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\title{Improvements on the GLOBAL Optimization Algorithm with Numerical
Tests}

\author{László Pál\footnote{Faculty of Business and Humanities, Sapientia
University, Csíkszereda, Roumania, plaszlo@inf.u-szeged.hu}, Tibor
Csendes\footnote{Institute of Informatics, University of Szeged, Hungary,
csendes@inf.u-szeged.hu}, Oscar H.\ Sendin\footnote{Instituto de
Investigaciones Marinas, IIM-CSIC Vigo, Spain, \{osendin,
julio\}@iim.csic.es},
and Julio R. Banga$^\ddag$}
\date{}
\maketitle

The task of global optimization is to find a solution in the solution set
for
which the objective function obtains its smallest value, the global minimum.

This talk presents the stochastic global optimization algorithm GLOBAL
\cite{3}, as a non-derivative version of the method of Boender et al.\
\cite{2}. We introduce a new Matlab based version of the original
Fortran and C
code together with some algorithmic improvements. The latter include a new,
BFGS local search procedure, a new Matlab implementation of the UNIRANDI
local
search method\cite{5}, an extended capability for larger dimensional
problems,
and further changes to improve the efficiency of the procedure. A special
attention has been devoted to increasing the reliability, and keeping
the low
computational complexity of the original implementation.

We illustrate the effectiveness of the method on a set of standard test
problems as well as hard global optimization problems \cite{1,6,7} and
compare the numerical results with the old version and with a new direct
search procedure, C-GRASP \cite{4}.
The first indicators are encouraging, and the new Matlab version of the
algorithm
GLOBAL should be available soon at the usual internet place ({\tt
www.inf.u-szeged.hu/$\sim$csendes/reg/regform.php}) for academic and
nonprofit
purposes.

\begin{thebibliography}{9}
\bibitem{1} Banga, J.R., C.G.\ Moles, and A.A.\ Alonso: Global
Optimization of
Bioprocesses using Stochastic and Hybrid Methods. In: C.A. Floudas and P.
Pardalos (eds.): Frontiers in Global Optimization, Springer, Berlin, 2003,
45--70

\bibitem{2} Boender, C.G.E., A.H.G.\ Rinnooy Kan, G.T.\ Timmer, and L.\
Stougie:
A stochastic method for global optimization, Mathematical Programming
22(1982)
125--140

\bibitem{3} Csendes, T.: Nonlinear parameter estimation by global
optimization -- efficiency and reliability. Acta Cybernetica 8(1988) 361-370

\bibitem{4} Hirsch, M.J., C.N.\ Meneses, P.M.\ Pardalos, and M.G.C.\
Resende, Global
optimization by continuous GRASP, accepted for publication in the
Optimization
Letters

\bibitem{5} Järvi, T.: A random search optimizer with an application
to a max-min
problem, Publications of the Institute for Applied Mathematics,
University of
Turku, No.\ 3, 1973.

\bibitem{6} Moles C.G., J.R.\ Banga, and K.\ Keller: Solving nonconvex
climate control
problems: pitfalls and algorithm performances. Applied Soft Computing
5(2004)
35--44
\bibitem{7} Moles C.G., G.\ Gutierrez, A.A.\ Alonso, and J.R.\ Banga:
Integrated process design
and control via global optimization -- A wastewater treatment plant case
study.
Chemical Engineering Research \& Design 81(2003) 507-517

\end{thebibliography}

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