A machine learning technique toward generating minimum energy structures of small boron clusters

The search for a global minimum related to molecular electronic structure and chemical bonding has received wide attention based on some theoretical calculations at various levels of theory. Particle swarm optimization (PSO) algorithm and modified PSO have been used to predict the energetically stable/metastable states associated with a given chemical composition. Out of a variety of techniques such as genetic algorithm, basin hopping, simulated annealing, PSO, and so on, PSO is considered to be one of the most suitable methods due to its various advantages over others. We use a swarm‐intelligence based parallel code to improve a PSO algorithm in a multidimensional search space augmented by quantum chemical calculations on gas phase structures at 0 K without any symmetry constraint to obtain an optimal solution. Our currently employed code is interfaced with Gaussian software for single point energy calculations. The code developed here is shown to be efficient. Small population size (small cluster) in the multidimensional space is actually good enough to get better results with low computational cost than the typical larger population. But for larger systems also the analysis is possible. One can try with a large number of particles as well. We have also analyzed how arbitrary and random structures and the local minimum energy structures gravitate toward the target global minimum structure. At the same time, we compare our results with that obtained from other evolutionary techniques.     

A comparative study of particle swarm optimization and its variants for phase stability and equilibrium calculations in multicomponent reactive and non-reactive systems

Particle swarm optimization is a novel evolutionary stochastic global optimization method that has gained popularity in the chemical engineering community. This optimization strategy has been successfully used for several applications including thermodynamic calculations. To the best of our knowledge, the performance of PSO in phase stability and equilibrium calculations for both multicomponent reactive and non-reactive mixtures has not yet been reported. This study introduces the application of particle swarm optimization and several of its variants for solving phase stability and equilibrium problems in multicomponent systems with or without chemical equilibrium. The reliability and efficiency of a number of particle swarm optimization algorithms are tested and compared using multicomponent systems with vapor–liquid and liquid–liquid equilibrium. Our results indicate that the classical particle swarm optimization with constant cognitive and social parameters is a reliable method and offers the best performance for global minimization of the tangent plane distance function and the Gibbs energy function in both reactive and non-reactive systems.     

Biologically driven neural platform invoking parallel electrophoretic separation and urinary metabolite screening

This work reveals a computational framework for parallel electrophoretic separation of complex biological macromolecules and model urinary metabolites. More specifically, the implementation of a particle swarm optimization (PSO) algorithm on a neural network platform for multiparameter optimization of multiplexed 24-capillary electrophoresis technology with UV detection is highlighted. Two experimental systems were examined: (1) separation of purified rabbit metallothioneins and (2) separation of model toluene urinary metabolites and selected organic acids. Results proved superior to the use of neural networks employing standard back propagation when examining training error, fitting response, and predictive abilities. Simulation runs were obtained as a result of metaheuristic examination of the global search space with experimental responses in good agreement with predicted values. Full separation of selected analytes was realized after employing optimal model conditions. This framework provides guidance for the application of metaheuristic computational tools to aid in future studies involving parallel chemical separation and screening. Adaptable pseudo-code is provided to enable users of varied software packages and modeling framework to implement the PSO algorithm for their desired use.     

Geometry optimizations of benzene clusters using a modified genetic algorithm

A modified genetic algorithm with real-number coding, non-uniform mutation and arithmetical crossover operators was described in this paper. A local minimization was used to improve the final solution obtained by the genetic algorithm. Using the exp-6-1 interatomic energy function, the modified genetic algorithm with local minimization (MGALM) was applied to the geometry optimization problem of small benzene clusters (C6H6)N(N = 2-7) to obtain the global minimum energy structures. MGALM is simple but the structures optimized are comparable to the published results obtained by parallel genetic algorithms.     

Nonplanarity at tri-coordinated aluminum and gallium: cyclic structures for X3Hn(m) (X = B, Al, Ga)

Structures and energies of X3H3(2-), X3H4-, X3H5, and X3H6+ (X = B, Al and Ga) were investigated theoretically at B3LYP/6-311G(d) level. The global minimum structures of B are not found to be global minima for Al and Ga. The hydrides of the heavier elements Al and Ga have shown a total of seven, six and eight minima for X3H3(2-), X3H(4-), and X3H5, respectively. However, X3H(6+) has three and four minima for Al and Ga, respectively. The nonplanar arrangements of hydrogens with respect to X3 ring is found to be very common for Al and Ga species. Similarly, species with lone pairs on heavy atoms dominate the potential energy surfaces of Al and Ga three-ring systems. The first example of a structure with tri-coordinate pyramidal arrangement at Al and Ga is found in X3H(4-) (2g), contrary to the conventional wisdom of C3H3+, B3H3, etc. The influence of pi-delocalization in stabilizing the structures decreases from X3H3(2-) to X3H6+ for heavier elements Al and Ga. In general, minimum energy structures of X3H4-, X3H5, and X3H6+ may be arrived at by protonating the minimum energy structures sequentially starting from X3H3(2-). The resonance stabilization energy (RSE) for the global minimum structures (or nearest structures to global minimum which contains pi-delocalization) is computed using isodesmic equations.     

Energy-directed tree search: an efficient systematic algorithm for finding the lowest energy conformation of molecules

We present a new systematic algorithm, energy-directed tree search (EDTS), for exploring the conformational space of molecules. The algorithm has been designed to reliably locate the global minimum (or, in the worst case, a structure within 4 kJ mol(-1) of this species) at a fraction of the cost of a full conformational search, and in this way extend the range of chemical systems for which accurate thermochemistry can be studied. The algorithm is inspired by the build-up approach but is performed on the original molecule as a whole, and objectively determines the combinations of torsional angles to optimise using a learning process. The algorithm was tested for a set of 22 large molecules, including open- and closed-shell species, stable structures and transition structures, and neutral and charged species, incorporating a range of functional groups (such as phenyl rings, esters, thioesters and phosphines), and covering polymers, peptides, drugs, and natural products. For most of the species studied the global minimum energy structure was obtained; for the rest the EDTS algorithm found conformations whose total electronic energies are within chemical accuracy from the true global minima. When the conformational space is searched at a resolution of 120 degrees , the cost of the EDTS algorithm (in its worst-case scenario) scales as 2(N) for large N (where N is the number of rotatable bonds), compared with 3(N) for the corresponding systematic search.     

H·(H2O)n clusters: microsolvation of the hydrogen atom via molecular ab initio gradient embedded genetic algorithm (GEGA)

A new version of the ab initio gradient embedded genetic algorithm (GEGA) program for finding the global minima on the potential energy surface (PES) of mixed clusters formed by molecules and atoms is reported. The performance of the algorithm is demonstrated on the neutral H·(H(2)O)(n) (n = 1-4) clusters, that is, a radical H atom solvated in 1-4 water molecules. These clusters are of a fundamental interest. The solvated hydrogen atom forms during photochemical events in water, or during scavenging of solvated electrons by acids, and transiently exists in biological systems and possibly in inclusion complexes in the deep ocean and in the ice shield of earth. The processes associated with its existence are intriguingly complex, however, and have been the subject of decades-long debates. Using GEGA, we explicate the apparently extreme structural diversity in the H·(H(2)O)(n) (n = 1-4) clusters. All considered clusters have four basic structural types: type I, where the H radical is weakly coordinated to the oxygen atom of one of the water molecules; type II, where H is weakly coordinated to a H atom of one of the water molecules; type III, consisting of H(2), the OH radical, and n - 1 H(2)O molecules; and type IV, consisting of H(3)O and n - 1 H(2)O. There are myriads of isomers of all four types. The lowest energy species of types I and II are the isoenergetic global minima. H·(H(2)O)(n) clusters appear to be a challenging case for GEGA because they have many shallow minima close in energy some of which are significantly less stable than the global minimum. Additionally, the global minima themselves have high structural degeneracy, they are only weakly bound, and they are prone to dissociation. GEGA performed exceptionally well in finding both the global and the low-energy local minima that were subsequently confirmed at higher levels of theory.     

Application of SiO2–water nanofluid to enhance oil recovery

The present study aims to investigate effects of nanofluid flooding on EOR and also compares its performance with water flooding in field scale using the published experimental data provided from core-scale studies. The nanofluid is based on water including silica nanoparticles. The relative permeability curves of water, nanofluid and oil for a light crude oil core sample obtained in an experimental study are used in this numerical investigation. A 2D heterogeneous reservoir model is constructed using the permeability and porosity of the last layer of SPE-10 model. It has been shown that nanofluid flooding can substantially improve the oil recovery in comparison with the water flooding case. Afterward, the operational parameters of the 13 injection and production wells have been optimized in order to meet the maximum cumulative oil production. First, pattern search (PS) algorithm was implemented which has a good convergence speed, but with a high probability of trapping in local optimum points. Particle swarm optimization (PSO) approach has also been employed, which requires a large number of population (to approach the global optimum) with so many simulations. Accordingly, a hybrid PSO–PS algorithm with confined domain is proposed. The hybrid algorithm starts with PSO and depending on the distribution density of the values of each parameter, confines the searching domain and provides a proper initial guess to be used by PS. It is concluded that the hybrid PSO–PS method could obtain the optimal solution with a high convergence speed and reduced possibility of trapping in local optimums.

     

Global optimization of binary Lennard-Jones clusters using three perturbation operators

Global optimization of binary Lennard-Jones clusters is a challenging problem in computational chemistry. The difficulty lies in not only that there are enormous local minima on the potential energy surface but also that we must determine both the coordinate position and the atom type for each atom and thus have to deal with both continuous and combinatorial optimization. This paper presents a heuristic algorithm (denoted by 3OP) which makes extensive use of three perturbation operators. With these operators, the proposed 3OP algorithm can efficiently move from a poor local minimum to another better local minimum and detect the global minimum through a sequence of local minima with decreasing energy. The proposed 3OP algorithm has been evaluated on a set of 96 × 6 instances with up to 100 atoms. We have found most putative global minima listed in the Cambridge Cluster Database as well as discovering 12 new global minima missed in previous research.     

Predicting two-dimensional boron-carbon compounds by the global optimization method

We adopt a global optimization method to predict two-dimensional (2D) nanostructures through the particle-swarm optimization (PSO) algorithm. By performing PSO simulations, we predict new stable structures of 2D boron-carbon (B-C) compounds for a wide range of boron concentrations. Our calculations show that: (1) All 2D B-C compounds are metallic except for BC(3) which is a magic case where the isolation of carbon six-membered ring by boron atoms results in a semi-conducting behavior. (2) For C-rich B-C compounds, the most stable 2D structures can be viewed as boron doped graphene structures, where boron atoms typically form 1D zigzag chains except for BC(3) in which boron atoms are uniformly distributed. (3) The most stable 2D structure of BC has alternative carbon and boron ribbons with strong in-between B-C bonds, which possesses a high thermal stability above 2000 K. (4) For B-rich 2D B-C compounds, there is a novel planar-tetracoordinate carbon motif with an approximate C(2)(v) symmetry.     

Prediction of RNA Secondary Structure Based on Particle Swarm Optimization

A novel method for the prediction of RNA secondary structure was proposed based on the particle swarm optimization(PSO). PSO is known to be effective in solving many different types of optimization problems and known for being able to approximate the global optimal results in the solution space. We designed an efficient objective function according to the minimum free energy, the number of selected stems and the average length of selected stems. We calculated how many legal stems there were in the sequence,...     

PK-means: A new algorithm for gene clustering

Microarray technology has been widely applied in study of measuring gene expression levels for thousands of genes simultaneously. Gene cluster analysis is found useful for discovering the function of gene because co-expressed genes are likely to share the same biological function. K-means is one of well-known clustering methods. However, it is sensitive to the selection of an initial clustering and easily becoming trapped in a local minimum. Particle-pair optimizer (PPO) is a variation on the traditional particle swarm optimization (PSO) algorithm, which is stochastic particle-pair based optimization technique that can be applied to a wide range of problems. In this paper we bridges PPO and K-means within the algorithm PK-means for the first time. Our results indicate that PK-means clustering is generally more accurate than K-means and Fuzzy K-means (FKM). PK-means also has better robustness for it is less sensitive to the initial randomly selected cluster centroids. Finally, our algorithm outperforms these methods with fast convergence rate and low computation load.     

Evaluation of stochastic global optimization methods for modeling vapor–liquid equilibrium data

Parameter estimation for vapor–liquid equilibrium (VLE) data modeling plays an important role in design, optimization and control of separation units. This optimization problem is very challenging due to the high non-linearity of thermodynamic models. Recently, several stochastic optimization methods such as Differential Evolution with Tabu List (DETL) and Particle Swarm Optimization (PSO) have evolved as alternative and reliable strategies for solving global optimization problems including parameter estimation in thermodynamic models. However, these methods have not been applied and compared with respect to other stochastic strategies such as Simulated Annealing (SA), Differential Evolution (DE) and Genetic Algorithm (GA) in the context of parameter estimation for VLE data modeling. Therefore, in this study several stochastic optimization methods are applied to solve parameter estimation problems for VLE modeling using both the classical least squares and maximum likelihood approaches. Specifically, we have tested and compared the reliability and efficiency of SA, GA, DE, DETL and PSO for modeling several binary VLE data using local composition models. These methods were also tested on benchmark problems for global optimization. Our results show that the effectiveness of these stochastic methods varies significantly between the different tested problems and also depends on the stopping criterion especially for SA, GA and PSO. Overall, DE and DETL have better performance for solving the parameter estimation problems in VLE data modeling.     

An evolutionary algorithm for the global optimization of molecular clusters: application to water, benzene, and benzene cation

We have developed an evolutionary algorithm (EA) for the global minimum search of molecular clusters. The EA is able to discover all the putative global minima of water clusters up to (H(2)O)(20) and benzene clusters up to (C(6)H(6))(30). Then, the EA was applied to search for the global minima structures of (C(6)H(6))(n)(+) with n = 2-20, some of which were theoretically studied for the first time. Our results for n = 2-6 are consistent with previous theoretical work that uses a similar interaction potential. Excluding the very symmetric global minimum structure for n = 9, the growth pattern of (C(6)H(6))(n)(+) with n ≥ 7 involves the (C(6)H(6))(2)(+) dimer motif, which is placed off-center in the cluster. Such observation indicates that potentials commonly used in the literature for (C(6)H(6))(n)(+) cannot reproduce the icosahedral-type packing suggested by the available experimental data.     

Lennard-Jones团簇最低能量构型的预测

针对Lennard-Jones(LJ)团簇的结构优化问题,在前人工作的基础上,提出了一个新的无偏优化算法,即DLS-TPIO(dynamic lattice searching method with two-phase local searchand interior operation)算法.对LJ2-650,LJ660,LJ665-680这666个实例进行了优化计算.为其中每个实例所找到的构型其势能均达到了剑桥团簇数据库中公布的最好记录.对LJ533与LJ536这两个算例,所达到的势能则优于先前的最好记录.在DLS-TPIO算法中,采用了内部操作,两阶段局部搜索方法以及动态格点搜索方法.在优化的前一阶段,内部操作将若干能量较高的表面原子移入团簇的内部,从而降低团簇的能量,并使其构型逐渐地变为有序.与此同时,两阶段局部搜索方法指导搜索进入更有希望的构型区域.这种做法显著地提高了算法的成功率.在优化的后一阶段,借用动态格点搜索方法对团簇表面原子的位置作进一步优化,以再一次降低团簇的能量.另外,为识别二十面体构型的中心原子,本文给出了一个简单的新方法.相比于文献中一些著名的无偏优化算法,DLS-TPIO算法具...     

Self-modeling curve resolution (SMCR) by particle swarm optimization (PSO)

Particle swarm optimization (PSO) combined with alternating least squares (ALS) is introduced to self-modeling curve resolution (SMCR) in this study for effective initial estimate. The proposed method aims to search concentration profiles or pure spectra which give the best resolution result by PSO. SMCR sometimes yields insufficient resolution results by getting trapped in a local minimum with poor initial estimates. The proposed method enables to reduce an undesirable effect of the local minimum in SMCR due to the advantages of PSO. Moreover, a new criterion based on global phase angle is also proposed for more effective performance of SMCR. It takes full advantage of data structure, that is to say, a sequential change with respect to a perturbation can be considered in SMCR with the criterion. To demonstrate its potential, SMCR by PSO is applied to concentration-dependent near-infrared (NIR) spectra of mixture solutions of oleic acid (OA) and ethanol. Its curve resolution performances are compared with SMCR with evolving factor analysis (EFA). The results show that SMCR by PSO yields significantly better curve resolution performances than those by EFA. It is revealed that SMCR by PSO is less sensitive to a local minimum in SMCR and it can be a new effective tool for curve resolution analysis.     

Hybrid particle swarm optimization and tabu search approach for selecting genes for tumor classification using gene expression data

Gene expression data are characterized by thousands even tens of thousands of measured genes on only a few tissue samples. This can lead either to possible overfitting and dimensional curse or even to a complete failure in analysis of microarray data. Gene selection is an important component for gene expression-based tumor classification systems. In this paper, we develop a hybrid particle swarm optimization (PSO) and tabu search (HPSOTS) approach for gene selection for tumor classification. The incorporation of tabu search (TS) as a local improvement procedure enables the algorithm HPSOTS to overleap local optima and show satisfactory performance. The proposed approach is applied to three different microarray data sets. Moreover, we compare the performance of HPSOTS on these datasets to that of stepwise selection, the pure TS and PSO algorithm. It has been demonstrated that the HPSOTS is a useful tool for gene selection and mining high dimension data.     

Global optimization of bimetallic cluster structures. II. Size-matched Ag-Pd, Ag-Au, and Pd-Pt systems

Genetic algorithm global optimization of Ag-Pd, Ag-Au, and Pd-Pt clusters is performed. The 34- and 38-atom clusters are optimized for all compositions. The atom-atom interactions are modeled by a semiempirical potential. All three systems are characterized by a small size mismatch and a weak tendency of the larger atoms to segregate at the surface of the smaller ones. As a result, the global minimum structures exhibit a larger mixing than in Ag-Cu and Ag-Ni clusters. Polyicosahedral structures present generally favorable energetic configurations, even though they are less favorable than in the case of the size-mismatched systems. A comparison between all the systems studied here and in the previous paper (on size-mismatched systems) is presented.     

Evaluation of Lipase Production by Genetic Algorithm and Particle Swarm Optimization and Their Comparative Study

This paper presents the nature-inspired genetic algorithm (GA) and particle swarm optimization (PSO) approaches for optimization of fermentation conditions of lipase production for enhanced lipase activity. The central composite non-linear regression model of lipase production served as the optimization problem for PSO and GA approaches. The overall optimized fermentation conditions obtained thereby, when verified experimentally, have brought about a significant improvement (more than 15 U/gds (gram dry substrate)) in the lipase titer value. The performance of both optimization approaches in terms of computational time and convergence rate has been compared. The results show that the PSO approach (96.18 U/gds in 46 generations) has slightly better performance and possesses better convergence and computational efficiency than the GA approach (95.34 U/gds in 337 generations). Hence, the proposed PSO approach with the minimal parameter tuning is a viable tool for optimization of fermentation conditions of enzyme production.