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 Cn 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.
Highlights
Over the past decades, studies on nature-inspired swarm intelligence based meta-heuristic algorithms have become a topic of paramount interest in the allied research fields
Each position vector representing a candidate solution in the hyperspace starts searching for the optima of a given function of several variables by updating generations in iterative process without much of any assumption leading to a minimum energy structure
The advancement of particles toward the global best position is attained via particle swarm optimizer ideology and they gravitate toward the global best solution with the help of the best variable memory values
Summary
Studies on nature-inspired swarm intelligence based meta-heuristic algorithms have become a topic of paramount interest in the allied research fields. Some advanced and more promising methods are continuously being proposed including random sampling method (Pickard and Needs, 2006, 2007, 2008), minima hopping (Kirkpatrick et al, 1983; Pannetier et al, 1990), basin hopping (Nayeem et al, 1991; Wales and Doye, 1997), meta-dynamics (Martonák et al, 2003, 2005; Guangneng et al, 2005), data mining (Mujica and Needs, 1997) and Particle Swarm Optimization (PSO) (Kennedy and Eberhart, 1995, 1999; Kennedy, 1997; Shi and Eberhart, 1998; Eberhart and Shi, 2001; Li, 2007; Özcan and Yilmaz, 2007; Poli, 2007, 2008; Barrera and Coello, 2009; Li M. et al, 2012; Qu et al, 2012; Bonyadi and Michalewicz, 2017), modified PSO (Zheng et al, 2007), adaptive particle swarm optimization (APSO) (Zhan et al, 2009), multi-dimensional PSO for dynamic environments (Zhi-Jie et al, 2009; Kiranyaz et al, 2011; Bhushan and Pillai, 2013), which show different numerical performances Out of these numerous techniques, PSO is a very renowned iterative process which works intelligently by utilizing the concept of exploring and exploiting together in the multidimensional search space for finding optimal or nearoptimal solutions. In order to check the efficiency of our proposed PSO method over some most familiar GO methods like advanced BH, SA, and GA methods, the results for C5 cluster have been analyzed, as a reference system
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