Global cluster geometry optimization by a phenotype algorithm with Niches: Location of elusive minima, and low-order scaling with cluster size

Abstract

The problem of global geometry optimization of clusters is addressed with a phenotype variant of the method of genetic algorithms, with several novel performance enhancements. The resulting algorithm is applied to Lennard–Jones clusters as benchmark system, with up to 150 atoms. The well‐known, difficult cases involving nonicosahedral global minima can be treated reliably using the concept of niches. The scaling of computer time with cluster size is approximately cubic, which is crucial for future applications to much larger clusters. © 1999 John Wiley & Sons, Inc. J Comput Chem 20: 1752–1759, 1999

On the Use of Different Potential Energy Functions in Rare-Gas Cluster Optimization by Genetic Algorithms: Application to Argon Clusters

“…In the past few years, a couple of approaches 11,12,42 were developed to deal with this double-funnel problem in a more efficient way. The technique introduced by Hartke 42 uses a parameter which controls the diversity of structural types in the population of the GA, preventing it from generating only icosahedral structures.…”

“…The technique introduced by Hartke 42 uses a parameter which controls the diversity of structural types in the population of the GA, preventing it from generating only icosahedral structures. In turn, Locatelli and Schoen 11,12 have proposed a transformation in the potential energy surface, so that the nonicosahedral global minima are much more likely to be found.…”

Basin hopping with occasional jumping

“…However, this jumping may induce the uphill moves which assist in the exploration of the next valley separated from the previous valley by a high barrier, and our BHOJ can successfully find out the lowest-energy structure at approximately 1400 steps. In comparison to the various sophisticated methods [21,22,23,24,25], our basinhopping with occasional jumping (BHOJ) is intuitively appealing and simple to implement. The performance of the algorithm seems better than most of the above algorithms.…”

“…[23,27] were also successfully located by our BHOJ though the success rates of these three cases were very low.…”

Genetic Algorithms in Application to the Geometry Optimization of Nanoparticles

“…Merging lower energy halves of two nanoparticles would increases the fitness of emerging child. 10-20% efficiency increment is observed in the study of Hartke [40] by the usage of this enhancement in the application of cut and splice crossover.…”