Clustering Global Optimization Research Articles

Structural Determination and Hierarchical Evolution of Transition Metal Clusters Based on an Improved Self-Adaptive Differential Evolution with Neighborhood Search Algorithm.

Determining the optimal structures and clarifying the corresponding hierarchical evolution of transition metal clusters are of fundamental importance for their applications. The global optimization of clusters containing a large number of atoms, however, is a vastly challenging task encountered in many fields of physics and chemistry. In this work, a high-efficiency self-adaptive differential evolution with neighborhood search (SaNSDE) algorithm, which introduced an optimized cross-operation and an improved Basin Hopping module, was employed to search the lowest-energy structures of CoN, PtN, and FeN (N = 3-200) clusters. The performance of the SaNSDE algorithm was first evaluated by comparing our results with the parallel results collected in the Cambridge Cluster Database (CCD). Subsequently, different analytical methods were introduced to investigate the structural and energetic properties of these clusters systematically, and special attention was paid to elucidating the structural evolution with cluster size by exploring their overall shape, atomic arrangement, structural similarity, and growth pattern. By comparison with those results listed in the CCD, 13 lower-energy structures of FeN clusters were discovered. Moreover, our results reveal that the clusters of three metals had different magic numbers with superior stable structures, most of which possessed high symmetry. The structural evolution of Co, Pt, and Fe clusters could be, respectively, considered as predominantly closed-shell icosahedral, Marks decahedral, and disordered icosahedral-ring growth. Further, the formation of shell structures was discovered, and the clusters with hcp-, fcc-, and bcc-like configurations were ascertained. Nevertheless, the growth of the clusters was not simply atom-to-atom piling up on a given cluster despite gradual saturation of the coordination number toward its bulk limit. Our work identifies the general growth trends for such a wide region of cluster sizes, which would be unbearably expensive in first-principles calculations, and advances the development of global optimization algorithms for the structural prediction of clusters.

Integrating firefly algorithm with density functional theory for global optimization of Al42− clusters

The crux of quantum chemistry lies in the minimization of energy functional to obtain the optimized geometry of a molecule. This involves formulating the energy minimization task as a global optimization (GO) problem and using an appropriate algorithm for determining the best solution out of a number of feasible solutions. Several new and unconventional algorithms are proposed that augment the efforts toward GO of clusters of atoms using rigorous quantum chemical methods. Among these, swarm intelligence-based nature-inspired metaheuristic algorithms have particularly drawn considerable attention. However, it still has certain drawbacks. In this work, we propose the use of firefly algorithm (FA) in conjunction with density functional theory (DFT)-based calculations for solving the GO problem and establish its superioriority in performance over particle swarm optimization (PSO) through extensive computational studies. Specifically, we show how such a “FA + DFT” approach can be used for GO of Al42− clusters. Each possible structure in the three-dimensional search space is treated as a firefly particle. Starting with an initial pool of particles, newer sets of particles are generated using an evolutionary mechanism, thereby moving toward solutions with particles having “better” structures. This novel approach also enables the possibility of incorporating molecule specific domain knowledge. For example, knowing that Al42− clusters are planar, we can restrict the search space so that only planar structures are explored, thereby achieving faster convergence of the algorithm. As an extension of the current technique, an important correlation between energy stabilization and aromaticity is established.

2 × 1D crossed strongly modulated gratings for polarization independent tunable narrowband transmission filters.

We design a narrowband polarization independent transmission guided mode resonance filter whose center wavelength is tunable with respect to the angle of incidence. The device is composed of two identical structures assembled back to back. Each half structure is a dielectric multilayer stack in which a grating is engraved. This so-called 2×1D crossed gratings component has already been demonstrated for reflection filtering [Opt. Lett.36, 1662 (2011)OPLEDP0146-959210.1364/OL.36.001662; Opt. Lett.39, 6038 (2014)OPLEDP0146-959210.1364/OL.39.006038]. The functioning in transmission requires the use of a high index material for the grating bumps. For the design, we resort to a clustering global optimization algorithm, used for the first time to our knowledge for grating structures. We demonstrated two filters with a quality factor of about 4000, tunable over more than 15 nm when the angle of incidence varies over a range of 4°, and with a transmittivity at resonance greater than 95% whatever the incident polarization.

Application of clustering global optimization to thin film design problems

Refinement techniques usually calculate an optimized local solution, which is strongly dependent on the initial formula used for the thin film design. In the present study, a clustering global optimization method is used which can iteratively change this initial formula, thereby progressing further than in the case of local optimization techniques. A wide panel of local solutions is found using this procedure, resulting in a large range of optical thicknesses. The efficiency of this technique is illustrated by two thin film design problems, in particular an infrared antireflection coating, and a solar-selective absorber coating.

Global optimization of clusters using electronic structure methods

Over the past decade, there has been a significant growth in the development and application of methods for performing global optimization (GO) of cluster and nanoparticle structures using first‐principles electronic structure methods coupled to sophisticated search algorithms. This has in part been driven by the desire to avoid the use of empirical potentials (EPs), especially in cases where no reliable potentials exist to guide the search toward reasonable regions of configuration space. This has been facilitated by improvements in the reliability of the search algorithms, increased efficiency of the electronic structure methods, and the development of faster, multiprocessor high‐performance computing architectures. In this review, we give a brief overview of GO algorithms, though concentrating mainly on genetic algorithm and basin hopping techniques, first in combination with EPs. The major part of the review then deals with details of the implementation and application of these search methods to allow exploration for global minimum cluster structures directly using electronic structure methods and, in particular, density functional theory. Example applications are presented, ranging from isolated monometallic and bimetallic clusters to molecular clusters and ligated and surface supported metal clusters. Finally, some possible future developments are highlighted. © 2013 Wiley Periodicals, Inc.

Refractive index determination of SiO2 layer in the UV/Vis/NIR range: spectrophotometric reverse engineering on single and bi-layer designs

In this paper we use spectrophotometric measurements and a Clustering Global Optimization procedure to determine the complex refractive index of SiO2 layer from 250 nm to 1250 nm. A special commercial optical module allows the reflection and transmission measurements to be made under exactly the same illumination and measurement conditions. We compare the index determination results obtained from two different single layer SiO2 samples, with high and low index glass substrates, respectively. We then determine the refractive index of SiO2 for a bi-layer design in which the first deposited layer is Ta2O5. The corresponding solutions are discussed and we show that the real part of the complex refractive index obtained for a bi-layer is slightly different to that found for a single layer investigation. When SiO2 is included inside a thin film stack, we propose the use of an index determination method in which a bi-layer is used for the real part of the complex refractive index, and single layer determination is used for the imaginary part of the refractive index in the UV range.

Exploitation of multiple incidences spectrometric measurements for thin film reverse engineering

In the present paper we determine the optical constants and thicknesses of multilayer thin film stacks, in the visible and near infrared ranges. These parameters are derived from the transmittance and reflectance spectra measured by a spectrophotometer, for several angles of incidence. Several examples are studied, from a simple single layer structure up to a 22-layer dielectric filter. We show that the use of a large number of incidence angles is an effective means of reducing the number of mathematical solutions and converging on the correct physical solution when the number of layers increases. More specifically, we provide an in-depth discussion of the approach used to extract the index and thickness of each layer, which is achieved by analysing the various mathematical solutions given by a global optimization procedure, based on as little as 6 and as many as 32 variable parameters. The results show that multiple incidences, lead to the true solution for a filter with a large number of layers. In the present study, a Clustering Global Optimization algorithm is used, and is shown to be efficient even for a high number of variable parameters. Our analysis allows the accuracy of the reverse engineering process to be estimated at approximately 1 nm for the thickness, and 2 10(-3) for the index of each layer in a 22-layer filter.

Reverse engineering from spectrophotometric measurements: performances and efficiency of different optimization algorithms

A large number of parameters is often required to describe optical dispersion laws, and it is only through the use of an appropriate global optimization procedure that an accurate thin-film index determination can be achieved. In this paper, we propose to investigate the respective performances of three different optimization algorithms, namely Simulated Annealing, Genetic Algorithm and Clustering Global Optimization and compare results with a commercial software dedicated to thin-film index determination. This study is restricted to the single-layer thin-film index determination of transparent and absorbing materials. It includes the theoretical study of simulated reflection and transmission spectra, and the experimental characterization of Ta2O5 and Si layers.

On the efficient computation of robust regression estimators

The problem of providing efficient and reliable robust regression algorithms is considered. The impact of global optimization methods, such as stopping conditions and clustering techniques, in the calculation of robust regression estimators is investigated. The use of stopping conditions permits us to devise new algorithms that perform as well as the existing algorithms in less time and with adaptive algorithm parameters. Clustering global optimization is shown to be a general framework encompassing many of the existing algorithms.

Dynamic lattice searching methods for optimization of clusters

Global optimization of clusters is a subject of intense interest in computational chemistry. Especially for large clusters, locating the global minima is a challenging problem. Two strategies are generally used for the problem, i.e., the stochastic optimization and the static modeling strategy. The former is known as unbiased global optimization method, while the latter is more efficient but biased. This review describes the development of a dynamic lattice searching (DLS) approach. In DLS, the lattices are constructed dynamically and optimization is achieved by searching these lattices. Therefore, DLS possesses the characteristics of both the stochastic and static methods. With the aim of improving the efficiency of DLS for optimization of large clusters, several variants of the method have been developed. The results show that DLS methods may be promising tools for fast modeling of large clusters. With this review, greater interests are expected for global optimization of atomic or molecular clusters.

The GLOBAL optimization method revisited

The multistart clustering global optimization method called GLOBAL has been introduced in the 1980s for bound constrained global optimization problems with black-box type objective function. Since then the technological environment has been changed much. The present paper describes shortly the revisions and updates made on the involved algorithms to utilize the novel technologies, and to improve its reliability. We discuss in detail the results of the numerical comparison with the old version and with C-GRASP, a continuous version of the GRASP method. According to these findings, the new version of GLOBAL is both more reliable and more efficient than the old one, and it compares favorably with C-GRASP too.

Global optimization of clusters, crystals, and biomolecules.

Finding the optimal solution to a complex optimization problem is of great importance in many fields, ranging from protein structure prediction to the design of microprocessor circuitry. Some recent progress in finding the global minima of potential energy functions is described, focusing on applications of the simple "basin-hopping" approach to atomic and molecular clusters and more complicated hypersurface deformation techniques for crystals and biomolecules. These methods have produced promising results and should enable larger and more complex systems to be treated in the future.