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

Abstract

A density matrix based soft-computing solution to the quantum mechanical problem of computing the molecular electronic structure of fairly long polythiophene (PT) chains is proposed. The soft-computing solution is based on a "random mutation hill climbing" scheme which is modified by blending it with a deterministic method based on a trial single-particle density matrix [P((0))(R)] for the guessed structural parameters (R), which is allowed to evolve under a unitary transformation generated by the Hamiltonian H(R). The Hamiltonian itself changes as the geometrical parameters (R) defining the polythiophene chain undergo mutation. The scale (λ) of the transformation is optimized by making the energy [E(λ)] stationary with respect to λ. The robustness and the performance levels of variants of the algorithm are analyzed and compared with those of other derivative free methods. The method is further tested successfully with optimization of the geometry of bipolaron-doped long PT chains.

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.…”

“…Our objective is now to maximize F for various choices of α, β and construct the Pareto-front [11,25]. However, unlike in our previous implementation [27] of density matrix based adaptive mutation hill climbing method, we adopt a more straightforward route to handle the constrained variational 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 .…”

Single string based global optimizer for geometry optimization in strongly coupled finite clusters: An adaptive mutation-driven strategy

“…All the particles are within the radius of 0.003 nm in the starting geometry. (b) The energy evolution profile (in the region close to the optimum structure) for LJ 38 cluster. To locate the GM, several restarts from different geometry were required.…”

“…In the context of traditional GA we would like to explore the viability of a single string based evolutionary technique, like the random mutation hill climbing method, 35 with additional built-in features for enforcing adaptive control on all the parameters of the search heuristic. There have been proposals to work with partially adaptive analogues of single string based "mutationonly" search heuristics [36][37][38][39][40] to offset, at least partially, the cost of working with a population in serial computation without losing on the ability to locate the GM. A single parent evolutionary algorithm 41 working with novel cutting and pasting operations on a single parent to produce new members has been quite successful in structure optimization.…”