Continuous optimization methods for ground-state searches of spin clusters

Computational methods were developed for ground-state searches of Heisenberg model spin clusters in which spin sites were represented by classical spin vectors. Simulated annealing, continuous genetic algorithm, and particle swarm optimization methods were applied for solving the problems. Because the results of these calculations were influenced by the settings of optimization parameters, effective parameter settings were also investigated. The results indicated that a continuous genetic algorithm is the most effective method for ground-state searches of Heisenberg model spin clusters, and that a mutation operator plays an important role in this genetic algorithm. These results provide useful information for solving physically or chemically important continuous optimization problems.

Graphical abstractComputational methods were developed for ground-state searches of Heisenberg model spin clusters in which spin sites were represented by classical spin vectors. The results indicated that a continuous genetic algorithm is the most effective method for ground-state searches of Heisenberg model spin clusters, and that a mutation operator plays an important role in this genetic algorithm.Figure optionsDownload full-size imageDownload as PowerPoint slideHighlights► Methods were developed for ground-state searches of Heisenberg model spin clusters. ► Efficient parameter settings of the search methods were investigated. ► The importance of local search in meta-heuristics was suggested.