Genetic algorithms and simulated annealing

Abstract

Many applications require either the maximisation or minimisation of a function. For example, in many fields of theoretical physics, a sum of least squares must be minimised, or the energy of a system must be minimised. Many of the standard numerical techniques which exist for the optimisation of functions apply to functions which can be specified in a relatively straightforward manner. However, many of the functions which arise in the modelling of semiconductor devices cannot be specified in this manner, and some of these functions can only be evaluated using many subsidiary functions and integrals. Genetic algorithms allow such sets of functions to be optimised using random processes to “breed” generations of solutions which should converge to the optimal solution. This chapter presents an introduction to genetic algorithms and simulated annealing. Sections of code written in C++ are used to illustrate the implementation of aspects of the subjects. The coefficients involved in the numerical approximation of the associated Fermi integrals are evaluated using these methods.