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Numerical Algorithms for the Parametric Continuation of Stiff ODEs Deriving from the Modeling of Combustion with Detailed Chemical Mechanisms Read chapter Read first chapter

2020 | OriginalPaper | Chapter

Objective and Violation Upper Bounds on a DIRECT-Filter Method for Global Optimization

Authors : M. Fernanda P. Costa, Ana Maria A. C. Rocha, Edite M. G. P. Fernandes

Published in: Numerical Computations: Theory and Algorithms

Publisher: Springer International Publishing

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Abstract

This paper addresses the problem of solving a constrained global optimization problem using a modification of the DIRECT method that incorporates the filter methodology to simultaneously minimize the objective function and the constraints violation. Thus, in the “Selection” step of the herein proposed DIRECT-filter algorithm, the hyperrectangles are classified in four categories and subsequently handled separately. The new algorithm also imposes upper bounds on the objective function and constraints violation aiming to discard some hyperrectangles from the process of identifying the potentially optimal ones. A heuristic to avoid the exploration of the hyperrectangles that have been mostly divided is also implemented. Preliminary numerical experiments are carried out to show the effectiveness of the imposed upper bounds on the objective and violation as well as the goodness of the heuristic.

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previous chapter A New Syntax for Diagrammatic Logic: A Generic Figures Approach
next chapter The Approximate Synthesis of Optimal Control for Heterogeneous Discrete Systems with Intermediate Criteria
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Metadata
Title
Objective and Violation Upper Bounds on a DIRECT-Filter Method for Global Optimization
Authors
M. Fernanda P. Costa
Ana Maria A. C. Rocha
Edite M. G. P. Fernandes
Copyright Year
2020
Book
Numerical Computations: Theory and Algorithms

Print ISBN: 978-3-030-40615-8

Electronic ISBN: 978-3-030-40616-5

Copyright Year: 2020

DOI
https://doi.org/10.1007/978-3-030-40616-5_5

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