Crystal structure prediction of materials with high symmetry using differential evolution

Modifications for the Differential Evolution Algorithm

Differential Evolution (DE) is a method of optimization used in symmetrical optimization problems and also in problems that are not even continuous, and are noisy and change over time. DE optimizes a problem with a population of candidate solutions and creates new candidate solutions per generation in combination with existing rules according to discriminatory rules. The present work proposes two variations for this method. The first significantly improves the termination of the method by proposing an asymptotic termination rule, which is based on the differentiation of the average of the function values in the population of DE. The second modification proposes a new scheme for a critical parameter of the method, which improves the method’s ability to better explore the search space of the objective function. The proposed variations have been tested on a number of problems from the current literature, and from the experimental results, it appears that the proposed modifications render the method quite robust and faster even in large-scale problems.

Crystal Structure Prediction Using an Age-Fitness Multiobjective Genetic Algorithm and Coordination Number Constraints

Crystal structure prediction (CSP) has emerged as one of the most important approaches for discovering new materials. CSP algorithms based on evolutionary algorithms and particle swarm optimization have discovered a great number of new materials. However, these algorithms based on ab initio calculation of free energy are inefficient. Moreover, they have severe limitations in terms of scalability. We recently proposed a promising crystal structure prediction method based on atomic contact maps, using global optimization algorithms to search for the Wyckoff positions by maximizing the match between the contact map of the predicted structure and the contact map of the true crystal structure. However, our previous contact-map-based CSP algorithms have two major limitations: (1) the loss of search capability due to getting trapped in local optima; (2) it only uses the connection of atoms in the unit cell to predict the crystal structure, ignoring the chemical environment outside the unit cell, which may lead to unreasonable coordination environments. Herein, we propose a novel multiobjective genetic algorithm for contact-map-based crystal structure prediction by optimizing three objectives, including contact map match accuracy, individual age, and coordination number match. Furthermore, we assign the age values to all the individuals of the GA and try to minimize the age, aiming to avoid the premature convergence problem. Our experimental results show that compared to our previous CMCrystal algorithm, our multiobjective crystal structure prediction algorithm (CMCrystalMOO) can reconstruct the crystal structure with higher quality and alleviate the problem of premature convergence. The source code is open sourced and can be accessed at https://github.com/usccolumbia/MOOCSP.