Abstract
A new procedure is suggested to improve genetic algorithms for the prediction of structures of nanoparticles. The strategy focuses on managing the creation of new individuals by evaluating the efficiency of operators (o1, o2,…,o13) in generating well-adapted offspring. This is done by increasing the creation rate of operators with better performance and decreasing that rate for the ones which poorly fulfill the task of creating favorable new generation. Additionally, several strategies (thirteen at this level of approach) from different optimization techniques were implemented on the actual genetic algorithm. Trials were performed on the general case studies of 26 and 55-atom clusters with binding energy governed by a Lennard-Jones empirical potential with all individuals being created by each of the particular thirteen operators tested. A 18-atom carbon cluster and some polynitrogen systems were also studied within REBO potential and quantum approaches, respectively. Results show that our management strategy could avoid bad operators, keeping the overall method performance with great confidence. Moreover, amongst the operators taken from the literature and tested herein, the genetic algorithm was faster when the generation of new individuals was carried out by the twist operator, even when compared to commonly used operators such as Deaven and Ho cut-and-splice crossover. Operators typically designed for basin-hopping methodology also performed well on the proposed genetic algorithm scheme.
Highlights
Clusters are aggregates of atoms or molecules whose structures remain between those of discrete atoms and of the bulk material (Johnston, 2003)
number of local minimizations (NLM) is the average number of local energy minimizations needed to achieve convergence to the global minimum, σx− is the standard error, defined as the standard deviation divided by the square root of the total number of samples, and Nfails is the percentage of seeds employed that did not achieve convergence for a specific build
We call attention to builds Twist operator (TO), Interior operator (IO), Plane-cut-splice crossover (PCCR), AUTO5, AUTO7, Surface angular operator (SAO), and immigration operator (IMM), which managed to find the global minimum on every run
Summary
Clusters are aggregates of atoms or molecules whose structures remain between those of discrete atoms and of the bulk material (Johnston, 2003). Their properties are composition and size dependent. For instance, is non-magnetic in the solid state, but its counterpart clusters may have non-zero magnetic moment (Moseler et al, 2001). Among the wide range of interesting cluster applications one could mention magnetic resonance imaging (Lu et al, 2017), water oxidation (Zhao et al, 2017), magnetic storage (Bader, 2006), and catalysis (Pelegrini et al, 2016). Finding the geometries of small clusters is a challenging task and requires a combination of theoretical and experimental techniques (Götz et al, 2012; Heiles et al, 2012)
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