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SCIENCE CHINA Information Sciences, Volume 64 , Issue 5 : 152204(2021) https://doi.org/10.1007/s11432-020-2894-9

Quantum beetle antennae search: a novel technique for the constrained portfolio optimization problem

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  • ReceivedFeb 10, 2020
  • AcceptedApr 1, 2020
  • PublishedMar 17, 2021

Abstract


References

[1] Markowitz H. Portfolio selection. The Journal Of Finance, 1952, 7(1):77--91. Google Scholar

[2] Chalermkraivuth K C, Chakraborty A, Clark M C, et al. Methods and systems for analytical-based multifactor multiobjective portfolio risk optimization. December 29 2009. US Patent 7,640,201. Google Scholar

[3] Li D, Ng W L. Optimal Dynamic Portfolio Selection: Multiperiod Mean-Variance Formulation. Math Finance, 2000, 10: 387-406 CrossRef Google Scholar

[4] Zhu H, Wang Y, Wang K. Particle Swarm Optimization (PSO) for the constrained portfolio optimization problem. Expert Syst Appl, 2011, 38: 10161-10169 CrossRef Google Scholar

[5] Branke J, Scheckenbach B, Stein M. Portfolio optimization with an envelope-based multi-objective evolutionary algorithm. Eur J Operational Res, 2009, 199: 684-693 CrossRef Google Scholar

[6] Doerner K, Gutjahr W J, Hartl R F. Pareto Ant Colony Optimization: A Metaheuristic Approach to Multiobjective Portfolio Selection. Ann Operations Res, 2004, 131: 79-99 CrossRef Google Scholar

[7] Ling S, Wang H, Liu P X. Adaptive fuzzy dynamic surface control of flexible-joint robot systems with input saturation. IEEE/CAA J Autom Sin, 2019, 6: 97-107 CrossRef Google Scholar

[8] Wang H, Liu P X, Zhao X. Adaptive Fuzzy Finite-Time Control of Nonlinear Systems With Actuator Faults. IEEE Trans Cybern, 2020, 50: 1786-1797 CrossRef Google Scholar

[9] Chang T J, Yang S C, Chang K J. Portfolio optimization problems in different risk measures using genetic algorithm. Expert Syst Appl, 2009, 36: 10529-10537 CrossRef Google Scholar

[10] Wang Q, Chen S, Luo X. An adaptive latent factor model via particle swarm optimization. Neurocomputing, 2019, 369: 176-184 CrossRef Google Scholar

[11] Cheng L, Liu W, Yang C. A Neural-Network-Based Controller for Piezoelectric-Actuated Stick-Slip Devices. IEEE Trans Ind Electron, 2018, 65: 2598-2607 CrossRef Google Scholar

[12] Deng G F and Lin W T. Ant colony optimization for markowitz mean-variance portfolio model. In: Proceedings of International Conference on Swarm, Evolutionary, and Memetic Computing. Berlin: Springer, 2010. 238--245. Google Scholar

[13] Ammar E, Khalifa H A. Fuzzy portfolio optimization a quadratic programming approach. Chaos Solitons Fractals, 2003, 18: 1045-1054 CrossRef Google Scholar

[14] Doerner K, Gutjahr W J, Hartl R F. Pareto Ant Colony Optimization: A Metaheuristic Approach to Multiobjective Portfolio Selection. Ann Operations Res, 2004, 131: 79-99 CrossRef Google Scholar

[15] Doerner K F, Gutjahr W J, Hartl R F. Pareto ant colony optimization with ILP preprocessing in multiobjective project portfolio selection. Eur J Operational Res, 2006, 171: 830-841 CrossRef Google Scholar

[16] Niu B, Xue B, Li L, et al. Symbiotic multi-swarm pso for portfolio optimization. In: Proceedings of International Conference on Intelligent Computing. Berlin: Springer, 2009. 776--784. Google Scholar

[17] Sadigh A N, Mokhtari H, Iranpoor M. Cardinality Constrained Portfolio Optimization Using a Hybrid Approach Based on Particle Swarm Optimization and Hopfield Neural Network. adv sci lett, 2012, 17: 11-20 CrossRef Google Scholar

[18] Ghazanfar Ahari S, Ghaffari-Nasab N, Makui A. A Portfolio Selection Using Fuzzy Analytic Hierarchy Process: A Case Study of Iranian pharmaceutical industry. IJIEC, 2011, 2: 225-236 CrossRef Google Scholar

[19] Raei R, Bahrani Jahromi M. Portfolio optimization using a hybrid of fuzzy ANP, VIKOR and TOPSIS. MSL, 2012, 2: 2473-2484 CrossRef Google Scholar

[20] Gupta P, Mehlawat M K, Mittal G. Asset portfolio optimization using support vector machines and real-coded genetic algorithm. J Glob Optim, 2012, 53: 297-315 CrossRef Google Scholar

[21] Guijarro F, Tsinaslanidis P E. A surrogate similarity measure for the mean-variance frontier optimisation problem under bound and cardinality constraints. J Operational Res Soc, 2019, : 1-16 CrossRef Google Scholar

[22] Guijarro F. A similarity measure for the cardinality constrained frontier in the mean-variance optimization model. J Operational Res Soc, 2018, 69: 928-945 CrossRef Google Scholar

[23] Yu L, Wang S, Wen F. Genetic algorithm-based multi-criteria project portfolio selection. Ann Oper Res, 2012, 197: 71-86 CrossRef Google Scholar

[24] García F, Guijarro F, Oliver J. Index tracking optimization with cardinality constraint: a performance comparison of genetic algorithms and tabu search heuristics. Neural Comput Applic, 2018, 30: 2625-2641 CrossRef Google Scholar

[25] Michaud R O. The Markowitz Optimization Enigma: Is 'Optimized' Optimal?. Financial Analysts J, 1989, 45: 31-42 CrossRef Google Scholar

[26] Yang C, Peng G, Li Y. Neural Networks Enhanced Adaptive Admittance Control of Optimized Robot-Environment Interaction. IEEE Trans Cybern, 2019, 49: 2568-2579 CrossRef Google Scholar

[27] Yang C, Luo J, Liu C. Haptics Electromyography Perception and Learning Enhanced Intelligence for Teleoperated Robot. IEEE Trans Automat Sci Eng, 2019, 16: 1512-1521 CrossRef Google Scholar

[28] Venturelli D, Kondratyev A. Reverse quantum annealing approach to portfolio optimization problems. Quantum Mach Intell, 2019, 1: 17-30 CrossRef Google Scholar

[29] Jin L, Li S, La H M. Manipulability Optimization of Redundant Manipulators Using Dynamic Neural Networks. IEEE Trans Ind Electron, 2017, 64: 4710-4720 CrossRef Google Scholar

[30] Shi Y, Zhang Y. Solving future equation systems using integral-type error function and using twice ZNN formula with disturbances suppressed. J Franklin Institute, 2019, 356: 2130-2152 CrossRef Google Scholar

[31] Marzec M. Portfolio optimization: applications in quantum computing. Handbook of High-Frequency Trading and Modeling in Finance. John Wiley & Sons, Inc., 2016. 73--106. Google Scholar

[32] Zhang Y, Qi Z, Yang M. Step-width theoretics and numerics of four-point general DTZN model for future minimization using Jury stability criterion. Neurocomputing, 2019, 357: 231-239 CrossRef Google Scholar

[33] Zhang Y, Qi Z, Qiu B. Zeroing Neural Dynamics and Models for Various Time-Varying Problems Solving with ZLSF Models as Minimization-Type and Euler-Type Special Cases [Research Frontier]. IEEE Comput Intell Mag, 2019, 14: 52-60 CrossRef Google Scholar

[34] Gruska J. Quantum computing, volume 2005. London: McGraw-Hill, 1999. Google Scholar

[35] Luo S. Quantum discord for two-qubit systems. Phys Rev A, 2008, 77: 042303 CrossRef ADS Google Scholar

[36] Bouwmeester D, Zeilinger A. The physics of quantum information: basic concepts. In: The Physics of Quantum Information. Berlin: Springer, 2000. Google Scholar

[37] Layeb A, Boussalia S R. A Novel Quantum Inspired Cuckoo Search Algorithm for Bin Packing Problem. IJITCS, 2012, 4: 58-67 CrossRef Google Scholar

[38] Yang S Y, Wang M, Jiao L C. A quantum particle swarm optimization. In: Proceedings of the 2004 Congress on Evolutionary Computation (IEEE Cat. No. 04TH8753), 2004. 320--324. Google Scholar

[39] Sun J, Feng B, and Xu W. Particle swarm optimization with particles having quantum behavior. In: Proceedings of the 2004 congress on evolutionary computation (IEEE Cat. No. 04TH8753), 2004. 325--331. Google Scholar

[40] Chen D, Li S, Wu Q. New Disturbance Rejection Constraint for Redundant Robot Manipulators: An Optimization Perspective. IEEE Trans Ind Inf, 2020, 16: 2221-2232 CrossRef Google Scholar

[41] Wang L, Niu Q, and Fei M. A novel quantum ant colony optimization algorithm. In: Proceedings of International Conference on Life System Modeling and Simulation. Berlin: Springer, 2007. 277--286. Google Scholar

[42] Duckworth J, Jager T, Ashauer R. Automated, high-throughput measurement of size and growth curves of small organisms in well plates. Sci Rep, 2019, 9: 10 CrossRef ADS Google Scholar

[43] Lee J C, Lin W M, Liao G C. Quantum genetic algorithm for dynamic economic dispatch with valve-point effects and including wind power system. Int J Electrical Power Energy Syst, 2011, 33: 189-197 CrossRef Google Scholar

[44] Sun Y, Zhang J, Li G. Optimized neural network using beetle antennae search for predicting the unconfined compressive strength of jet grouting coalcretes. Int J Numer Anal Methods Geomech, 2019, 43: 801-813 CrossRef ADS Google Scholar

[45] Wu Q, Shen X, Jin Y. Intelligent Beetle Antennae Search for UAV Sensing and Avoidance of Obstacles. Sensors, 2019, 19: 1758 CrossRef Google Scholar

[46] Lin M, Li Q. A Hybrid Optimization Method of Beetle Antennae Search Algorithm and Particle Swarm Optimization. dtetr, 2018, CrossRef Google Scholar

[47] Fei S W, He C X. Prediction of dissolved gases content in power transformer oil using BASA-based mixed kernel RVR model. Int J Green Energy, 2019, 16: 652-656 CrossRef Google Scholar

[48] Li Q, Wang Z, and Wei A. Research on optimal scheduling of wind-pv-hydro-storage power complementary system based on bas algorithm. In: Proceedings of IOP Conference Series: Materials Science and Engineering, 2019. 072059. Google Scholar

[49] Wang J and Chen H. BSAS: Beetle swarm antennae search algorithm for optimization problems. 2018,. arXiv Google Scholar

[50] Li Q, Wei A, and Zhang Z. Application of economic load distribution of power system based on bas-pso. In: Proceedings of IOP Conference Series: Materials Science and Engineering, 2019. 072056. Google Scholar

[51] Wu Q, Lin H, Jin Y. A new fallback beetle antennae search algorithm for path planning of mobile robots with collision-free capability. Soft Comput, 2020, 24: 2369-2380 CrossRef Google Scholar

[52] Mu Y, Li B, An D. Three-Dimensional Route Planning Based on the Beetle Swarm Optimization Algorithm. IEEE Access, 2019, 7: 117804 CrossRef Google Scholar

[53] Mu Y, Li B, An D. Three-Dimensional Route Planning Based on the Beetle Swarm Optimization Algorithm. IEEE Access, 2019, 7: 117804 CrossRef Google Scholar

[54] Fan Y, Shao J, Sun G. Optimized PID Controller Based on Beetle Antennae Search Algorithm for Electro-Hydraulic Position Servo Control System. Sensors, 2019, 19: 2727 CrossRef Google Scholar

[55] Xie S, Chu X, Zheng M. Ship predictive collision avoidance method based on an improved beetle antennae search algorithm. Ocean Eng, 2019, 192: 106542 CrossRef Google Scholar

[56] Khan A H, Li S, Luo X. Obstacle Avoidance and Tracking Control of Redundant Robotic Manipulator: An RNN-Based Metaheuristic Approach. IEEE Trans Ind Inf, 2020, 16: 4670-4680 CrossRef Google Scholar

[57] Kim J H, Kim W C, Fabozzi F J. Portfolio selection with conservative short-selling. Finance Res Lett, 2016, 18: 363-369 CrossRef Google Scholar

[58] Sharpe W F. The Sharpe Ratio. JPM, 1994, 21: 49-58 CrossRef Google Scholar

[59] Jiang X and Li S. BAS: beetle antennae search algorithm for optimization problems. 2017,. arXiv Google Scholar

[60] Wang H, Xiaoping Liu P, Xie X. Adaptive fuzzy asymptotical tracking control of nonlinear systems with unmodeled dynamics and quantized actuator. Inf Sci, 2018, CrossRef Google Scholar

[61] Zhang Y, Li S, and Xu B. Convergence analysis of beetle antennae search algorithm and its applications. 2019,. arXiv Google Scholar

[62] Adorio E P, Diliman U. Mvf-multivariate test functions library in c for unconstrained global optimization. Quezon City, 2005. 100--104. Google Scholar

  • Figure 1

    (Color online) (a) The variation in optimal solution when QBAS runs for $20$ times on each function with different initial conditions. It can be seen that all the functions are near their global convergence value. (b) All the four functions converge to their global minima within $120$ iterations.

  • Figure 2

    (Color online) The histogram of the return values of four known companies, i.e., Amazon (AMZN), Facebook (FB), IBM, and Google (GOOGL), included in our portfolio selection problem. The time period is from $21$ March $2019$ to $18$ April 2019.

  • Figure 3

    (Color online) Performance and comparison of QBAS for $20$ stocks with the other meta-heuristic algorithms including BAS, PSO, and GA. (a) is the comparison of overall objective function value $F(E)$, (b) shows the Sharpe-ratio (S-raitio), and (c) is for equality constraint $S(E).$

  • Figure 4

    (Color online) Performance and comparison of QBAS for $50$ stocks with the other meta-heuristic algorithms including BAS, PSO, and GA. (a) is the comparison of overall objective function value $F(E)$, (b) shows the Sharpe-ratio (S-raitio), and (c) is for equality constraint $S(E).$

  • Figure 5

    (Color online) Performance and comparison of QBAS for $75$ stocks with the other meta-heuristic algorithms including BAS, PSO, and GA. (a) is the comparison of overall objective function value $F(E)$, (b) shows the Sharpe-ratio (S-raitio), and protect łinebreak (c) is for equality constraint $S(E).$

  • Figure 6

    (Color online) Performance and comparison of QBAS for $100$ stocks with the other meta-heuristic algorithms including BAS, PSO, and GA. (a) is the comparison of overall objective function value $F(E)$, (b) shows the Sharpe-ratio (S-raitio), and protect łinebreak (c) is for equality constraint $S(E).$

  •   

    Algorithm 1 Beetle antennae search

    $\textbf{Input:~}\text{Write~an~objective~function~$F(X),$~where}$$X~=~\{X_1,X_2,~X_3,\ldots,X_N\};$

    $\text{Initialize:~}~X_o~\text{and~}~d^n;$

    $\textbf{Output:~}~X_{\rm~best},~F_{\rm~best}$;

    $\textbf{while}~\{n~<~K\}$

    $\text{Generate~random~vector~}~{c}~\text{~and~calculate}$$X_r~\text{~and~}~X_l~\text{~using}$ (14) $\text{and}$ (15) $\text{~respectively}$;

    $\text{Update~the~position~$X^n$~of~the~beetle~using}$ (17);

    $\textbf{if}~(~F(X^n)~>~F_{\rm~best})$

    $F_{\rm~best}~=~F(X^n)$;

    $X_{\rm~best}~=~X^n$;

    $\textbf{end~if}$

    $\text{Update~the~step~controlling~parameter~$d^n$~using}$ (18).

    $\textbf{end~while}$

  • Table 1  

    Table 1Benchmark functions to test the performance of QBAS

    Function $F(x)$ $F_{\rm~min}$ Properties
    Ackley: $~-20~{\rm~exp}(-0.2~\sqrt{(\frac{1}{n}~\sum_{i=1}^{n}~x_i^2)}-{\rm~exp}(\frac{1}{n}\sum_{i=1}^{n}{\rm~cos}(2\pi)))~+~20~+{\rm~exp}(1)$ $0$
    Continuous,
    non-convex,
    and
    multimodal
    Rastrigin: $~10n~+~\sum_{i=1}^{n}~(x_i^2~-~10~{\rm~cos}(2\pi~x_i))$ $0$
    Beale: $~(1.5~-~x_1~+~x_1x_2)^2~+~(2.25~-x_1~+~x_1~x_2^2)^2~+~(2.625~-~x_1~+~x_1~x_2^3)^2~$ $0$
    Levi N.13: ${\rm~sin}^2(3\pi~x_1)~+~(x_1-1)^2(1+{\rm~sin}^2(3\pi~x_2))~+~(x_2~-1)^2(1+{\rm~sin}^2(2\pi~x_2))$ $0$
  • Table 2  

    Table 2Four portfolios' results of QBAS solver, BAS solver, PSO solver, and GA solver

    Portfolio
    Algorithm 20 stocks 50 stocks 75 stocks 100 stocks
    $F(E)$ S-ratio $S(E)$ $F(E)$ S-ratio $S(E)$ $F(E)$ S-ratio $S(E)$ $F(E)$ S-ratio $S(E)$
    QBAS solver 10.22 9.210 1.042 5.140 12.42 1.001 25.79 33.78 1.016 50.076 55.38 0.926
    BAS solver 4.024 4.942 0.967 4.704 4.08 1.052 10.02 30.35 1.016 20.087 30.48 1.075
    PSO solver 4.093 5.352 0.828 4.812 6.25 0.604 5.319 26.23 0.964 20.012 34.84 1.033
    GA solver 8.723 6.591 0.996 4.810 5.50 0.973 12.29 25.07 1.012 20.074 24.55 0.986
  •   

    Algorithm 2 Quantum beetle antennae search

    $\textbf{Input:~}\text{Write~an~objective~function}~$ $F(X)$ (13), where$X~=~\{X_1,X_2,~X_3,\ldots,~X_N\};$

    $\text{Initialize:~}~X_o~\text{and~}~d^n$;

    $\textbf{Output:~}~X_{\rm~best},~F_{\rm~best}$;

    $\textbf{while}~\{n~<~K\}$

    $\text{Generate~random~vector~}~{c}~\text{~and~calculate}$$X_r~\text{~and~}~X_l~\text{~using}$ (14) $\text{and}$ (15) $\text{respectively;~}$

    Compute the value of $L$ using (32);

    $u~=~{\rm~rand}(0,1)$

    $\textbf{if}~({\rm~rand}(0,1)~>~0.5)$

    $X^n~=~X^{n-1}~-~\frac{L}{2}{\rm~ln}(\frac{1}{u})$;

    $\textbf{else}$

    $X^n~=~X^{n-1}~+~\frac{L}{2}{\rm~ln}(\frac{1}{u})$;

    $\textbf{end~if}$

    $\textbf{if}~(~F(X^n)~>~F_{\rm~best})$

    $F_{\rm~best}~=~F(X^n)$;

    $X_{\rm~best}~=~X^n$;

    $\textbf{end~if}$

    $\text{Update~the~step~controlling~parameter~$d^n$~using}$ (18).

    $\textbf{end~while}$