On a smoothed penalty-based algorithm for global optimization

Ana Maria A. C. Rocha (), M. Fernanda P. Costa () and Edite M. G. P. Fernandes ()
Additional contact information
Ana Maria A. C. Rocha: University of Minho
M. Fernanda P. Costa: University of Minho
Edite M. G. P. Fernandes: Algoritmi Research Centre, University of Minho

Journal of Global Optimization, 2017, vol. 69, issue 3, No 3, 585 pages

Abstract: Abstract This paper presents a coercive smoothed penalty framework for nonsmooth and nonconvex constrained global optimization problems. The properties of the smoothed penalty function are derived. Convergence to an $$\varepsilon $$ ε -global minimizer is proved. At each iteration k, the framework requires the $$\varepsilon ^{(k)}$$ ε ( k ) -global minimizer of a subproblem, where $$\varepsilon ^{(k)} \rightarrow \varepsilon $$ ε ( k ) → ε . We show that the subproblem may be solved by well-known stochastic metaheuristics, as well as by the artificial fish swarm (AFS) algorithm. In the limit, the AFS algorithm convergence to an $$\varepsilon ^{(k)}$$ ε ( k ) -global minimum of the real-valued smoothed penalty function is guaranteed with probability one, using the limiting behavior of Markov chains. In this context, we show that the transition probability of the Markov chain produced by the AFS algorithm, when generating a population where the best fitness is in the $$\varepsilon ^{(k)}$$ ε ( k ) -neighborhood of the global minimum, is one when this property holds in the current population, and is strictly bounded from zero when the property does not hold. Preliminary numerical experiments show that the presented penalty algorithm based on the coercive smoothed penalty gives very competitive results when compared with other penalty-based methods.

Keywords: Global optimization; Penalty function; Artificial fish swarm; Markov chains (search for similar items in EconPapers)
Date: 2017
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10898-017-0504-2 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jglopt:v:69:y:2017:i:3:d:10.1007_s10898-017-0504-2

Ordering information: This journal article can be ordered from
http://www.springer. ... search/journal/10898

DOI: 10.1007/s10898-017-0504-2

Access Statistics for this article

Journal of Global Optimization is currently edited by Sergiy Butenko

More articles in Journal of Global Optimization from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().