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.     

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.     

Isobaric vapor-liquid equilibrium for binary systems containing benzothiophene

Isobaric vapor-liquid equilibrium (VLE) of the following systems was measured with a recirculation still: benzothiophene + dodecane at 99.6 kPa, benzothiophene + 1-dodecene at 100.1 kPa, and benzothiophene + 1-octanol at 100 kPa. All systems studied exhibit positive deviation from Raoult's law. A minimum temperature azeotrope was found in the systems benzothiophene + dodecane (x₁ = 0.491, P = 99.6 kPa, T = 484.72 K) and benzothiophene + 1-dodecene (x₁ = 0.185, P = 100.1 kPa, T = 484.45 K). No azeotropic behavior was found in benzothiophene + 1-octanol system at 100 kPa. The experimental results were correlated with the Wilson model and compared to COSMO-SAC predictive model. Liquid and vapor phase compositions were determined with gas chromatography. All measured data sets passed the thermodynamic consistency tests. The activity coefficients at infinite dilution are also presented.     

A combination of modified particle swarm optimization algorithm and support vector machine for gene selection and tumor classification

In the analysis of gene expression profiles, the number of tissue samples with genes expression levels available is usually small compared with the number of genes. This can lead either to possible overfitting or even to a complete failure in analysis of microarray data. The selection of genes that are really indicative of the tissue classification concerned is becoming one of the key steps in microarray studies. In the present paper, we have combined the modified discrete particle swarm optimization (PSO) and support vector machines (SVM) for tumor classification. The modified discrete PSO is applied to select genes, while SVM is used as the classifier or the evaluator. The proposed approach is used to the microarray data of 22 normal and 40 colon tumor tissues and showed good prediction performance. It has been demonstrated that the modified PSO is a useful tool for gene selection and mining high dimension data.     

Global minimum structure searches via particle swarm optimization

Novel implementation of the evolutionary approach known as particle swarm optimization (PSO) capable of finding the global minimum of the potential energy surface of atomic assemblies is reported. This is the first time the PSO technique has been used to perform global optimization of minimum structure search for chemical systems. Significant improvements have been introduced to the original PSO algorithm to increase its efficiency and reliability and adapt it to chemical systems. The developed software has successfully found the lowest-energy structures of the LJ(26) Lennard-Jones cluster, anionic silicon hydride Si(2)H(5) (-), and triply hydrated hydroxide ion OH(-) (H(2)O)(3). It requires relatively small population sizes and demonstrates fast convergence. Efficiency of PSO has been compared with simulated annealing, and the gradient embedded genetic algorithm.     

Evaluation of repulsive particle swarm method for phase equilibrium and phase stability problems

Phase equilibrium and stability problems are of crucial importance in simulation, design and optimization of several separation processes. Recently, these problems have been solved using minimization of Gibbs free energy, using global optimization techniques. In this paper, repulsive particle swarm (RPS), a recent global optimization technique is explored for the solution of phase stability and phase equilibrium.     

Prediction of vapor-liquid equilibrium data of the system MTBE + methanol + ethanol by PRSV2 EOS

The Stryjek and Vera (1986) [9] modification of Peng-Robinson (PRSV2) equation of state has been applied for modeling vapor-liquid equilibrium of the systems MTBE + methanol, MTBE + ethanol and methanol + ethanol. Binary interaction parameters for mixing rules have been estimated by using experimental data at the atmospheric pressure. The calculated binary interaction parameters were used for predicting azeotropic behavior at high pressure and also for isobaric equilibrium points which showed an excellent agreement with experimental data. In addition, estimated binary interaction parameters for binary systems were used for ternary system (MTBE + methanol + ethanol). The predictions deviated only slightly from the experimental data. The results show PRSV2 can be used for VLE prediction of polar systems.     

Cure kinetic parameter estimation of thermosetting resins with isothermal data by using particle swarm optimization

The heuristic algorithms have shown to be a powerful tool in parameter estimation. Among these algorithms, particle swarm optimization (PSO) has become a method whose application has been increasing quickly. In the present work a new way for parameter estimation from cure kinetic model of polymeric resin using a differential-algebraic approach is shown. The PSO was applied to minimize the least squares function and to find the parameters from an autocatalytic model for describing cure kinetics of thermosetting resins. The isothermal data were obtained at four temperatures: 318, 333, 348 and 363 K. Three parameter estimation procedures were compared for finding a parameter set for all temperatures simultaneously. In the first one, called classical method, a curing rate was calculated with experimental values of the degree of cure and the temperature. In the second and third methods, the curing rate was obtained from the integration of a differential-algebraic system and the main difference between them is the objective function and the way to determine the ultimate reaction heat. All methods showed good results; however, the third method was more accurate than the others. The confidence regions of all parameters were found and they were used to give us indication whether the parameters estimated here by different methods are statistically different.     

Generalized Gaussian reference curve measurement model for high‐performance liquid chromatography with diode array detector separation and its solution by multi‐target intermittent particle swarm optimization

In order to separate a high‐performance liquid chromatography with diode array detector (HPLC‐DAD) data set to chromatogram peaks and spectra for all compounds, a separation method based on the model of generalized Gaussian reference curve measurement (GGRCM) and the algorithm of multi‐target intermittent particle swarm optimization (MIPSO) is proposed in this paper. A parameter θ is constructed to generate a reference curve r(θ) for a chromatogram peak based on its physical principle. The GGRCM model is proposed to calculate the fitness ε(θ) for every θ, which indicates the possibility for the HPLC‐DAD data set to contain a chromatogram peak similar to the r(θ). The smaller the fitness is, the higher the possibility. The algorithm of MIPSO is then introduced to calculate the optimal parameters by minimizing the fitness mentioned earlier. Finally, chromatogram peaks are constructed based on these optimal parameters, and the spectra are calculated by an estimator. Through the simulations and experiments, the following conclusions are drawn: (i) the GGRCM‐MIPSO method can extract chromatogram peaks from simulation data set without knowing the number of the compounds in advance even when a severe overlap and white noise exist and (ii) the GGRCM‐MIPSO method can be applied to the real HPLC‐DAD data set. Copyright © 2014 John Wiley & Sons, Ltd.     

Multivariate curve resolution-particle swarm optimization: A high-throughput approach to exploit pure information from multi-component hyphenated chromatographic signals

Multivariate curve resolution-particle swarm optimization (MCR-PSO) algorithm is proposed to exploit pure chromatographic and spectroscopic information from multi-component hyphenated chromatographic signals. This new MCR method is based on rotation of mathematically unique PCA solutions into the chemically meaningful MCR solutions. To obtain a proper rotation matrix, an objective function based on non-fulfillment of constraints is defined and is optimized using particle swarm optimization (PSO) algorithm. Initial values of rotation matrix are calculated using local rank analysis and heuristic evolving latent projection (HELP) method. The ability of MCR-PSO in resolving the chromatographic data is evaluated using simulated gas chromatography–mass spectrometry (GC–MS) and high-performance liquid chromatography–diode array detection (HPLC–DAD) data. To present a comprehensive study, different number of components and various levels of noise under proper constraints of non-negativity, unimodality and spectral normalization are considered. Calculation of the extent of rotational ambiguity in MCR solutions for different chromatographic systems using MCR-BANDS method showed that MCR-PSO solutions are always in the range of feasible solutions like true solutions. In addition, the performance of MCR-PSO is compared with other popular MCR methods of multivariate curve resolution-objective function minimization (MCR-FMIN) and multivariate curve resolution-alternating least squares (MCR-ALS). The results showed that MCR-PSO solutions are rather similar or better (in some cases) than other MCR methods in terms of statistical parameters. Finally MCR-PSO is successfully applied in the resolution of real GC–MS data. It should be pointed out that in addition to multivariate resolution of hyphenated chromatographic signals, MCR-PSO algorithm can be straightforwardly applied to other types of separation, spectroscopic and electrochemical data.     

SODOCK: swarm optimization for highly flexible protein-ligand docking

Protein-ligand docking can be formulated as a parameter optimization problem associated with an accurate scoring function, which aims to identify the translation, orientation, and conformation of a docked ligand with the lowest energy. The parameter optimization problem for highly flexible ligands with many rotatable bonds is more difficult than that for less flexible ligands using genetic algorithm (GA)-based approaches, due to the large numbers of parameters and high correlations among these parameters. This investigation presents a novel optimization algorithm SODOCK based on particle swarm optimization (PSO) for solving flexible protein-ligand docking problems. To improve efficiency and robustness of PSO, an efficient local search strategy is incorporated into SODOCK. The implementation of SODOCK adopts the environment and energy function of AutoDock 3.05. Computer simulation results reveal that SODOCK is superior to the Lamarckian genetic algorithm (LGA) of AutoDock, in terms of convergence performance, robustness, and obtained energy, especially for highly flexible ligands. The results also reveal that PSO is more suitable than the conventional GA in dealing with flexible docking problems with high correlations among parameters. This investigation also compared SODOCK with four state-of-the-art docking methods, namely GOLD 1.2, DOCK 4.0, FlexX 1.8, and LGA of AutoDock 3.05. SODOCK obtained the smallest RMSD in 19 of 37 cases. The average 2.29 A of the 37 RMSD values of SODOCK was better than those of other docking programs, which were all above 3.0 A.     

Estimation of solid vapor pressures of pure compounds at different temperatures using a multilayer network with particle swarm algorithm

Solid vapor pressures (P^S) of pure compounds have been estimated at several temperatures using a hybrid model that includes an artificial neural network with particle swarm optimization and a group contribution method. A total of 700 data points of solid vapor pressure versus temperature, corresponding to 70 substances, have been used to train the neural network developed using Matlab. The following properties were considered as input parameters: 36 structural groups, molecular mass, dipole moment, temperature and pressure in the triple point (upper limit of the sublimation curve), and the limiting value P^S → 0 as T → 0 (lower limit of the sublimation curve). Then, the solid vapor pressures of 28 other solids (280 data points) have been predicted and results compared to experimental data from the literature. The study shows that the proposed method represents an excellent alternative for the prediction of solid vapor pressures from the knowledge of some other available properties and from the structure of the molecule.     

Isothermal vapor-liquid equilibria for methanol and 2,3-dimethyl-2-butene at 343.15 K, 353.15 K, 363.15 K, 373.15 K

Isothermal vapor-liquid equilibrium (VLE) data were measured for the binary system methanol and 2,3-dimethyl-2-butene at 343.15 K, 353.15 K, 363.15 K, 373.15 K, respectively. The measurements were carried out in a novel recirculation equilibrium equipment. Three activity coefficient models including Wilson, NRTL and UNIQUAC, as well as the Soave-Redlich-Kwong equation of state were used to correlate the experimental data. The correlation results showed that a good consistency between the experimental data and the Wilson model can be achieved.     

Estimation of rotation ambiguity in multivariate curve resolution with charged particle swarm optimization (cPSO‐MCR)

Rotation ambiguity (RA) in multivariate curve resolution (MCR) is an undesirable case, when the physicochemical constraints are not sufficiently strong to provide a unique resolution of the data matrix of the mixtures into spectra and concentration profiles of individual chemical components. RA is often met in MCR of overlapped chromatographic peaks, kinetic and equilibrium data, and fluorescence two‐dimensional spectra. In case of RA, a single candidate solution has little practical value. So, the whole set of feasible solutions should be characterized somehow. It is a quite intricate task in a general case. In the present paper, a method was proposed to estimate RA with charged particle swarm optimization (cPSO), a population‐based algorithm. The criteria for updating the particles were modified, so that the swarm converged to the steady state, which spanned the set of feasible solutions. The performance of cPSO‐MCR was demonstrated on test functions, simulated datasets, and real‐world data. Good accordance of the cPSO‐MCR results with the analytical solutions (Borgen plots) was observed. cPSO‐MCR was also shown to be capable of estimating the strength of the constraints and of revealing RA in noisy data. As compared with analytical methods, cPSO‐MCR is simpler to implement, expands to more than three chemical compounds, is immune to noise, and can be easily adapted to virtually all types of constraints and objective functions (constraint based or residue based). cPSO‐MCR also provides natural visual information about the level of RA in spectra and concentration profiles, similar to the methods of two extreme solutions (e.g., MCR‐BANDS). Copyright © 2014 John Wiley & Sons, Ltd.     

Prediction of vapor-liquid equilibrium from excess enthalpy data for binary ether +n-alkane or cyclohexane mixtures

Vapor liquid equilibrium (VLE) is successfully predicted from excess enthalpy H^E data for binary ether + n-alkane or cyclohexane mixtures. Parameters for the continuous linear association model (CLAM) and for the UNIQUAC Model for the excess Gibbs energy G^E were determined from H^E data measured at a low temperature (ambient temperature). These parameters are used to predict VLE data at low and high temperatures. The dependence of the accuracy of predictions on the set of H^E data chosen to evaluate the parameters and on the model for G^E are discussed.     

A wavelength selection method based on random decision particle swarm optimization with attractor for near‐infrared spectral quantitative analysis

In this paper, we proposed a wavelength selection method based on random decision particle swarm optimization with attractor for near‐infrared (NIR) spectra quantitative analysis. The proposed method was incorporated with partial least square (PLS) to construct a prediction model. The proposed method chooses the current own optimal or the current global optimal to calculate the attractor. Then the particle updates its flight velocity by the attractor, and the particle state is updated by the random decision with the new velocity. Moreover, the root‐mean‐square error of cross‐validation is adopted as the fitness function for the proposed method. In order to demonstrate the usefulness of the proposed method, PLS with all wavelengths, uninformative variable elimination by PLS, elastic net, genetic algorithm combined with PLS, the discrete particle swarm optimization combined with PLS, the modified particle swarm optimization combined with PLS, the neighboring particle swarm optimization combined with PLS, and the proposed method are used for building the components quantitative analysis models of NIR spectral datasets, and the effectiveness of these models is compared. Two application studies are presented, which involve NIR data obtained from an experiment of meat content determination using NIR and a combustion procedure. Results verify that the proposed method has higher predictive ability for NIR spectral data and the number of selected wavelengths is less. The proposed method has faster convergence speed and could overcome the premature convergence problem. Furthermore, although improving the prediction precision may sacrifice the model complexity under a certain extent, the proposed method is overfitted slightly. Copyright © 2015 John Wiley & Sons, Ltd.     

Excess thermodynamic properties and vapor-liquid equilibrium data for then-butylamine+p-dioxane system at 25°C

Excess values of molar volumes, viscosities, molar enthalpies, Gibbs molar energies, surface tensions and molar diamagnetic susceptibilities were calculated at 25°C for then-butylamine+p-dioxane system. The observed deviations from the ideality were explained on the basis of intermolecular interactions. Van Laar's equations were the best in predicting activity coefficients for this system.     

Multi-swarm UPSO algorithm based on seed strategy for atomic clusters structure optimization

Particle Swarm Optimization (PSO) algorithm is prone to get trapped in local optima and insufficient information exchange among particles. To solve this problem, this paper proposes a Multi-swarm Unified Particle Swarm Optimization algorithm based on Seed Strategy (SS-DMS-UPSO) to optimize the atomic clusters structure. In this algorithm, the population is divided into some sub-populations evolving randomly and evenly, and each sub-population uses UPSO algorithm with different unification factors to evolve independently in parallel. After a certain number of independent evolution, the particles of all sub-populations are merged into a new population, and the population is again randomly divided into average sub-populations. Iterate the algorithm repeatedly in this way. And finally the global best particle can be obtained. The experimental results show that the SS-DMS-UPSO algorithm can search for the optimal structure or extremely similar optimal structure for atomic clusters with atomic numbers between 2 and 31. For atomic clusters with atomic numbers between 32 and 35, the algorithm can find its approximate optimal structure. Compared with other algorithms, the difference between the lowest energy value and the ideal energy value obtained by the SS-DMS-UPSO algorithm is much smaller. It means that its optimal structure of the atomic clusters is closer to the stable structure, and the algorithm is more stable, which proves the effectiveness of the SS-DMS-UPSO algorithm.