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

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.