Abstract
This paper addresses the problem of solving a bound constrained global optimization problem by a population-based stochastic coordinate descent method. To improve efficiency, a small subpopulation of points is randomly selected from the original population, at each iteration. The coordinate descent directions are based on the gradient computed at a special point of the subpopulation. This point could be the best point, the center point or the point with highest score. Preliminary numerical experiments are carried out to compare the performance of the tested variants. Based on the results obtained with the selected problems, we may conclude that the variants based on the point with highest score are more robust and the variants based on the best point less robust, although they win on efficiency but only for the simpler and easy to solve problems.
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References
Bottou, L., Curtis, F.E., Nocedal, J.: Optimization methods for large-scale machine learning. Technical Report arXiv:1606.04838v3, Computer Sciences Department, University of Wisconsin-Madison (2018)
Rocha, A.M.A.C., Costa, M.F.P., Fernandes, E.M.G.P.: A stochastic coordinate descent for bound constrained global optimization. AIP Conf. Proc. 2070, 020014 (2019)
Kvasov, D.E., Mukhametzhanov, M.S.: Metaheuristic vs. deterministic global optimization algorithms: the univariate case. Appl. Math. Comput. 318, 245–259 (2018)
Nesterov, Y.: Efficiency of coordinate descent methods on huge-scale optimization problems. SIAM J. Optim. 22(2), 341–362 (2012)
Wright, S.J.: Coordinate descent algorithms. Math. Program. Series B 151(1), 3–34 (2015)
Liu, H., Xu, S., Chen, X., Wang, X., Ma, Q.: Constrained global optimization via a DIRECT-type constraint-handling technique and an adaptive metamodeling strategy. Struct. Multidisc. Optim. 55(1), 155–177 (2017)
Ali, M.M., Khompatraporn, C., Zabinsky, Z.B.: A numerical evaluation of several stochastic algorithms on selected continuous global optimization test problems. J. Glob. Optim. 31(4), 635–672 (2005)
Acknowledgments
This work has been supported by FCT – Fundação para a Ciência e Tecnologia within the Projects Scope: UID/CEC/00319/2019 and UID/MAT/00013/2013.
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Rocha, A.M.C., Costa, M.F.P., Fernandes, E.G.P. (2020). A Population-Based Stochastic Coordinate Descent Method. In: Le Thi, H., Le, H., Pham Dinh, T. (eds) Optimization of Complex Systems: Theory, Models, Algorithms and Applications. WCGO 2019. Advances in Intelligent Systems and Computing, vol 991. Springer, Cham. https://doi.org/10.1007/978-3-030-21803-4_2
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DOI: https://doi.org/10.1007/978-3-030-21803-4_2
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