Modified Particle Swarm Optimization Algorithms for the Generation of Stable Structures of Carbon Clusters, Cn (n = 3–6, 10)

Abstract

Particle Swarm Optimization (PSO), a population based technique for stochastic search in a multidimensional space, has so far been employed successfully for solving a variety of optimization problems including many multifaceted problems, where other popular methods like steepest descent, gradient descent, conjugate gradient, Newton method, etc. do not give satisfactory results. Herein, we propose a modified PSO algorithm for unbiased global minima search by integrating with density functional theory which turns out to be superior to the other evolutionary methods such as simulated annealing, basin hopping and genetic algorithm. The present PSO code combines evolutionary algorithm with a variational optimization technique through interfacing of PSO with the Gaussian software, where the latter is used for single point energy calculation in each iteration step of PSO. Pure carbon and carbon containing systems have been of great interest for several decades due to their important role in the evolution of life as well as wide applications in various research fields. Our study shows how arbitrary and randomly generated small C n clusters ( n = 3–6, 10) can be transformed into the corresponding global minimum structure. The detailed results signify that the proposed technique is quite promising in finding the best global solution for small population size clusters.

Atomic Clusters: Structure, Reactivity, Bonding, and Dynamics

“…DFT-PSO adjusts each particle's trajectory at every time stamp while following the convergence criteria. We have successfully implemented these techniques to find the GM configurations for small-sized nonmetallic clusters such as Boron (B 5 and B 6 ) (Yuan et al, 2014), Carbon (C 5 ) (Jana et al, 2019), and polynitrogen clusters (N 4 2and N 6 4-) (Mitra et al, 2021), and metallic clusters such as Al 4 2- (Mitra et al, 2020), Au n (n 2-8), and Au n Ag m (2 ≤ n+m ≤ 8) (Mitra et al, 2021).…”

“…Various models/empirical potentials (EPs) such as Lennard-Jones (LJ), Born-Mayer, Sutton-Chen, Gupta and Murrell-Mottram potentials can effectively explain the bonding within various clusters. A number of studies performed by Chattaraj et al reveal that PSO is more efficient than commonly used techniques such as GA, SA, and BH for finding the GM of small clusters (Mitikiri et al, 2018;Jana et al, 2019). Further developments over PSO algorithm have been accomplished.…”

“…Global optimization of boron clusters (B 5 and B 6 ) has been studied using an advanced PSO approach by Mitikiri et al (2018). Jana et al (2019) performed a similar study on carbon clusters, C n (n 3-6,10) by using a modified PSO algorithm. Mitra et al (2020) reported the global optimization of Al 4 2clusters by using firefly algorithm along with DFT.…”

Image-based stroke rat brain atrophy volume and infarct volume computation

“…where c 0 is an inertial parameter affecting the movement propagation given by last velocity value, and two acceleration coefficients c 1 and c 2 , respectively, are the importance of personal best value and the importance of social best value; rand 1 and rand 2 are two random numbers between [0, 1]. Shi and Eberhart [21] indicated that choosing c 0 ϵ [0.8, 1.2] results in faster convergence, hence, in this study, we set c 0 = 1. Generally, c 1 and c 2 are set to 2.…”

Search for Global Minimum Structures of P2n+1+ (n = 1–15) Using xTB-Based Basin-Hopping Algorithm

“…Since the numbers of local minima grow quickly with the size of clusters, the global optimization becomes a very difficult task to overcome. Thus, different search algorithms and methodologies, including the genetic algorithm (GA) (Hartke, 1993;Deaven and Ho, 1995;Hartke, 1995;Daven et al, 1996;Rogan et al, 2013;Kanters and Donald, 2014;Shayeghi et al, 2015;Lazauskas et al, 2017;Rabanal-León et al, 2018;Jäger et al, 2019;Yañez et al, 2019) and relative evolutionary algorithm (EA) (Zhou et al, 2020), the swarm intelligence algorithm (Wang et al, 2012;Jana et al, 2019) and others, have been proposed and applied in the past decades (Zhang and Glezakou, 2020).…”