Abstract
This paper proposes a self-adaptive penalty function and presents a penalty-based algorithm for solving nonsmooth and nonconvex constrained optimization problems. We prove that the general constrained optimization problem is equivalent to a bound constrained problem in the sense that they have the same global solutions. The global minimizer of the penalty function subject to a set of bound constraints may be obtained by a population-based meta-heuristic. Further, a hybrid self-adaptive penalty firefly algorithm, with a local intensification search, is designed, and its convergence analysis is established. The numerical experiments and a comparison with other penalty-based approaches show the effectiveness of the new self-adaptive penalty algorithm in solving constrained global optimization problems.
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Acknowledgements
The authors would like to thank the referees, the Associate Editor and the Editor-in-Chief for their valuable comments and suggestions to improve the paper. This work has been supported by COMPETE: POCI-01-0145-FEDER-007043 and FCT—Fundação para a Ciência e Tecnologia within the Projects UID/CEC/00319/2013 and UID/MAT/00013/2013.
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Costa, M.F.P., Francisco, R.B., Rocha, A.M.A.C. et al. Theoretical and Practical Convergence of a Self-Adaptive Penalty Algorithm for Constrained Global Optimization. J Optim Theory Appl 174, 875–893 (2017). https://doi.org/10.1007/s10957-016-1042-7
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DOI: https://doi.org/10.1007/s10957-016-1042-7