Limits...
Evolving random fractal Cantor superlattices for the infrared using a genetic algorithm.

Bossard JA, Lin L, Werner DH - J R Soc Interface (2016)

Bottom Line: Fractal geometry, often described as the geometry of Nature, can be used to mimic structures found in Nature, but deterministic fractals produce structures that are too 'perfect' to appear natural.Furthermore, we introduce fractal random Cantor bars as a candidate for generating both ordered and 'chaotic' superlattices, such as the ones found in silvery fish.We present optimized superlattices demonstrating broadband reflection as well as single and multiple pass bands in the near-infrared regime.

View Article: PubMed Central - PubMed

Affiliation: Department of Electrical Engineering, The Pennsylvania State University, 211A Electrical Engineering East, University Park, PA 16802, USA jab678@psu.edu.

No MeSH data available.


Related in: MedlinePlus

(a) Flowchart shows the operation of the genetic algorithm optimizer. (b) Illustration shows the crossover and mutation operators used to produce offspring from two parent chromosomes. The binary offspring1 chromosome has been mapped to an equivalent stage 4 multi-generator Cantor superlattice. (Online version in colour.)
© Copyright Policy - open-access
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC4759801&req=5

RSIF20150975F4: (a) Flowchart shows the operation of the genetic algorithm optimizer. (b) Illustration shows the crossover and mutation operators used to produce offspring from two parent chromosomes. The binary offspring1 chromosome has been mapped to an equivalent stage 4 multi-generator Cantor superlattice. (Online version in colour.)

Mentions: In order to exploit the multi-generator Cantor bar fractal to generate superlattices with desired spectral properties, a GA was employed to evolve the superlattice structure. The GA is a robust stochastic optimizer that has been used to solve a variety of challenging electromagnetic design problems [17]. The GA is a popular optimizer within the electromagnetics community, because it is simple to implement and capable of solving problems with many design parameters. The GA itself is inspired by Nature as it emulates the natural evolutionary process, so combining it with the multi-generator fractal model allows us to not only mimic the superlattice geometries identified in Nature, but also to evolve optimum designs as would happen in Nature. The operating principle of the GA comes from the Darwinian notion of natural selection, where a population of design candidates competes for survival at each iteration of the optimization process. The operation of the GA is illustrated by a flowchart in figure 4a. Each population member has a binary chromosome, or a string of bits, into which the design parameters are encoded. At every iteration in the design process, all population members are evaluated for fitness and then ranked according to the individual member fitness. Members with better fitness are selected for procreation via tournament selection and then mated by crossing over their genetic data to produce two new offspring in the next generation. Crossover is accomplished by randomly selecting a point along the chromosome and then swapping the data from both chromosomes after the crossover point to produce two offspring that both contain genetic data from the two parents. A mutation operator is also applied to the new population members that randomly flips a small percentage of bits in their chromosomes, so that new regions of the parameter space are continually explored. The crossover and mutation operations are illustrated in figure 4b.Figure 4.


Evolving random fractal Cantor superlattices for the infrared using a genetic algorithm.

Bossard JA, Lin L, Werner DH - J R Soc Interface (2016)

(a) Flowchart shows the operation of the genetic algorithm optimizer. (b) Illustration shows the crossover and mutation operators used to produce offspring from two parent chromosomes. The binary offspring1 chromosome has been mapped to an equivalent stage 4 multi-generator Cantor superlattice. (Online version in colour.)
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4759801&req=5

RSIF20150975F4: (a) Flowchart shows the operation of the genetic algorithm optimizer. (b) Illustration shows the crossover and mutation operators used to produce offspring from two parent chromosomes. The binary offspring1 chromosome has been mapped to an equivalent stage 4 multi-generator Cantor superlattice. (Online version in colour.)
Mentions: In order to exploit the multi-generator Cantor bar fractal to generate superlattices with desired spectral properties, a GA was employed to evolve the superlattice structure. The GA is a robust stochastic optimizer that has been used to solve a variety of challenging electromagnetic design problems [17]. The GA is a popular optimizer within the electromagnetics community, because it is simple to implement and capable of solving problems with many design parameters. The GA itself is inspired by Nature as it emulates the natural evolutionary process, so combining it with the multi-generator fractal model allows us to not only mimic the superlattice geometries identified in Nature, but also to evolve optimum designs as would happen in Nature. The operating principle of the GA comes from the Darwinian notion of natural selection, where a population of design candidates competes for survival at each iteration of the optimization process. The operation of the GA is illustrated by a flowchart in figure 4a. Each population member has a binary chromosome, or a string of bits, into which the design parameters are encoded. At every iteration in the design process, all population members are evaluated for fitness and then ranked according to the individual member fitness. Members with better fitness are selected for procreation via tournament selection and then mated by crossing over their genetic data to produce two new offspring in the next generation. Crossover is accomplished by randomly selecting a point along the chromosome and then swapping the data from both chromosomes after the crossover point to produce two offspring that both contain genetic data from the two parents. A mutation operator is also applied to the new population members that randomly flips a small percentage of bits in their chromosomes, so that new regions of the parameter space are continually explored. The crossover and mutation operations are illustrated in figure 4b.Figure 4.

Bottom Line: Fractal geometry, often described as the geometry of Nature, can be used to mimic structures found in Nature, but deterministic fractals produce structures that are too 'perfect' to appear natural.Furthermore, we introduce fractal random Cantor bars as a candidate for generating both ordered and 'chaotic' superlattices, such as the ones found in silvery fish.We present optimized superlattices demonstrating broadband reflection as well as single and multiple pass bands in the near-infrared regime.

View Article: PubMed Central - PubMed

Affiliation: Department of Electrical Engineering, The Pennsylvania State University, 211A Electrical Engineering East, University Park, PA 16802, USA jab678@psu.edu.

No MeSH data available.


Related in: MedlinePlus