### Abstract

We present a genetic algorithm that we developed in order to address computationally expensive optimization problems in optical engineering. The idea consists of working with a population of individuals representing possible solutions to the problem. The best individuals are selected. They generate new individuals for the next generation. Random mutations in the coding of parameters are introduced. This strategy is repeated from generation to generation until the algorithm converges to the global optimum of the problem considered. For computationally expensive problems, one can analyze the data collected by the algorithm in order to infer more rapidly the final solution. The use of a mutation operator that acts on randomly-shifted Gray codes helps the genetic algorithm escape local optima and enables a wider diversity of displacements. These techniques reduce the computational cost of optical engineering problems, where the design parameters have a finite resolution and are limited to a realistic range. We demonstrate the performance of this algorithm by considering a set of 22 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 broadband absorption of electromagnetic radiations.

Original language | English |
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Pages (from-to) | 17-36 |

Number of pages | 20 |

Journal | Jordan Journal of Physics |

Volume | 12 |

Issue number | 1 |

Publication status | Published - 1 Jan 2019 |

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*Jordan Journal of Physics*, vol. 12, no. 1, pp. 17-36.

**A genetic algorithm for addressing computationally expensive optimization problems in optical engineering.** / Mayer, Alexandre; Lobet, Michaël.

Research output: Contribution to journal › Article

TY - JOUR

T1 - A genetic algorithm for addressing computationally expensive optimization problems in optical engineering

AU - Mayer, Alexandre

AU - Lobet, Michaël

PY - 2019/1/1

Y1 - 2019/1/1

N2 - We present a genetic algorithm that we developed in order to address computationally expensive optimization problems in optical engineering. The idea consists of working with a population of individuals representing possible solutions to the problem. The best individuals are selected. They generate new individuals for the next generation. Random mutations in the coding of parameters are introduced. This strategy is repeated from generation to generation until the algorithm converges to the global optimum of the problem considered. For computationally expensive problems, one can analyze the data collected by the algorithm in order to infer more rapidly the final solution. The use of a mutation operator that acts on randomly-shifted Gray codes helps the genetic algorithm escape local optima and enables a wider diversity of displacements. These techniques reduce the computational cost of optical engineering problems, where the design parameters have a finite resolution and are limited to a realistic range. We demonstrate the performance of this algorithm by considering a set of 22 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 broadband absorption of electromagnetic radiations.

AB - We present a genetic algorithm that we developed in order to address computationally expensive optimization problems in optical engineering. The idea consists of working with a population of individuals representing possible solutions to the problem. The best individuals are selected. They generate new individuals for the next generation. Random mutations in the coding of parameters are introduced. This strategy is repeated from generation to generation until the algorithm converges to the global optimum of the problem considered. For computationally expensive problems, one can analyze the data collected by the algorithm in order to infer more rapidly the final solution. The use of a mutation operator that acts on randomly-shifted Gray codes helps the genetic algorithm escape local optima and enables a wider diversity of displacements. These techniques reduce the computational cost of optical engineering problems, where the design parameters have a finite resolution and are limited to a realistic range. We demonstrate the performance of this algorithm by considering a set of 22 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 broadband absorption of electromagnetic radiations.

KW - genetic algorithm

KW - Gray code

KW - quadratic approximation

KW - metamaterial

KW - broadband absorber

UR - http://www.scopus.com/inward/record.url?scp=85065902888&partnerID=8YFLogxK

M3 - Article

VL - 12

SP - 17

EP - 36

JO - Jordan Journal of Physics

JF - Jordan Journal of Physics

SN - 1994-7607

IS - 1

ER -