A genetic algorithm for addressing computationally expensive optimization problems in optical engineering

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Abstract

We present a genetic algorithm that we developed in order to address computationally expensive optimizationproblems in optical engineering. The idea consists in working with a population of individuals that representpossible solutions to the problem. The best individuals are selected. They generate new individuals for thenext generation. Random mutations in the coding of parameters are introduced. This strategy is repeated fromgeneration to generation until the algorithm converges to the global optimum of the problem considered. Forcomputationally expensive problems, one can analyze the data collected by the algorithm in order to infer morerapidly the final solution. The use of a mutation operator that acts on randomly-shifted Gray codes helps thegenetic algorithm to escape local optima and enables a wider diversity of displacements. These techniques reducethe computational cost of optical engineering problems, where the design parameters have a finite resolution andare limited to a realistic range. We demonstrate the performance of this algorithm by considering a set of22 benchmark problems in 5, 10 and 20 dimensions that reflect the conditions of these engineering problems.We finally show how these techniques accelerate the determination of optimal structures for the broadbandabsorption of electromagnetic radiations.
Original languageEnglish
Pages (from-to)17-36
Number of pages19
JournalJordan Journal of Physics
Volume12
Issue number1
Publication statusPublished - 2019

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genetic algorithms
engineering
optimization
mutations
escape
electromagnetic radiation
coding
costs
operators

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    Cite this

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    abstract = "We present a genetic algorithm that we developed in order to address computationally expensive optimizationproblems in optical engineering. The idea consists in working with a population of individuals that representpossible solutions to the problem. The best individuals are selected. They generate new individuals for thenext generation. Random mutations in the coding of parameters are introduced. This strategy is repeated fromgeneration to generation until the algorithm converges to the global optimum of the problem considered. Forcomputationally expensive problems, one can analyze the data collected by the algorithm in order to infer morerapidly the final solution. The use of a mutation operator that acts on randomly-shifted Gray codes helps thegenetic algorithm to escape local optima and enables a wider diversity of displacements. These techniques reducethe computational cost of optical engineering problems, where the design parameters have a finite resolution andare limited to a realistic range. We demonstrate the performance of this algorithm by considering a set of22 benchmark problems in 5, 10 and 20 dimensions that reflect the conditions of these engineering problems.We finally show how these techniques accelerate the determination of optimal structures for the broadbandabsorption of electromagnetic radiations.",
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    AU - Mayer, Alexandre

    AU - Lobet, Michaël

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    N2 - We present a genetic algorithm that we developed in order to address computationally expensive optimizationproblems in optical engineering. The idea consists in working with a population of individuals that representpossible solutions to the problem. The best individuals are selected. They generate new individuals for thenext generation. Random mutations in the coding of parameters are introduced. This strategy is repeated fromgeneration to generation until the algorithm converges to the global optimum of the problem considered. Forcomputationally expensive problems, one can analyze the data collected by the algorithm in order to infer morerapidly the final solution. The use of a mutation operator that acts on randomly-shifted Gray codes helps thegenetic algorithm to escape local optima and enables a wider diversity of displacements. These techniques reducethe computational cost of optical engineering problems, where the design parameters have a finite resolution andare limited to a realistic range. We demonstrate the performance of this algorithm by considering a set of22 benchmark problems in 5, 10 and 20 dimensions that reflect the conditions of these engineering problems.We finally show how these techniques accelerate the determination of optimal structures for the broadbandabsorption of electromagnetic radiations.

    AB - We present a genetic algorithm that we developed in order to address computationally expensive optimizationproblems in optical engineering. The idea consists in working with a population of individuals that representpossible solutions to the problem. The best individuals are selected. They generate new individuals for thenext generation. Random mutations in the coding of parameters are introduced. This strategy is repeated fromgeneration to generation until the algorithm converges to the global optimum of the problem considered. Forcomputationally expensive problems, one can analyze the data collected by the algorithm in order to infer morerapidly the final solution. The use of a mutation operator that acts on randomly-shifted Gray codes helps thegenetic algorithm to escape local optima and enables a wider diversity of displacements. These techniques reducethe computational cost of optical engineering problems, where the design parameters have a finite resolution andare limited to a realistic range. We demonstrate the performance of this algorithm by considering a set of22 benchmark problems in 5, 10 and 20 dimensions that reflect the conditions of these engineering problems.We finally show how these techniques accelerate the determination of optimal structures for the broadbandabsorption of electromagnetic radiations.

    KW - genetic algorithm

    KW - Gray code

    KW - quadratic approximation

    KW - metamaterial

    KW - broadband absorber

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