Theoretical and practical convergence of a self-adaptive penalty algorithm for constrained global optimization

• Published in: Journal of optimization theory and applications Vol. 174; no. 3; pp. 875 - 893
• Main Authors: Costa, M. Fernanda P., Francisco, Rogério Brochado, Rocha, Ana Maria A. C., Fernandes, Edite Manuela da G. P.
• Format: Journal Article
• Language: English
• Published: New York Springer 01.09.2017; Springer US; Springer Nature B.V
• Subjects: Adaptive algorithms; Algorithms; Applications of Mathematics; Calculus of Variations and Optimal Control; Optimization; Ciências Naturais; Convergence; Engineering; Firefly algorithm; Global optimization; Heuristic methods; Matemáticas; Mathematics; Mathematics and Statistics; Nonlinear programming; Operations Research/Decision Theory; Optimization; Penalty function; Science & Technology; Theory of Computation; Self-adaptive penalty; Global optimization; 90C26; 90C59; 90C30; Firefly algorithm
• ISSN: 0022-3239; 1573-2878
• DOI: 10.1007/s10957-016-1042-7

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. 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 - Funda¸c˜ao para a Ciˆencia e Tecnologia within the projects UID/CEC/00319/2013 and UID/MAT/00013/2013.