The Genetic Algorithm: Using Biology to Compute Liquid Crystal Director Configurations

Abstract

The genetic algorithm is an optimization routine for finding the solution to a problem that requires a function to be minimized. It accomplishes this by creating a population of solutions and then producing “offspring” solutions from this population by combining two “parental” solutions in much the way that the DNA of biological parents is combined in the DNA of offspring. Strengths of the algorithm include that it is simple to implement, no trial solution is required, and the results are fairly accurate. Weaknesses include its slow computational speed and its tendency to find a local minimum that does not represent the global minimum of the function. By minimizing the elastic, surface, and electric free energies, the genetic algorithm is used to compute the liquid crystal director configuration for a wide range of situations, including one- and two-dimensional problems with various forms of boundary conditions, with and without an applied electric field. When appropriate, comparisons are made with the exact solutions. Ways to increase the performance of the algorithm as well as how to avoid various pitfalls are discussed.