Local search with quadratic approximation in genetic algorithms for expensive optimization problems

Elizabeth F. Wanner*, Frederico G. Guimaraes, Ricardo H.C. Takahashi, Peter J. Fleming

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

In this paper, we propose a local search methodology to be coupled with a Genetic Algorithm to solve optimization problems with non-linear constraints. This methodology uses quadratic approximations for both objective function and constraints. In the local search phase, these quadratic approximations define an associated problem that is solved using a linear matrix inequality (LMI) formulation. The number of function evaluations needed for finding the point of optimum is significantly reduced with this procedure, what makes the proposed methodology suitable for dealing with costly blackbox optimization problems. A case study is presented: the well-known TEAM 22 benchmark problem, an expensive problem of electromagnetic design. The results show that the hybrid algorithm has a better performance when compared to the same Genetic Algorithm without the proposed local search operator.

Original languageEnglish
Title of host publication2007 IEEE Congress on Evolutionary Computation, CEC 2007
PublisherIEEE
Pages677-683
Number of pages7
ISBN (Print)1424413400, 9781424413409
DOIs
Publication statusPublished - 1 Dec 2007
Event2007 IEEE Congress on Evolutionary Computation, CEC 2007 - , Singapore
Duration: 25 Sep 200728 Sep 2007

Conference

Conference2007 IEEE Congress on Evolutionary Computation, CEC 2007
CountrySingapore
Period25/09/0728/09/07

Fingerprint

Quadratic Approximation
Local Search
Genetic algorithms
Genetic Algorithm
Optimization Problem
Methodology
Function evaluation
Linear matrix inequalities
Mathematical operators
Nonlinear Constraints
Evaluation Function
Hybrid Algorithm
Black Box
Matrix Inequality
Linear Inequalities
Objective function
Benchmark
Formulation
Operator
Local search (optimization)

Cite this

Wanner, E. F., Guimaraes, F. G., Takahashi, R. H. C., & Fleming, P. J. (2007). Local search with quadratic approximation in genetic algorithms for expensive optimization problems. In 2007 IEEE Congress on Evolutionary Computation, CEC 2007 (pp. 677-683). [4424536] IEEE. https://doi.org/10.1109/CEC.2007.4424536
Wanner, Elizabeth F. ; Guimaraes, Frederico G. ; Takahashi, Ricardo H.C. ; Fleming, Peter J. / Local search with quadratic approximation in genetic algorithms for expensive optimization problems. 2007 IEEE Congress on Evolutionary Computation, CEC 2007. IEEE, 2007. pp. 677-683
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Wanner, EF, Guimaraes, FG, Takahashi, RHC & Fleming, PJ 2007, Local search with quadratic approximation in genetic algorithms for expensive optimization problems. in 2007 IEEE Congress on Evolutionary Computation, CEC 2007., 4424536, IEEE, pp. 677-683, 2007 IEEE Congress on Evolutionary Computation, CEC 2007, Singapore, 25/09/07. https://doi.org/10.1109/CEC.2007.4424536

Local search with quadratic approximation in genetic algorithms for expensive optimization problems. / Wanner, Elizabeth F.; Guimaraes, Frederico G.; Takahashi, Ricardo H.C.; Fleming, Peter J.

2007 IEEE Congress on Evolutionary Computation, CEC 2007. IEEE, 2007. p. 677-683 4424536.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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N2 - In this paper, we propose a local search methodology to be coupled with a Genetic Algorithm to solve optimization problems with non-linear constraints. This methodology uses quadratic approximations for both objective function and constraints. In the local search phase, these quadratic approximations define an associated problem that is solved using a linear matrix inequality (LMI) formulation. The number of function evaluations needed for finding the point of optimum is significantly reduced with this procedure, what makes the proposed methodology suitable for dealing with costly blackbox optimization problems. A case study is presented: the well-known TEAM 22 benchmark problem, an expensive problem of electromagnetic design. The results show that the hybrid algorithm has a better performance when compared to the same Genetic Algorithm without the proposed local search operator.

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Wanner EF, Guimaraes FG, Takahashi RHC, Fleming PJ. Local search with quadratic approximation in genetic algorithms for expensive optimization problems. In 2007 IEEE Congress on Evolutionary Computation, CEC 2007. IEEE. 2007. p. 677-683. 4424536 https://doi.org/10.1109/CEC.2007.4424536