Direct search for wave operator by a Genetic Algorithm (GA): Route to few eigenvalues of a Hamiltonian

Abstract

A Genetic Algorithm is invoked to search out the wave operator leading to the determination of a few eigenvalues and eigenvectors of a specially designed real symmetric matrix (Durand matrix) that simulates a Hamiltonian supporting bound states coupled to continuum.The performance is compared with that of a standard iterative method for different partition sizes, and parallelizability of the GA-based approach is tested.In many cases the GA-based approach smoothly converges while the standard iterative schemes diverge.

A constrained variational approach to the designing of low transport band gap materials: A multiobjective random mutation hill climbing method

“…MOGAs work with large populations. Considering limitations to our computational resources, we propose to use the weighted cost function approach with ARMHC method as the searching device [26][27][28]. The weighted costfunction approach is possibly the simplest way to handle a MOO problem.…”

“…where l is a randomly chosen integer, m is an adaptive mutation intensity [27,28] and r is a random number in the range 0 ≤ r ≤ 1. This transformation is applied to all those R o k s in S(R) for which a random number r k (0, 1) generated in a set of "n" trials (called a generation) is less than a preassigned mutation probability p m .…”

Blending Determinism with Evolutionary Computing: Applications to the Calculation of the Molecular Electronic Structure of Polythiophene

“…We choose one of the parameters, say the k th parameter, randomly with a probability p m for mutation. The mutation induces a small change in the chosen parameter ( R k ) in the following manner: R k ′ = R k + ( − 1 ) l Δ m r where l is a random integer, r is a random number in the range (0, 1), and Δ m is a directed mutation intensity (see later). The mutated string s ( R 1 , R 2 , R 3 , ..., R k ′ , ..., R m , ..., R M ) is used to generate the π-electron Hamiltonian H e π ( R ′), which in turn generates the unitary transformation matrix U λ = e − i λ H e π ( R′ ) where λ defines the scale of the transformation.…”

Pure and Hybrid Evolutionary Computing in Global Optimization of Chemical Structures: from Atoms and Molecules to Clusters and Crystals

“…The + or − sign is chosen with a probability of 0.5. ∆ m is the mutation intensity, dynamically adjusted on the basis of the degree of acceptability of mutation over a number of past generations [55,56].…”