Genetic Algorithms for Interior Comparative Optimization of Standard BCS Parameters in Selected Superconductors and High-Temperature Superconductors

Abstract

Inverse least squares numerical optimization, 3D/4D interior optimization, and 3D/4D graphical optimization software and algorithm programming have been presented in a series of previous articles on the applications of the BCS theory of superconductivity and TC dual/multiobjective optimizations. This study deals with the comparison/validation of the optimization results using several different methods, namely, classical inverse least squares (ILS), genetic algorithms (GA), 3D/4D interior optimization, and 2D/3D/4D graphical optimization techniques. The results comprise Tikhonov regularization algorithms and mathematical methods for all the research subjects. The findings of the mathematical programming for optimizing type I chrome isotope superconductors are validated with the genetic algorithms and compared to previous results of 3D/4D interior optimization. Additional rulings present a hypothesis of the new ‘molecular effect’ model/algorithm intended to be proven for Hg-cuprate-type high-temperature superconductors. In molecular effect optimization, inverse least squares and inverse least squares polynomial methods are applied with acceptable numerical and 2D graphical optimization solutions. For the BCS isotope effect and molecular effect, linearization logarithmic transformations for model formula software are implemented in specific programs. The solutions show accuracy with low programming residuals and confirm these findings. The results comprise two strands, the modeling for the isotope effect and molecular effect hypotheses and the development of genetic algorithms and inverse least squares-improved programming methods. Electronic physics applications in superconductors and high-temperature superconductors emerged from the rulings. Extrapolated applications for new modeling for the theory of superconductivity emerged from the numerical and image data obtained.