A journal of IEEE and CAA , publishes high-quality papers in English on original theoretical/experimental research and development in all areas of automation
Volume 7 Issue 2
Mar.  2020

IEEE/CAA Journal of Automatica Sinica

  • JCR Impact Factor: 11.8, Top 4% (SCI Q1)
    CiteScore: 17.6, Top 3% (Q1)
    Google Scholar h5-index: 77, TOP 5
Turn off MathJax
Article Contents
Ameer Hamza Khan, Xinwei Cao, Shuai Li, Vasilios N. Katsikis and Liefa Liao, "BAS-ADAM: An ADAM Based Approach to Improve the Performance of Beetle Antennae Search Optimizer," IEEE/CAA J. Autom. Sinica, vol. 7, no. 2, pp. 461-471, Mar. 2020. doi: 10.1109/JAS.2020.1003048
Citation: Ameer Hamza Khan, Xinwei Cao, Shuai Li, Vasilios N. Katsikis and Liefa Liao, "BAS-ADAM: An ADAM Based Approach to Improve the Performance of Beetle Antennae Search Optimizer," IEEE/CAA J. Autom. Sinica, vol. 7, no. 2, pp. 461-471, Mar. 2020. doi: 10.1109/JAS.2020.1003048

BAS-ADAM: An ADAM Based Approach to Improve the Performance of Beetle Antennae Search Optimizer

doi: 10.1109/JAS.2020.1003048
More Information
  • In this paper, we propose enhancements to Beetle Antennae search (BAS) algorithm, called BAS-ADAM, to smoothen the convergence behavior and avoid trapping in local-minima for a highly non-convex objective function. We achieve this by adaptively adjusting the step-size in each iteration using the adaptive moment estimation (ADAM) update rule. The proposed algorithm also increases the convergence rate in a narrow valley. A key feature of the ADAM update rule is the ability to adjust the step-size for each dimension separately instead of using the same step-size. Since ADAM is traditionally used with gradient-based optimization algorithms, therefore we first propose a gradient estimation model without the need to differentiate the objective function. Resultantly, it demonstrates excellent performance and fast convergence rate in searching for the optimum of non-convex functions. The efficiency of the proposed algorithm was tested on three different benchmark problems, including the training of a high-dimensional neural network. The performance is compared with particle swarm optimizer (PSO) and the original BAS algorithm.

     

  • loading
  • [1]
    H. Q. Wang, P. X. Liu, X. J. Xie, X. P. Liu, T. Hayat, and F. E. Alsaadi, “Adaptive fuzzy asymptotical tracking control of nonlinear systems with unmodeled dynamics and quantized actuator,” Inf. Sci., DOI: 10.1016/j.ins.2018.04.011
    [2]
    C. G. Yang, J. Luo, C. Liu, M. Li, and S. L. Dai, “Haptics electromyography perception and learning enhanced intelligence for teleoperated robot,” IEEE Trans. Autom. Sci. Eng., vol. 16, no. 4, pp. 1512–1521, Oct. 2019. doi: 10.1109/TASE.2018.2874454
    [3]
    X. Luo, H. Wu, H. Q. Yuan, and M. C. Zhou, “Temporal pattern-aware QoS prediction via biased non-negative latent factorization of tensors,” IEEE Trans. Cybern., DOI: 10.1109/TCYB.2019.2903736
    [4]
    L. Bottou, F. E. Curtis, and J. Nocedal, “Optimization methods for large-scale machine learning,” SIAM Rev., vol. 60, no. 2, pp. 223–311, May 2018. doi: 10.1137/16M1080173
    [5]
    S. Theodoridis, Machine Learning: A Bayesian and Optimization Perspective. San Diego: Academic Press, 2015.
    [6]
    T. Liu, B. Tian, Y. F. Ai, L. Li, D. P. Cao, and F. Y. Wang, “Parallel reinforcement learning: a framework and case study,” IEEE/CAA J. Autom. Sinica, vol. 5, no. 4, pp. 827–835, Jul. 2018. doi: 10.1109/JAS.2018.7511144
    [7]
    H. Q. Wang, S. W. Liu, and X. B. Yang, “Adaptive neural control for non-strict-feedback nonlinear systems with input delay,” Inf. Sci., vol. 514, pp. 605–616, Apr. 2020. doi: 10.1016/j.ins.2019.09.043
    [8]
    X. Luo, Z. G. Liu, S. Li, M. S. Shang, and Z. D. Wang, “A fast non-negative latent factor model based on generalized momentum method,” IEEE Trans. Syst., Man, Cybern.: Syst., DOI: 10.1109/TSMC.2018.2875452
    [9]
    D. P. Kingma and J. Ba, “Adam: a method for stochastic optimization,” arXiv: 1412.6980, 2014.
    [10]
    S. Ruder, “An overview of gradient descent optimization algorithms,” arXiv: 1609.04747, 2016.
    [11]
    Y. Shi and Y. N. Zhang, “Solving future equation systems using integral-type error function and using twice ZNN formula with disturbances suppressed,” J. Franklin Ins., vol. 356, no. 4, pp. 2130–2152, Mar. 2019. doi: 10.1016/j.jfranklin.2018.11.026
    [12]
    L. Xiao, S. Li, F. J. Lin, Z. G. Tan, and A. H. Khan, “Zeroing neural dynamics for control design: comprehensive analysis on stability, robustness, and convergence speed,” IEEE Trans. Ind. Informatics, vol. 15, no. 5, pp. 2605–2616, May 2019. doi: 10.1109/TII.2018.2867169
    [13]
    Y. N. Zhang, Z. Y. Qi, B. B. Qiu, M. Yang, and M. L. Xiao, “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., vol. 14, no. 3, pp. 52–60, Aug. 2019. doi: 10.1109/MCI.2019.2919397
    [14]
    Y. N. Zhang, Z. Y. Qi, M. Yang, J. J. Guo, and H. C. Huang, “Step-width theoretics and numerics of four-point general DTZN model for future minimization using jury stability criterion,” Neurocomputing, vol. 357, pp. 231–239, Sept. 2019. doi: 10.1016/j.neucom.2019.04.054
    [15]
    R. Johnson and T. Zhang, “Accelerating stochastic gradient descent using predictive variance reduction,” in Proc. 26th Int. Conf. Neural Information Processing Systems, Red Hook, USA, 2013, pp. 315–323.
    [16]
    X. Luo, D. X. Wang, M. C. Zhou, and H. Q. Yuan, "Latent factor-based recommenders relying on extended stochastic gradient descent algorithms," IEEE Trans. Syst., Man, Cybern.: Syst., DOI: 10.1109/TSMC.2018.2884191
    [17]
    J. D. Lee, M. Simchowitz, M. I. Jordan, and B. Recht, “Gradient descent only converges to minimizers,” in Proc. 29th Annu. Conf. Learning Theory, 2016, pp. 1246–1257.
    [18]
    W. N. Chen, J. Zhang, H. S. H. Chung, W. L. Zhong, W. G. Wu, and Y. H. Shi, “A novel set-based particle swarm optimization method for discrete optimization problems,” IEEE Trans. Evol. Comput., vol. 14, no. 2, pp. 278–300, Apr. 2010. doi: 10.1109/TEVC.2009.2030331
    [19]
    S. Ling, H. Q. Wang, and P. X. Liu, “Adaptive fuzzy dynamic surface control of flexible-joint robot systems with input saturation,” IEEE/CAA J. Autom. Sinica, vol. 6, no. 1, pp. 97–107, Jan. 2019. doi: 10.1109/JAS.2019.1911330
    [20]
    H. Nguyen-Xuan, G. Liu, C. a. Thai-Hoang, and T. Nguyen-Thoi, “An edge-based smoothed finite element method (ES-FEM) with stabilized discrete shear gap technique for analysis of reissner-mindlin plates,” Computer Methods in Applied Mechanics and Engineering, vol. 199, no. 9–12, pp. 471–489, Jan. 2010. doi: 10.1016/j.cma.2009.09.001
    [21]
    A. H. Khan, S. Li, and X. Luo, “Obstacle avoidance and tracking control of redundant robotic manipulator: an RNN based metaheuristic approach,” IEEE Trans. Ind. Informatics, DOI: 10.1109/TII.2019.2941916
    [22]
    Y. Zhou, L. J. Kong, Z. Y. Wu, S. P. Liu, Y. Q. Cai, and Y. Liu, “Ensemble of multi-objective metaheuristic algorithms for multi-objective unconstrained binary quadratic programming problem,” Appl. Soft Comput., vol. 81, pp. 105485, Aug. 2019. doi: 10.1016/j.asoc.2019.105485
    [23]
    J. A. Parejo, A. Ruiz-Cortes, S. Lozano, and P. Fernandez, “Metaheuristic optimization frameworks: a survey and benchmarking,” Soft Comput., vol. 16, no. 3, pp. 527–561, Mar. 2012. doi: 10.1007/s00500-011-0754-8
    [24]
    C. Blum, A. Roli, and M. Sampels, Hybrid Metaheuristics: An Emerging Approach to Optimization. Heidelberg, Germany: Springer, 2008.
    [25]
    H. Q. Wang, P. X. Liu, X. D. Zhao, and X. P. Liu, “Adaptive fuzzy finite-time control of nonlinear systems with actuator faults,” IEEE Trans. Cybern., DOI: 10.1109/TCYB.2019.2902868
    [26]
    O. Roeva and T. Slavov, “Pid controller tuning based on metaheuristic algorithms for bioprocess control,” Biotechnol. Biotechnol. Equip., vol. 26, no. 5, pp. 3267–3277, Apr. 2012. doi: 10.5504/BBEQ.2012.0065
    [27]
    A. Song, W. N. Chen, T. L. Gu, H. Q. Yuan, S. Kwong, and J. Zhang, “Distributed virtual network embedding system with historical archives and set-based particle swarm optimization,” IEEE Trans. Syst., Man, Cybern.: Syst., DOI: 10.1109/TSMC.2018.2884523
    [28]
    C. G. Yang, G. Z. Peng, Y. N. Li, R. X. Cui, L. Cheng, and Z. J. Li, “Neural networks enhanced adaptive admittance control of optimized robot-environment interaction,” IEEE Trans. Cybern., vol. 49, no. 7, pp. 2568–2579, Jul. 2019. doi: 10.1109/TCYB.2018.2828654
    [29]
    L. Cheng, W. C. Liu, C. G. Yang, T. W. Huang, Z. G. Hou, and M. Tan, “A neural-network-based controller for piezoelectric-actuated stick-slip devices,” IEEE Trans. Ind. Electron., vol. 65, no. 3, pp. 2598–2607, Mar. 2018. doi: 10.1109/TIE.2017.2740826
    [30]
    H. Y. Liu, L. Cheng, M. Tan, and Z. G. Hou, “Containment control of general linear multi-agent systems with multiple dynamic leaders: a fast sliding mode based approach,” IEEE/CAA J. Autom. Sinica, vol. 1, no. 2, pp. 134–140, Apr. 2014. doi: 10.1109/JAS.2014.7004542
    [31]
    H. Y. Liu, M. C. Zhou, and Q. Liu, “An embedded feature selection method for imbalanced data classification,” IEEE/CAA J. Autom. Sinica, vol. 6, no. 3, pp. 703–715, May 2019. doi: 10.1109/JAS.2019.1911447
    [32]
    X. Luo, Z. D. Wang, and M. S. Shang, “An instance-frequency-weighted regularization scheme for non-negative latent factor analysis on high-dimensional and sparse data,” IEEE Trans. Syst., Man, Cybern.: Syst., DOI: 10.1109/TSMC.2019.2930525
    [33]
    X. S. Yang, Nature-Inspired Metaheuristic Algorithms, Beckington, UK: Luniver Press, 2008.
    [34]
    J. Krause, J. Cordeiro, R. S. Parpinelli, and H. S. Lopes, “A survey of swarm algorithms applied to discrete optimization problems,” in Swarm Intelligence and Bio-Inspired Computation, X. S. Yang, Z. H. Cui, R. B. Xiao, A. H. Gandomi, and M. Karamanoglu, Eds. London, UK: Elsevier, 2013, pp. 169–191.
    [35]
    H. Shayanfar and F. S. Gharehchopogh, “Farmland fertility: a new metaheuristic algorithm for solving continuous optimization problems,” Appl. Soft Comput., vol. 71, pp. 728–746, Oct. 2018. doi: 10.1016/j.asoc.2018.07.033
    [36]
    E. Wari and W. H. Zhu, “A survey on metaheuristics for optimization in food manufacturing industry,” Appl. Soft Comput., vol. 46, pp. 328–343, Sep. 2016. doi: 10.1016/j.asoc.2016.04.034
    [37]
    X. Luo, M. C. Zhou, S. Li, Z. H. You, Y. N. Xia, and Q. S. Zhu, “A nonnegative latent factor model for large-scale sparse matrices in recommender systems via alternating direction method,” IEEE Trans. Neural Networks Learn. Syst., vol. 27, no. 3, pp. 579–592, Mar. 2016. doi: 10.1109/TNNLS.2015.2415257
    [38]
    X. Luo, M. C. Zhou, Y. N. Xia, and Q. S. Zhu, “An efficient non-negative matrix-factorization-based approach to collaborative filtering for recommender systems,” IEEE Trans. Ind. Informatics, vol. 10, no. 2, pp. 1273–1284, May 2014. doi: 10.1109/TII.2014.2308433
    [39]
    J. Q. Li, H. Y. Sang, Q. K. Pan, P. Y. Duan, and K. Z. Gao, “Solving multi-area environmental/economic dispatch by Pareto-based chemical-reaction optimization algorithm,” IEEE/CAA J. Autom. Sinica, vol. 6, no. 5, pp. 1240–1250, Sep. 2019. doi: 10.1109/JAS.2017.7510454
    [40]
    P. J. Angeline, G. M. Saunders, and J. B. Pollack, “An evolutionary algorithm that constructs recurrent neural networks,” IEEE Trans. Neural Networks, vol. 5, no. 1, pp. 54–65, Jan. 1994. doi: 10.1109/72.265960
    [41]
    W. S. Gao and C. Shao, “Iterative dynamic diversity evolutionary algorithm for constrained optimization,” Acta Autom. Sinica, vol. 40, no. 11, pp. 2469–2479, Nov. 2014. doi: 10.1016/S1874-1029(14)60398-0
    [42]
    S. Gupta, K. Deep, A. A. Heidari, H. Moayedi, and H. L. Chen, “Harmonized salp chain-built optimization,” Eng. Comput., DOI: 10.1007/s00366-019-00871-5
    [43]
    D. E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning. Reading, USA: Addion Wesley, 1989.
    [44]
    F. P. Such, V. Madhavan, E. Conti, J. Lehman, K. O. Stanley, and J. Clune, “Deep neuroevolution: genetic algorithms are a competitive alternative for training deep neural networks for reinforcement learning,” arXiv: 1712.06567, 2017.
    [45]
    J. Kennedy and R. Eberhart, “Particle swarm optimization,” in Proc. IEEE Int. Conf. Neural Networks, Perth, Australia, 2001, pp. 1942–1948.
    [46]
    J. J. Wang and T. Kumbasar, “Parameter optimization of interval type-2 fuzzy neural networks based on PSO and BBBC methods,” IEEE/CAA J. Autom. Sinica, vol. 6, no. 1, pp. 247–257, Jan. 2019. doi: 10.1109/JAS.2019.1911348
    [47]
    H. Shi, L. Wang, and T. G. Chu, “Swarming behavior of multi-agent systems,” J. Control Theory Appl., vol. 2, no. 4, pp. 313–318, Nov. 2004. doi: 10.1007/s11768-004-0034-6
    [48]
    M. G. Hinchey, R. Sterritt, and C. Rouff, “Swarms and swarm intelligence,” Computer, vol. 40, no. 4, pp. 111–113, Apr. 2007. doi: 10.1109/MC.2007.144
    [49]
    X. Feng, Y. B. Wang, H. Q. Yu, and F. Luo, “A novel intelligence algorithm based on the social group optimization behaviors,” IEEE Trans. Syst.,Man,Cybern.:Syst., vol. 48, no. 1, pp. 65–76, Jan. 2018. doi: 10.1109/TSMC.2016.2586973
    [50]
    M. Dorigo and G. Di Caro, “Ant colony optimization: a new meta-heuristic,” in Proc. Congr. Evolutionary Computation, Washington, USA, 1999, pp. 1470–1477.
    [51]
    M. Neshat, G. Sepidnam, M. Sargolzaei, and A. N. Toosi, “Artificial fish swarm algorithm: a survey of the state-of-the-art, hybridization, combinatorial and indicative applications,” Artif. Intell. Rev., vol. 42, no. 4, pp. 965–997, Dec. 2014. doi: 10.1007/s10462-012-9342-2
    [52]
    X. Y. Jiang and S. Li, “Bas: beetle antennae search algorithm for optimization problems,” arXiv: 1710.10724, 2017.
    [53]
    X. Y. Jiang and S. Li, “Beetle antennae search without parameter tuning (BAS-WPT) for multi-objective optimization,” arXiv: 1711.02395, 2017.
    [54]
    X. S. Yang and S. Deb, “Engineering optimisation by cuckoo search,” arXiv: 1005.2908, 2010.
    [55]
    J. Zhao, S. X. Liu, M. C. Zhou, X. W. Guo, and L. Qi, “Modified cuckoo search algorithm to solve economic power dispatch optimization problems,” IEEE/CAA J. Autom. Sinica, vol. 5, no. 4, pp. 794–806, Jul. 2018. doi: 10.1109/JAS.2018.7511138
    [56]
    A. R. Mehrabian and C. Lucas, “A novel numerical optimization algorithm inspired from weed colonization,” Ecological Informatics, vol. 1, no. 4, pp. 355–366, Dec. 2006. doi: 10.1016/j.ecoinf.2006.07.003
    [57]
    S. Nakrani and C. Tovey, “On honey bees and dynamic server allocation in internet hosting centers,” Adapt. Behav., vol. 12, no. 3–4, pp. 223–240, Dec. 2004. doi: 10.1177/105971230401200308
    [58]
    D. Karaboga and B. Akay, “A survey: algorithms simulating bee swarm intelligence,” Artif. Intell. Rev., vol. 31, no. 1–4, pp. 61–85, Jun. 2009. doi: 10.1007/s10462-009-9127-4
    [59]
    X. S. Yang, "Firefly algorithms for multimodal optimization," in Proc. 5th Int. Symp. Stochastic Algorithms: Foundations and Applications, Sapporo, Japan, 2009, pp. 169–178.
    [60]
    S. Mirjalili, S. M. Mirjalili, and A. Lewis, “Grey wolf optimizer,” Adv. Eng. Softw., vol. 69, pp. 46–61, Mar. 2014. doi: 10.1016/j.advengsoft.2013.12.007
    [61]
    S. Gupta and K. Deep, “A novel random walk grey wolf optimizer,” Swarm Evol. Comput., vol. 44, pp. 101–112, Feb. 2019. doi: 10.1016/j.swevo.2018.01.001
    [62]
    S. Gupta and K. Deep, “An opposition-based chaotic grey wolf optimizer for global optimisation tasks,” J. Exp. Theor. Artif. Intell., vol. 31, no. 5, pp. 751–779, 2019. doi: 10.1080/0952813X.2018.1554712
    [63]
    S. Gupta and K. Deep, “Improved sine cosine algorithm with crossover scheme for global optimization,” Knowl.-Based Syst., vol. 165, pp. 374–406, Feb. 2019. doi: 10.1016/j.knosys.2018.12.008
    [64]
    S. Gupta and K. Deep, “A hybrid self-adaptive sine cosine algorithm with opposition based learning,” Expert Syst. Appl., vol. 119, pp. 210–230, Apr. 2019. doi: 10.1016/j.eswa.2018.10.050
    [65]
    M. S. Shang, X. Luo, Z. G. Liu, J. Chen, Y. Yuan, and M. C. Zhou, “Randomized latent factor model for high-dimensional and sparse matrices from industrial applications,” IEEE/CAA J. Autom. Sinica, vol. 6, no. 1, pp. 131–141, Jan. 2019. doi: 10.1109/JAS.2018.7511189
    [66]
    Z. Y. Zhu, Z. Y. Zhang, W. S. Man, X. Q. Tong, J. Z. Qiu, and F. F. Li, “A new beetle antennae search algorithm for multi-objective energy management in microgrid,” in Proc. 13th IEEE Conf. Industrial Electronics and Applications, Wuhan, China, 2018, pp. 1599–1603.
    [67]
    X. Y. Yin and Y. Ma, “Aggregation service function chain mapping plan based on beetle antennae search algorithm,” in Proc. 2nd Int. Conf. Telecommunications and Communication Engineering, Beijing, China, 2018, pp. 225–230.
    [68]
    X. M. Lin, Y. F. Liu, and Y. L. Wang, “Design and research of DC motor speed control system based on improved BAS,” in Proc. Chinese Automation Congr., Xi’an, China, 2018, pp. 3701–3705.
    [69]
    Y. T. Sun, J. F. Zhang, G. C. Li, Y. H. Wang, J. B. Sun, and C. Jiang, “Optimized neural network using beetle antennae search for predicting the unconfined compressive strength of jet grouting coalcretes,” Int. J. Numer. Anal. Methods Geomech., vol. 43, no. 4, pp. 801–813, Mar. 2019. doi: 10.1002/nag.2891
    [70]
    Q. Wu, X. D. Shen, Y. Z. Jin, Z. Y. Chen, S. Li, A. H. Khan, and D. C. Chen, “Intelligent beetle antennae search for UAV sensing and avoidance of obstacles,” Sensors, vol. 19, no. 8, pp. 1758, Apr. 2019. doi: 10.3390/s19081758
    [71]
    M. J. Lin and Q. H. Li, “A hybrid optimization method of beetle antennae search algorithm and particle swarm optimization,” DEStech Trans. Engineering and Technology Research, 2018.
    [72]
    Q. Wu, H. Lin, Y. Z. Jin, Z. Y. Chen, S. Li, and D. C. Chen, “A new fallback beetle antennae search algorithm for path planning of mobile robots with collision-free capability,” Soft Comput., vol. 24, no. 3, pp. 2369–2380, Feb. 2020. doi: 10.1007/s00500-019-04067-3
    [73]
    Y. Q. Fan, J. P. Shao, and G. T. Sun, “Optimized PID controller based on beetle antennae search algorithm for electro-hydraulic position servo control system,” Sensors, vol. 19, no. 12, pp. 2727, Jun. 2019. doi: 10.3390/s19122727
    [74]
    S. Xie, X. M. Chu, M. Zheng, and C. G. Liu, “Ship predictive collision avoidance method based on an improved beetle antennae search algorithm,” Ocean Eng., vol. 192, pp. 106542, Nov. 2019. doi: 10.1016/j.oceaneng.2019.106542
    [75]
    J. H. Yang and Z. R. Peng, “Beetle-swarm evolution competitive algorithm for bridge sensor optimal placement in SHM,” IEEE Sens. J., DOI: 10.1109/JSEN.2019.2934996.
    [76]
    N. Qian, “On the momentum term in gradient descent learning algorithms,” Neural Networks, vol. 12, no. 1, pp. 145–151, Jan. 1999. doi: 10.1016/S0893-6080(98)00116-6
    [77]
    J. Duchi, E. Hazan, and Y. Singer, “Adaptive subgradient methods for online learning and stochastic optimization,” J. Machine Learning Research, vol. 12, pp. 2121–2159, Jun. 2011.
    [78]
    M. D. Zeiler, “ADADELTA: an adaptive learning rate method,” arXiv: 1212.5701, 2012.
    [79]
    A. P. Engelbrecht, “Fitness function evaluations: a fair stopping condition?” in Proc. IEEE Symp. Swarm Intelligence, Orlando, USA, 2014, pp. 1–8.
    [80]
    I. Sutskever, O. Vinyals, and Q. V. Le, “Sequence to sequence learning with neural networks,” arXiv: 1409.3215, 2014.
    [81]
    Mathworks, MATLAB: Global Optimization Toolbox 2018b. The Mathworks Inc., 2018.

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Figures(6)

    Article Metrics

    Article views (1472) PDF downloads(66) Cited by()

    Highlights

    • Incorporating the concept of gradient into a metaheuristic optimization framework.
    • Using the ADAM update-rule to adjust the step-size adaptively.
    • Experimental demonstration of smooth convergence and faster convergence near the valley.

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return