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

• Main Author: Costa, M. Fernanda P.
• Publication Date: 2017
• Other Authors: Francisco, Rogério Brochado, Rocha, Ana Maria A. C., Fernandes, Edite Manuela da G. P.
• Format: Article
• Language: eng
• Source: Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
• Download full: http://hdl.handle.net/1822/49143
• topic: Global optimization; Self-adaptive penalty; Firefly algorithm; Ciências Naturais::Matemáticas; Science & Technology

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.