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Projeto de investigação
Improving the performance and moving to newer dimensions in Derivative-Free Optimization
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Contributions to the development of an integrated toolbox of solvers in Derivative-Free Optimization
Publication . Tavares, Sérgio Filipe Faustino; Duarte, Vítor; Custódio, Ana; Medeiros, Pedro
This dissertation is framed on the ongoing research project BoostDFO - Improving
the performance and moving to newer dimensions in Derivative-Free Optimization. The final
goal of this project is to develop efficient and robust algorithms for Global and/or
Multiobjective Derivative-free Optimization. This type of optimization is typically required
in complex scientific/industrial applications, where the function evaluation is
time-consuming and derivatives are not available for use, neither can be numerically
approximated. Often problems present several conflicting objectives or users aspire to
obtain global solutions.
Inspired by successful approaches used in single objective local Derivative-free Optimization,
we intend to address the inherent problem of the huge execution times by
resorting to parallel/cloud computing and carrying a detailed performance analysis. As
result, an integrated toolbox for solving single/multi objective, local/global Derivativefree
Optimization problems is made available, with recommendations for taking advantage
of parallelization and cloud computing, providing easy access to several efficient and
robust algorithms and allowing to tackle harder Derivative-free Optimization problems.
INCORPORATING RADIAL BASIS FUNCTIONS IN GLOBAL AND LOCAL DIRECT SEARCH
Publication . Baptista, Bruno Alexandre da Anunciação; Custódio, Ana; Brás, Carmo
GLODS is a global derivative-free optimization algorithm, relying on local directional
direct search, aided by a clever multistart strategy that does not conduct all the lines of
search until the end. In 2015, time of the first release of the corresponding solver, GLODS
was shown to be competitive when compared to state-of-the-art algorithms, such as MCS
or DIRECT.
GLODS resorts to sampling techniques to look for minima on a global scale, not
taking advantage of the information gathered in previous iterations. As such, the main
goal of this work is to replace the pseudo-random sampling approach, used by GLODS
to initialize new lines of search, by the minimization of global models of the objective
function, defined using radial basis functions, and computed using the points previously
evaluated by the algorithm. This should allow a better placement of the starting points for
new local lines of search, and, in turn, significantly increase the numerical performance
of the algorithm.
Naturally, incorporating radial basis functions in GLODS poses new challenges. In
this work, we will address questions such as which radial basis functions to use, which
points should be selected to compute them, how to minimize these functions, and how to
take advantage of their minima in the execution of the algorithm.
The new version of GLODS, incorporating radial basis functions, was calibrated to
its best numerical performance, and then compared against other state-of-the-art solvers,
such as MCS, DIRECT, MATSuMoTo, and ZOOpt. The results obtained are strongly
positive. The new algorithm clearly outperforms its previous version, and is competitive
with the other solvers tested.
Finally, parallel strategies were implemented and tested. Results showed that it is
very beneficial to evaluate multiple points simultaneously, for objective functions whose
evaluation time is as low as 0.1 seconds. The proposed algorithm, called BoostGLODS, is
a cutting-edge, powerful and efficient parallel global derivative-free optimization algo-
rithm.
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Entidade financiadora
Fundação para a Ciência e a Tecnologia
Programa de financiamento
3599-PPCDT
Número da atribuição
PTDC/MAT-APL/28400/2017