Comprehensive Genetic Algorithm Research Articles

Structures and bonding characteristics of KCl(H2O)n clusters with n = 1-10 based on density functional theory.

Aqueous inorganic salt solutions play a prominent role in both physiological and chemical experiments, and significant attention has been directed toward understanding the mechanisms underlying salt dissolution. In our effort to elucidate the hydration process of potassium chloride, we employed a comprehensive genetic algorithm to explore the structures of KCl(H2O)n (n = 1-10). A series of stable structures were identified by high-level abinitio optimization and single-point energy calculations with a zero-point energy correction. An analysis of the probability distribution of KCl(H2O)1-10 revealed that clusters with high probability at low temperatures exhibit reduced probabilities at higher temperatures, while others become more prevalent. When n = 1-9, the contact ion pair configurations or partially dissociated structures dominate in the system, and the probability distribution plot shows that the proportion of the solvent-separated ion pair (SSIP) structures of KCl(H2O)n is very small, while the SSIP configuration in KCl(H2O)10 becomes a stable structure with increasing temperature. The results from natural bond orbital analysis reveal a stronger interaction between chloride ions and water molecules. These findings provide valuable insights for a more comprehensive understanding of the intricacies of potassium chloride dissolution in water.

Optimization of S2-alar-iliac screw (S2AI) fixation in adult spine deformity using a comprehensive genetic algorithm and finite element model personalized to patient geometry and bone mechanical properties.

To optimize the biomechanical performance of S2AI screw fixation using a genetic algorithm (GA) and patient-specific finite element analysis integrating bone mechanical properties. Patient-specific pelvic finite element models (FEM), including one normal and one osteoporotic model, were created from bi-planar multi-energy X-rays (BMEXs). The genetic algorithm (GA) optimized screw parameters based on bone mass quality (BM method) while a comparative optimization method maximized the screw corridor radius (GEO method). Biomechanical performance was evaluated through simulations, comparing both methods using pullout and toggle tests. The optimal screw trajectory using the BM method was more lateral and caudal with insertion angles ranging from 49° to 66° (sagittal plane) and 29° to 35° (transverse plane). In comparison, the GEO method had ranges of 44° to 54° and 24° to 30° respectively. Pullout forces (PF) using the BM method ranged from 5 to 18.4kN, which were 2.4 times higher than the GEO method (2.1-7.7kN). Toggle loading generated failure forces between 0.8 and 10.1kN (BM method) and 0.9-2.9kN (GEO method). The bone mass surrounding the screw representing the fitness score and PF of the osteoporotic case were correlated (R2 > 0.8). Our study proposed a patient-specific FEM to optimize the S2AI screw size and trajectory using a robust BM approach with GA. This approach considers surgical constraints and consistently improves fixation performance.

Effects of Na+ and Cl- on hydrated clusters by abinitio study.

A comprehensive genetic algorithm is used to perform a global search for Cl-(H2O)1-9 and NaCl(H2O)1-9. The structural optimization, energy calculations, vibrational characteristics, and charge distribution were performed at an abinitio high-level theory. Combined with the calculation results of Na+(H2O)1-6 by Wang et al. [Front. Chem. 7, 624 (2019)] in our group, we systematically investigate these three systems at the same theoretical level. A comparison of bond lengths reveals that in Cl-(H2O)n, the inclusion of Na+ to form NaCl(H2O)n reduces the average distance between Cl- and H2O, indicating that Na+ has a stabilizing effect on ionic hydrogen bonds. Conversely, in Na+(H2O)n, the introduction of Cl- weakens the interactions between Na+ and H2O. In the NaCl(H2O)1-9 structures searched by the genetic algorithm, the ground-state configurations correspond to contact ion pairs, and the solvent-separated ion pair structures appear when n = 7. Furthermore, the anharmonic corrected infrared spectra of Cl-(H2O)1-5 and NaCl(H2O)1-4 exhibit good agreement with the experimental results. According to charge analysis of NaCl(H2O)n, it is observed that charge transfer primarily occurs from Cl- to H2O, resulting in the presence of negative charges on the water molecules. These findings are helpful to understand the effects of Na+ and Cl- on hydrated clusters at the molecular level.

Revisiting the stable structures of gold clusters: Au n (n = 16–25) by artificial neural network potential

Identifying the stable structures of gold (Au) clusters is a huge challenge in cluster science. In this work, we have searched the ground-state structures of neutral Au n (n = 16–25) clusters using the potential of an artificial neural network (ANN) trained with density functional theory (DFT) data. Compared with the DFT data, the root mean square error of binding energy predicted by the ANN potential is about 8.66 meV/atom. Applying the ANN potential to search the ground-state structures by comprehensive genetic algorithm, we have found several new candidates of Au18, Au22, and Au23, which have not been previously reported. Au18 has a hollow cage structure, whereas Au22 and Au23 are flat cage structures. From the electronic analysis, we elucidate the stability mechanism of the newly found structures that are associated with the electronic shell closure of superatomic orbitals. Additonally, we also clarified how to clean a database to train an efficient ANN potential in detail. Overall, this work proves that applying machine learning to the description of atomic interactions can accelerate the search of ground-state structures of clusters and help to find new candidates for stable cluster structures.

Theoretical prediction for growth behavior and electronic properties of monoanionic Ru2Gen− (n = 3–20) clusters

We present a detailed theoretical study on the structural and electronic properties of monoanionic Ru2Gen− (n = 3–20) clusters using comprehensive genetic algorithm combined with density functional theory (CGA-DFT). It is shown that the geometrical growth patterns of the ground state Ru2Gen− clusters are polyhedral pyramidal structures with n ≤ 9 and gradually to form pentagonal prism-based structures with two endohedral Ru atoms from 10 ≤ n ≤ 15, then the structures evolve into a oblate cage-like configuration with two Ru atoms in center from cluster sizes n ≥ 16. In general, one extra electron will influence the geometric structures of Ru2Gen clusters to compare with their neutral ones we have studied. Based on the obtained ground state structures, we find that the clusters of Ru2Ge10−, Ru2Ge12− and Ru2Ge14− have relatively higher structural and chemical stability in which Ru2Ge14− is more prominent through the analysis of binding energy, second order of energy difference and highest occupied and lowest unoccupied molecular orbital (HOMO-LUMO) gap. Furthermore, we analyzed natural charge, natural electronic configuration, the frontier molecular orbitals and orbital composition to verify the clusters of Ru2Gen− with n = 10, 12, 14 and 16 have relatively higher chemical stability owning to the less contribution of Ru-d orbitals. In addition, the clusters of Ru2Ge3−, Ru2Ge4−, Ru2Ge6−, Ru2Ge10− and Ru2Ge16− have magnetic moment of 3 μB, while others are 1 μB. And also the vertical detachment energy (VDE) and adiabatic detachment energy (ADE) for all ground state clusters are computed to support future experiment.

Ground-State Structures of Hydrated Calcium Ion Clusters From Comprehensive Genetic Algorithm Search.

We searched the lowest-energy structures of hydrated calcium ion clusters Ca2+(H2O)n (n = 10–18) in the whole potential energy surface by the comprehensive genetic algorithm (CGA). The lowest-energy structures of Ca2+(H2O)10–12 clusters show that Ca2+ is always surrounded by six H2O molecules in the first shell. The number of first-shell water molecules changes from six to eight at n = 12. In the range of n = 12–18, the number of first-shell water molecules fluctuates between seven and eight, meaning that the cluster could pack the water molecules in the outer shell even though the inner shell is not full. Meanwhile, the number of water molecules in the second shell and the total hydrogen bonds increase with an increase in the cluster size. The distance between Ca2+ and the adjacent water molecules increases, while the average adjacent O-O distance decreases as the cluster size increases, indicating that the interaction between Ca2+ and the adjacent water molecules becomes weaker and the interaction between water molecules becomes stronger. The interaction energy and natural bond orbital results show that the interaction between Ca2+ and the water molecules is mainly derived from the interaction between Ca2+ and the adjacent water molecules. The charge transfer from the lone pair electron orbital of adjacent oxygen atoms to the empty orbital of Ca2+ plays a leading role in the interaction between Ca2+ and water molecules.

Superatomic Signature and Reactivity of Silver Clusters with Oxygen: Double Magic Ag 17 – with Geometric and Electronic Shell Closure

Understanding the stability and reactivity of silver clusters toward oxygen provides insights to design new materials of coinage metals with atomic precision. Herein, we report a systematic study o...

TM4B18 0/- (TM = Hf, Ta, W, Re, Os): new structure construction with TM doped B wheel units.

We report the global search for the lowest energy structures of the transition metal (TM) doped B clusters, TM4B180/− (TM = Hf, Ta, W, Re, Os) and their electronic properties. A combination of the comprehensive genetic algorithm (CGA) method with density functional theory (DFT) calculations shows that they are composed of four planar TM@B9 wheel units by sharing B atoms, except for Os4B180/−, which consists of two types of planar molecular wheels of Os@B7 and Os@B8. Among these nanoclusters, it is found that the Ta4B18 cluster has a closed-shell with a large HOMO–LUMO gap of 2.61 eV. Adaptive natural density partitioning analysis (AdNDP) reveals that the Ta4B18 cluster has σ antiaromaticity and π aromaticity, i.e., a conflicting aromaticity. The simulated photoelectron spectra (PES) of all anionic clusters are also provided for future experimental investigations.

Structure Evolution of Transition Metal-doped Gold Clusters M@Au12 (M = 3d–5d): Across the Periodic Table

The comprehensive genetic algorithm (CGA) incorporated with density functional theory (DFT) calculations were used for a global search of the potential energy surfaces of M@Au12 (M = 3d–5d) cluster...

Structures and vertical detachment energies of water cluster anions (H2O)−n with n = 6–11

The structures and vertical detachment energies (VDEs) of water cluster anions (H2O)− with n = 6–11 are examined by an unbiased global search algorithm, namely comprehensive genetic algorithm (CGA) combined with density functional theory. Benchmark evaluation shows that the B3LYP-D3/6-31(+,3+)G* level of theory could give comparable accuracy of MP2/6-31(+,3 +)G* about the geometric property of water cluster anions. Meanwhile, the energies simulated at the MP2/6-31(+,3 +)G* level of theory converge to the results of CCSD(T)/6-31(+,3 +)G* level. Therefore, the relative energies and VDE of water cluster anions are calculated at the MP2/6-31(+,3 +)G*//B3LYP-D3/6-31(+,3 +)G* level of theory. The structures of (H2O)6–11− clusters obtained from CGA represent that the excess electron destroys the hydrogen bond network and forms an electron hole in most structures. The water cluster anions prefer to form three-membered rings and four-membered rings. As the cluster size increases, the VDE of the water cluster anions increases because the excess electron becomes less diffuse in the larger-sized clusters. Our work gives a comprehensive study about the excess electron disturbing the small-sized neutral water clusters.

Structural Evolution of Medium-Sized Phosphorus Clusters (P20–P36) from Ab Initio Global Search

The ground state configurations of phosphorus clusters, Pn (n = 20–36), were investigated by using the comprehensive genetic algorithm combined with the first-principles calculation method. The medium sized phosphorus structures are assembled with small subunits P1, P4, P6, P7, P8, and P10, which are jointed by a P2 dimer. These phosphorus clusters can be divided into three groups by the subunit number, i.e. P20 with two, P21–30 with three, and P31–36 with four subunits, respectively. All the Pn clusters in the third group can be regarded as adding a P8 subunit and a P2 dimer to the corresponding clusters Pn−10. The binding energy per atom and the HOMO–LUMO gap show distinct odd–even oscillations. It was found that the even-sized clusters are more stable than the odd-sized ones. All the atoms of the even-sized clusters are threefold, while the odd-sized clusters always have only one twofold atom in P1 or P7 unit. For larger sized Pn clusters with 38 ≤ n ≤ 78, we compared the configurations consisting of pure P8 units and mixed P8 and P10 units. Clusters with mixed P8 and P10 units are always energetically favorable.

Hydrated Sodium Ion Clusters [Na+(H2O)n (n = 1-6)]: An ab initio Study on Structures and Non-covalent Interaction.

Structural, thermodynamic, and vibrational characteristics of water clusters up to six water molecules incorporating a single sodium ion [Na+(H2O)n (n = 1–6)] are calculated using a comprehensive genetic algorithm combined with density functional theory on global search, followed by high-level ab initio calculation. For n ≥ 4, the coordinated water molecules number for the global minimum of clusters is 4 and the outer water molecules connecting with coordinated water molecules by hydrogen bonds. The charge analysis reveals the electron transfer between sodium ions and water molecules, providing an insight into the variations of properties of O–H bonds in clusters. Moreover, the simulated infrared (IR) spectra with anharmonic correction are in good agreement with the experimental results. The O–H stretching vibration frequencies show redshifts comparing with a free water molecule, which is attributed to the non-covalent interactions, including the ion–water interaction, and hydrogen bonds. Our results exhibit the comprehensive geometries, energies, charge, and anharmonic vibrational properties of Na+(H2O)n (n = 1–6), and reveal a deeper insight of non-covalent interactions.

Lunar Rover Path Planning Based on Comprehensive Genetic Algorithm Based on Slip Prediction

Aiming at the problem that the lunar rover path planning algorithm generally has slow convergence rate, falls into local optimal solution, neglects the mutual applicability of environment modeling technology and path planning algorithm, a comprehensive genetic algorithm based on virtual three-dimensional model is proposed. By setting the genetic factor unchanged, the terrain comprehensive cost function is added to set the fitness function. Using genetic algorithm and improved comprehensive genetic algorithm, after 100 simulation experiments, the improved comprehensive genetic algorithm has good search performance, fast convergence and high stability. The key words of this paper are as follows: path planning, terrain comprehensive cost function, genetic algorithm.

Weight restrictions in Data Envelopment Analysis: A comprehensive Genetic Algorithm based approach for incorporating value judgments

The basic DEA model experiences the weights flexibility problem which is resolved by the method of weight restrictions. The current research incorporating Decision Makers’ (DMs) preferences into weight restrictions is subject to serious limitations such as lacking a framework for dual role factors and not incorporating organizational hierarchy in decision-making.The proposed Genetic Algorithm (GA) based approach for weight restrictions incorporates a dual role factor and organizational hierarchy in decision-making. The approach involves finding a set of weights which are at a minimum distance from all the DMs’ preferences. The approach is flexible and is able to generate a common set of weights and Decision Making Unit (DMU) specific weight restrictions simultaneously.Results from model validation in a well-known automobile spare parts manufacturer in India indicate that the majority of suppliers perceived as highly efficient were actually found to be inefficient in the GA based weight restrictions model.A major contribution of this study is a robust approach to deal with multiple DMs and DEA weights flexibility problem. Another key highlight of the research is translating DMs preferences into a distance function. Using that as a fitness measure within the proposed Evolutionary Algorithms has been done for the first time in the presence of multiple DMs.

A comprehensive genetic algorithm for design optimization of Z-bar loader working mechanism

The operation mechanism is generally considered as a key component of a wheel loader. Its working performance has great influence on the service life, stability, efficiency and economy of the loader. This paper establishes a mathematical model of Z-bar loader mechanism in polar coordinate with four-bar linkage and six-bar Watt linkage synthesis, investigates the working performance, such as mechanism transmission ratio, carry stability, parallelism, dumping in any position, bucket flat setting, maximum dig depth, extreme transmission angle and so on. Then we explore new design methods of joint-position of Z-bar loader linkage between tilt cylinder and loader frame to perfect some of the performance. A new method, comprehensive genetic algorithm, is presented to optimize non-linear equation with multi-constraints, and the results improve the multidisciplinary performance. Furthermore, a virtual prototype of the working mechanism is modeled to simulate and verify the optimization results.

Comparison of Policies Derived from Stochastic Dynamic Programming and Genetic Algorithm Models

A comprehensive Genetic Algorithm (GA) model has been developed and applied to derive optimal operational strategies of a multi-purpose reservoir, namely Perunchani Reservoir, in Kodaiyar Basin in Tamil Nadu, India. Most of the water resources problem involves uncertainty, in order to see that the GA model takes care of uncertainty in the input variable, the result of the GA model is compared with the performance of a detailed Stochastic Dynamic Programming (SDP) model. The SDP models are well established and proved that it takes care of uncertainty in-terms of either implicit or explicit approach. In the present study, the objective function of the models is set to minimize the annual sum of squared deviation from desired target release and desired storage volume. In the SDP model the optimal policies are derived by varying the state variables from 3 to 9 representative class intervals, and then the cases are evaluated for their performance using a simulation model for longer length of inflow data, generated using a Thomas–Fiering model. From the performance of the SDP model policies, it is found that the system encountered irrigation deficit, whereas GA model satisfied the demand to a greater extent. The sensitivity analysis of the GA model in selecting optimal population, optimal crossover probability and the optimal number of generations showed the values of 150, 0.76 and 175 respectively. On comparing the performance of SDP model policy with GA model, it is found that GA model has resulted in a lesser irrigation deficit. Thus based on the present case study, it may be concluded that the GA model performs better than the SDP model.

A new comprehensive genetic algorithm method for optimal overcurrent relays coordination

For optimal co-ordination of overcurrent relays, linear programming techniques such as simplex, two-phase simplex and dual simplex are used. Another way of optimal coordination program is using artificial intelligent system such as genetic algorithm (GA). In this paper, a powerful optimal coordination method based on GA is introduced. The objective function (OF) is developed to solve the problems of miscoordination and continuous or discrete time setting multiplier (TSM) or time dial setting (TDS). In other words; the novelty of the paper is the modification of the existing objective function of GA, by introducing a new parameter and adding a new term to OF, to handle miscoordination problems both for continues and discrete TSM or TDS. The method is applied to two different power system networks and from the obtained results it is revealed that the new method is efficient, accurate and flexible.