premia?: Testing the out-of-sample accuracy of linear and nonlinear forecasts. Journal of Applied Business Research (JABR), 12(3), 120-132.
Eguchi, T., Hirasawa, K., Hu, J., & Ota, N. (2006). A study of evolutionary multiagent models based on symbiosis. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 36(1), 179-193.
Ertenlice, O., & Kalayci, C. B. (2018). A survey of swarm intelligence for portfolio optimization: Algorithms and applications. Swarm and evolutionary computation, 39, 36-52.
Esfahanipour, A., & Mousavi, S. (2011). A genetic programming model to generate risk-adjusted technical trading rules in stock markets. Expert Systems with Applications, 38(7), 8438-8445.
Feng, Y., Zhang, B., & Peng, J. (2023). Mean-risk model for uncertain portfolio selection with background risk and realistic constraints. Journal of Industrial & Management Optimization, 19(7).
Fernández, A., & Gómez, S. (2007). Portfolio selection using neural networks. Computers & Operations Research, 34(4), 1177-1191.
Fieldsend, J. E., Matatko, J., & Peng, M. (2004). Cardinality constrained portfolio optimisation. Paper presented at the International Conference on Intelligent Data Engineering and Automated Learning.
Fogarasi, N., & Levendovszky, J. (2013). Sparse, mean reverting portfolio selection using simulated annealing. Algorithmic Finance, 2(3-4), 197-211.
Frajtova-Michalikova, K., Spuchľakova, E., & Misankova, M. (2015). Portfolio Optimization. Procedia Economics and Finance, 26, 1102-1107.
Golberg, D. E. (1989). Genetic algorithms in search, optimization, and machine learning. Addion wesley, 1989, 102.
Golmakani, H. R., & Alishah, E. J. (2008). Portfolio selection using an artificial immune system. Paper presented at the Information Reuse and Integration, 2008. IRI 2008. IEEE International Conference on.
Golmakani, H. R., & Fazel, M. (2011). Constrained portfolio selection using particle swarm optimization. Expert Systems with Applications, 38(7), 8327-8335.
Guijarro, F. (2018). A similarity measure for the cardinality constrained frontier in the mean–variance optimization model. Journal of the Operational Research Society, 69(6), 928-945.
Gunjan, A., & Bhattacharyya, S. (2023). A brief review of portfolio optimization techniques. Artificial Intelligence Review, 56(5), 3847-3886. doi:10.1007/s10462-022-10273-7
Hajnoori, A., Amiri, M., & Alimi, A. (2013). Forecasting stock price using grey-fuzzy technique and portfolio optimization by invasive weed optimization algorithm. Decision Science Letters, 2(3), 175-184.
Hardoroudi, N. D., Keshvari, A., Kallio, M., & Korhonen, P. (2017). Solving cardinality constrained mean-variance portfolio problems via MILP. Annals of Operations Research, 254(1-2), 47-59.
Hirasawa, K., Eguchi, T., Zhou, J., Yu, L., Hu, J., & Markon, S. (2008). A double-deck elevator group supervisory control system using genetic network programming. IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews), 38(4), 535-550.
Hirasawa, K., Okubo, M., Katagiri, H., Hu, J., & Murata, J. (2001). Comparison between genetic network programming (GNP) and genetic programming (GP). Paper presented at the Evolutionary Computation, 2001. Proceedings of the 2001 Congress on.
Holland, J. H. (1975). Adaptation in natural and artificial systems: an introductory analysis with applications to biology, control, and artificial intelligence: U Michigan Press.
Huang, H.-H., & Wang, C.-P. (2013). Portfolio selection and portfolio frontier with background risk. The North American Journal of Economics and Finance, 26, 177-196.
Huang, X. (2008). Portfolio selection with a new definition of risk. European Journal of Operational Research, 186(1), 351-357.
Jaaman, S. H. H., Lam, W. H., & Isa, Z. (2011). Different Downside Risk Approaches in Portfolio Optimisation. Journal of Quality Measurement and Analysis JQMA, 7(1), 77-84.
Jalota, H., & Thakur, M. (2018). Genetic algorithm designed for solving portfolio optimization problems subjected to cardinality constraint. International Journal of System Assurance Engineering and Management, 9(1), 294-305.
Jawad, M., Naz, M., & Muqaddus, H. (2024). A multi-criteria decision-making approach for portfolio selection by using an automatic spherical fuzzy AHP algorithm. Journal of the Operational Research Society, 75(1), 85-98.
Jia, J., & Dyer, J. S. (1996). A standard measure of risk and risk-value models. Management Science, 42(12), 1691-1705.
Jiang, C., Ma, Y., & An, Y. (2016). Portfolio selection with a systematic skewness constraint. The North American Journal of Economics and Finance, 37, 393-405.
Jimbo, H. C., Ngongo, I. S., Andjiga, N. G., Suzuki, T., & Onana, C. A. (2017). Portfolio Optimization under Cardinality Constraints: A Comparative Study. Open Journal of Statistics, 7(04), 731.
Jin, Y., Qu, R., & Atkin, J. Constrained portfolio optimisation: the state-of-the-art Markowitz models. In: The 2016 International Conference on Operations Research and Enterprise Systems, 23-25 February 2016, Rome, Italy.
Kalayci, C. B., Ertenlice, O., Akyer, H., & Aygoren, H. (2017). An artificial bee colony algorithm with feasibility enforcement and infeasibility toleration procedures for cardinality constrained portfolio optimization. Expert Systems with Applications, 85, 61-75.
Kalayci, C. B., Ertenlice, O., Akyer, H., & Aygoren, H. (2017). A review on the current applications of genetic algorithms in mean-variance portfolio optimization Ortalama-varyans portföy optimizasyonunda genetik algoritma uygulamaları üzerine bir literatür araştırması.
KAMILI, H., & RIFFI, M. E. (2015). PORTFOLIO SELECTION USING THE CAT SWARM OPTIMIZATION. Journal of Theoretical & Applied Information Technology, 74(3).
Kandakoglu, M., Walther, G., & Ben Amor, S. (2024). The use of multi-criteria decision-making methods in project portfolio selection: a literature review and future research directions. Annals of Operations Research, 332(1), 807-830.
Kao, Y., & Cheng, H.-T. (2013). Bacterial foraging optimization approach to portfolio optimization. Computational Economics, 42(4), 453-470.
Katagiri, H., Hirasawa, K., Hu, J., Murata, J., & Kosaka, M. (2002). Network structure oriented evolutionary model: Genetic network programming. Transactions of the Society of Instrument and Control Engineers, 38(5), 485-494.
Kennedy, J., & Eberhart, R. (1942). Particle Swarm Optimization: IEEE International Conference on Neural Networks, 1995. Perth: IEEE, 19951.
Kessaci, Y. (2017). A multi-objective continuous genetic algorithm for financial portfolio optimization problem. Paper presented at the Proceedings of the Genetic and Evolutionary Computation Conference Companion.
Kirkpatrick, S., Gelatt, C. D., & Vecchi, M. P. (1983). Optimization by simulated annealing. Science, 220(4598), 671-680.
Konno, H., & Yamamoto, R. (2005). A mean-variance-skewness model: algorithm and applications. International Journal of Theoretical and Applied Finance, 8(04), 409-423.
Konno, H., & Yamazaki, H. (1991). Mean-absolute deviation portfolio optimization model and its applications to Tokyo stock market. Management science, 37(5), 519-531.
Koza, J. R. (1992). Genetic programming: on the programming of computers by means of natural selection (Vol. 1): MIT press.
Lam, M. (2004). Neural network techniques for financial performance prediction: integrating fundamental and technical analysis. Decision support systems, 37(4), 567-581.
Le Thi, H. A., Moeini, M., & Dinh, T. P. (2009). Portfolio selection under downside risk measures and cardinality constraints based on DC programming and DCA. Computational Management Science, 6(4), 459-475.
Liagkouras, K., & Metaxiotis, K. (2014). A new probe guided mutation operator and its application for solving the cardinality constrained portfolio optimization problem. Expert Systems with Applications, 41(14), 6274-6290.
Liagkouras, K., & Metaxiotis, K. (2016). A new efficiently encoded multiobjective algorithm for the solution of the cardinality constrained portfolio optimization problem. Annals of Operations Research, 1-39.
Liagkouras, K., & Metaxiotis, K. (2018). Handling the complexities of the multi-constrained portfolio optimization problem with the support of a novel MOEA. Journal of the Operational Research Society, 1-19.
Lim, K. (2024). Covariance Matrix Analysis for Optimal Portfolio Selection. Available at SSRN 4874008.
Lin, C.-C., & Liu, Y.-T. (2008). Genetic algorithms for portfolio selection problems with minimum transaction lots. European Journal of Operational Research, 185(1), 393-404.
Lin, D., Wang, S., & Yan, H. (2001). A multiobjective genetic algorithm for portfolio selection problem.
Lin, S.-Y., Horng, S.-J., Kao, T.-W., Huang, D.-K., Fahn, C.-S., Lai, J.-L., . . . Kuo, I.-H. (2010). An efficient bi-objective personnel assignment algorithm based on a hybrid particle swarm optimization model. Expert Systems with Applications, 37(12), 7825-7830.
Liu, S.-T. (2011). The mean-absolute deviation portfolio selection problem with interval-valued returns. Journal of computational and applied mathematics, 235(14), 4149-4157.
Lwin, K., & Qu, R. (2013). A hybrid algorithm for constrained portfolio selection problems. Applied Intelligence, 39(2), 251-266.
Lwin, K., Qu, R., & Kendall, G. (2014). A learning-guided multi-objective evolutionary algorithm for constrained portfolio optimization. Applied Soft Computing, 24, 757-772.
Ma, X., Gao, Y., & Wang, B. (2012). Portfolio optimization with cardinality constraints based on hybrid differential evolution. AASRI Procedia, 1, 311-317.
Mabu, S., Hirasawa, K., & Hu, J. (2004). Genetic network programming with reinforcement learning and its performance evaluation. Paper presented at the Genetic and Evolutionary Computation Conference.
Mabu, S., Hirasawa, K., & Hu, J. (2007). A graph-based evolutionary algorithm: genetic network programming (GNP) and its extension using reinforcement learning. Evolutionary Computation, 15(3), 369-398.
Mabu, S., Hirasawa, K., Hu, J., & Murata, J. (2002). Online learning of genetic network programming (gnp). Paper presented at the CEC.
Macedo, L. L., Godinho, P., & Alves, M. J. (2017). Mean-semivariance portfolio optimization with multiobjective evolutionary algorithms and technical analysis rules. Expert Systems with Applications, 79, 33-43.
Maringer, D., & Kellerer, H. (2003). Optimization of cardinality constrained portfolios with a hybrid local search algorithm. Or Spectrum, 25(4), 481-495.
Markowitz, H. (1952). Portfolio selection. The journal of finance, 7(1), 77-91.
Mishra, S. K., Panda, G., & Majhi, B. (2016). Prediction based mean-variance model for constrained portfolio assets selection using multiobjective evolutionary algorithms. Swarm and evolutionary computation, 28, 117-130.
Mishra, S. K., Panda, G., & Majhi, R. (2014). Constrained portfolio asset selection using multiobjective bacteria foraging optimization. Operational Research, 14(1), 113-145.
Monge, J. F. (2017). Cardinality constrained portfolio selection via factor models. arXiv preprint arXiv:1708.02424.
Moral-Escudero, R., Ruiz-Torrubiano, R., & Suárez, A. (2006). Selection of optimal investment portfolios with cardinality constraints. Paper presented at the Evolutionary Computation, 2006. CEC 2006. IEEE Congress on.
Mozafari, M., Jolai, F., & Tafazzoli, S. (2011). A new IPSO-SA approach for cardinality constrained portfolio optimization. International Journal of Industrial Engineering Computations, 2(2), 249-262.
Murray, W., & Shek, H. (2012). A local relaxation method for the cardinality constrained portfolio optimization problem. Computational Optimization and Applications, 53(3), 681-709.
Mutunge, P., & Haugland, D. (2018). Minimizing the tracking error of cardinality constrained portfolios. Computers & Operations Research, 90, 33-41.
Ni, Q., Yin, X., Tian, K., & Zhai, Y. (2017). Particle swarm optimization with dynamic random population topology strategies for a generalized portfolio selection problem. Natural Computing, 16(1), 31-44.
Oh, K. J., Kim, T. Y., Min, S.-H., & Lee, H. Y. (2006). Portfolio algorithm based on portfolio beta using genetic algorithm. Expert Systems with Applications, 30(3), 527-534.
Ruiz-Torrubiano, R., & Suárez, A. (2010). Hybrid approaches and dimensionality reduction for portfolio selection with cardinality constraints. IEEE Computational Intelligence Magazine, 5(2), 92-107.
Sabar, N. R., Turky, A., Leenders, M., & Song, A. (2018). Multi-population Genetic Algorithm for Cardinality Constrained Portfolio Selection Problems. Paper presented at the International Conference on Computational Science.
Saborido, R., Ruiz, A. B., Bermúdez, J. D., Vercher, E., & Luque, M. (2016). Evolutionary multi-objective optimization algorithms for fuzzy portfolio selection. Applied Soft Computing, 39, 48-63.
Sadigh, A. N., Mokhtari, H., Iranpoor, M., & Ghomi, S. (2012). Cardinality constrained portfolio optimization using a hybrid approach based on particle swarm optimization and Hopfield neural network. Advanced Science Letters, 17(1), 11-20.
Sadjadi, S. J., Gharakhani, M., & Safari, E. (2012). Robust optimization framework for cardinality constrained portfolio problem. Applied Soft Computing, 12(1), 91-99.
Samuelson, P. (1958). The fundamental approximation theorem of portfolio analysis in terms of means variances and higher moments. Review of Economic Studies, 25, 65-86.
Shaw, D. X., Liu, S., & Kopman, L. (2008). Lagrangian relaxation procedure for cardinality-constrained portfolio optimization. Optimisation Methods & Software, 23(3), 411-420.
Skolpadungket, P., Dahal, K., & Harnpornchai, N. (2007). Portfolio optimization using multi-obj ective genetic algorithms. Paper presented at the Evolutionary Computation, 2007. CEC 2007. IEEE Congress on.
Soleimani, H., Golmakani, H. R., & Salimi, M. H. (2009). Markowitz-based portfolio selection with minimum transaction lots, cardinality constraints and regarding sector capitalization using genetic algorithm. Expert Systems with Applications, 36(3), 5058-5063.
Streichert, F., & Tanaka-Yamawaki, M. (2006). The effect of local search on the constrained portfolio selection problem. Paper presented at the Evolutionary Computation, 2006. CEC 2006. IEEE Congress on.
Suthiwong, D., & Sodanil, M. (2016). Cardinality-constrained portfolio optimization using an improved quick artificial bee colony algorithm. Paper presented at the Computer Science and Engineering Conference (ICSEC), 2016 International.
Thakur, M., Meghwani, S. S., & Jalota, H. (2014). A modified real coded genetic algorithm for constrained optimization. Applied Mathematics and Computation, 235, 292-317.
Thomaidis, N. S. (2010). Active portfolio management from a fuzzy multi-objective programming perspective. Paper presented at the European Conference on the Applications of Evolutionary Computation.
Tian, F., Li, D. J., Fu, Q., Zhu, Z. F., Fu, Y. C., Wang, X. K., & Sun, C. Q. (2006). Construction of introgression lines carrying wild rice (Oryza rufipogon Griff.) segments in cultivated rice (Oryza sativa L.) background and characterization of introgressed segments associated with yield-related traits. Theoretical and Applied Genetics, 112(3), 570-580.
Tuba, M., & Bacanin, N. (2014). Artificial bee colony algorithm hybridized with firefly algorithm for cardinality constrained mean-variance portfolio selection problem. Applied Mathematics & Information Sciences, 8(6), 2831.
Vercher, E., & Bermúdez, J. D. (2015). Portfolio optimization using a credibility mean-absolute semi-deviation model. Expert Systems with Applications, 42(20), 7121-7131.
Wang, X., Wang, B., Li, T., Li, H., & Watada, J. (2023). Multi-criteria fuzzy portfolio selection based on three-way decisions and cumulative prospect theory. Applied Soft Computing, 134, 110033.
Wang, Z., Liu, S., & Kong, X. (2012). Artificial bee colony algorithm for portfolio optimization problems. International Journal of Advancements in Computing Technology, 4(4), 8-16.
Woodside-Oriakhi, M., Lucas, C., & Beasley, J. E. (2011). Heuristic algorithms for the cardinality constrained efficient frontier. European Journal of Operational Research, 213(3), 538-550.
Yang, S.-C., Lin, T.-L., Chang, T.-J., & Chang, K.-J. (2011). A semi-variance portfolio selection model for military investment assets. Expert Systems with Applications, 38(3), 2292-2301.
Yin, X., Ni, Q., & Zhai, Y. (2015). A novel PSO for portfolio optimization based on heterogeneous multiple population strategy. Paper presented at the Evolutionary Computation (CEC), 2015 IEEE Congress on.
Yu, J., Ge, J., Heuveling, J., Schneider, E., & Yang, M. (2015). Structural basis for substrate specificity of an amino acid ABC transporter. Proceedings of the National Academy of Sciences, 201415037.
Yu, L., Wang, S., & Lai, K. K. (2008). Neural network-based mean–variance–skewness model for portfolio selection. Computers & Operations Research, 35(1), 34-46.
Yuen, S. Y., Chow, C. K., Zhang, X., & Lou, Y. (2016). Which algorithm should I choose: an evolutionary algorithm portfolio approach. Applied Soft Computing, 40, 654-673.
Zhang, P. (2015). Multi-period possibilistic mean semivariance portfolio selection with cardinality constraints and its algorithm. Journal of Mathematical Modelling and Algorithms in Operations Research, 14(2), 239-253.
Zhang, P. (2016). An interval mean–average absolute deviation model for multiperiod portfolio selection with risk control and cardinality constraints. Soft Computing, 20(3), 1203-1212.
Zhang, P. (2018). Chance-constrained multiperiod mean absolute deviation uncertain portfolio selection. Journal of Industrial & Management Optimization, 14208-14217.
Zhang, P., & Li, B. (2017). The Admissible Multiperiod Mean Variance Portfolio Selection Problem with Cardinality Constraints. Industrial Engineering & Management Systems, 16(1), 118-128.
Zhang, P., & Zhang, W.-G. (2014). Multiperiod mean absolute deviation fuzzy portfolio selection model with risk control and cardinality constraints. Fuzzy Sets and Systems, 255, 74-91.
Zhou, Z., Jin, Q., Xiao, H., Wu, Q., & Liu, W. (2018). Estimation of cardinality constrained portfolio efficiency via segmented DEA. Omega, 76, 28-37.
Zhou, Z., Liu, X., Xiao, H., Wu, S., & Liu, Y. A DEA-based MOEA/D algorithm for portfolio optimization. Cluster Computing, 1-10.