Basin-hopping Research Articles

Exploring Nanocluster Potential Energy Surfaces via Deep Reinforcement Learning: Strategies for Global Minimum Search.

The search for global minimum (GM) configurations in nanoclusters is complicated by intricate potential energy landscapes replete with numerous local minima. The complexity of these landscapes escalates with increasing cluster size and compositional diversity. Evolutionary algorithms, such as genetic algorithms, are hampered by slow convergence rates and a propensity for prematurely settling on suboptimal solutions. Likewise, the basin hopping technique faces difficulties in navigating these complex landscapes effectively, particularly at larger scales. These challenges highlight the need for more sophisticated methodologies to efficiently scan the potential energy surfaces of nanoclusters. In response, our research has developed a novel deep reinforcement learning (DRL) framework specifically designed to explore the potential energy surfaces (PES) of nanoclusters, aiming to identify the GM configurations along with other low-energy states. This study demonstrates the framework's effectiveness in managing various nanocluster types, including both mono- and multimetallic compositions, and its proficiency in navigating complex energy landscapes. The model is characterized by remarkable adaptability and sustained efficiency, even as cluster sizes and feature vector dimensions increase. The demonstrated adaptability of DRL in this context underscores its considerable potential in materials science, particularly for the efficient discovery and optimization of novel nanomaterials. To the best of our knowledge, this is the first DRL framework designed for the GM search in nanoclusters, representing a significant innovation in the field.

Mutation Operator for Resonance Flybys in Moon Tour Design Optimization

The global optimization of the moon tour design problem is addressed in this paper. These missions are usually designed using graphical methods or grid search, which require simplifying assumptions, and a skillful mission designer. The grid search methods are computationally intense. Trajectories with a high number of flybys and multiple resonance flybys are usually hard to optimize, especially with small-size/short-period flyby moons. This work proposes a new mutation operator that is incorporated with the Monotonic Basin Hopping in the Evolutionary Mission Trajectory Generator tool; this mutation operator increases the exploration of resonance flybys to improve convergence in moon tour design optimization problems. In this work, the Hidden Genes Genetic Algorithm is used to optimize the undetermined number of moon flybys. A Europa Clipper-like mission is optimized assuming two-body dynamics, and a validation study for the proposed resonance mutation operator is presented. The results include an optimized baseline solution and a new solution with a different sequence of flybys with a different sequence of flybys for the Europa Clipper-like mission, in addition to an optimized moon tour in the Saturnian system.

Dynamical investigation of NinAgm (n + m = 147, 309, 561) nanoalloys with core–shell orderings

ABSTRACT The structures and dynamical properties of core–shell bimetallic Ni-Ag nanoalloys varying with different sizes and compositions have been studied using Monte Carlo (MC) and Molecular Dynamic (MD) simulations. We have considered the compositions in which the size of the core increases while the total number of atoms is fixed. In this sense, two (Ni13Ag134, Ni55Ag92), three (Ni13Ag296, Ni55Ag254, Ni147Ag162) and four (Ni13Ag548, Ni55Ag506, Ni147Ag414 and Ni309Ag252) compositions were considered for 147, 309 and 561 atoms, respectively. Highly symmetric Mackay icosahedral structures with centred symmetric cores appear for these specific sizes and compositions. Also, smaller Ni atoms tend to occupy the core and Ag atoms prefer to segregate to the surface of the nanoalloy due to its lower surface and cohesive energy. Then, the lowest energy structures obtained by Basin Hopping MC simulations were used as initial configurations for melting simulations. The transitions between different chemical ordering patterns with increasing temperature are possible in these systems while they are still in the solid state. Although there are clear differences in the melting process of the compositions with increasing size of the core, for all cases, surface melting occurs indicating that the Ag shell melts before the inner Ni core.

A performance analysis of Basin hopping compared to established metaheuristics for global optimization

A performance analysis of Basin hopping compared to established metaheuristics for global optimization

Growth mechanism prediction for nanoparticles via structure matching polymerization.

Exploring structural and component evolution remains a challenging scientific problem for nanoscience. We propose a novel approach called principle of minimization of structure matching polymerization (SMP) change to rapidly explore the global minimum structure on the potential energy surface (PES). The new method can map low-dimensional stable structures to high-dimensional local minima, and this will make it possible for us to study the growth mechanisms of nanoparticles. Some new lowest-energy structures were found by SMP methods for sulfuric acid (SA)-dimethylamine (DMA) systems relative to previous studies. Additionally, we found that the growth process of boron clusters is mainly that the small-size boron clusters are continuously added to large-size boron clusters by structure matching for Bn (n = 2-36) systems, Bm + Bk → Bn, where m + k = n and 1 ≤ k ≤ 3. The SMP approach can greatly improve the search efficiency of other unbiased global optimization algorithms, such as basin-hopping (BH) and genetic algorithm (GA), with an enhancement of up to 19- and 7-fold relative to traditional BH and GA algorithms for searching the global minima of Bn (n = 14-22) systems. The SMP approach is general and flexible and can be applied to different kinds of problems, such as material structure design, crystal structure prediction, and new drug generation.

Structures and stability of K+ cation solvated in Arn clusters

The solvation of K+ cation plays an important role in various phenomena such as biological procedures, geological time, and archaeological properties. Monte Carlo (MC) simulation and DFT method are employed to study the structural and energetic characteristics of the K + Arn (n = 1–14) clusters. The potential model (PM) and the Basin-Hopping (BH) method are the foundation of the MC simulation. The pairwise PM (PW-PM) is improved by introducing the N-body interactions via the polarizable potential model (PPM). On the other side, the DFT functional M05–2X, combined with the 6–311++G(3d2f,2p) basis set, and the Grimme dispersion correction GD3 was used to deeply investigate the geometrical properties and the relative stability of the K + Arn clusters. Starting from n = 12, a structural transition from square antiprism (SA) to icosahedron (ICOS) form is detected. Additionally, the PPM allows us to examine the largest sizes (n = 15–54). Herein, the first ICOS layers are found for n = 12 and 54 cluster sizes, respectively. The binding energy and the second energy difference as a function of cluster size are used to evaluate the relative stability of K + Arn clusters. The obtained data are in concordance with the available results in the literature.

Nature of Zirconia on a Copper Inverse Catalyst Under CO2 Hydrogenation Conditions.

The growing concern over the escalating levels of anthropogenic CO2 emissions necessitates effective strategies for its conversion to valuable chemicals and fuels. In this research, we embark on a comprehensive investigation of the nature of zirconia on a copper inverse catalyst under the conditions of CO2 hydrogenation to methanol. We employ density functional theory calculations in combination with the Grand Canonical Basin Hopping method, enabling an exploration of the free energy surface including a variable amount of adsorbates within the relevant reaction conditions. Our focus centers on a model three-atom Zr cluster on a Cu(111) surface decorated with various OH, O, and formate ligands, noted Zr3Ox (OH)y (HCOO)z/Cu(111), revealing major changes in the active site induced by various reaction parameters such as the gas pressure, temperature, conversion levels, and CO2/H2 feed ratios. Through our analysis, we have unveiled insights into the dynamic behavior of the catalyst. Specifically, under reaction conditions, we observe a large number of composition and structures with similar free energy for the catalyst, with respect to changing the type, number, and binding sites of adsorbates, suggesting that the active site should be regarded as a statistical ensemble of diverse structures that interconvert.

Development of surrogate-optimization models for a novel transcritical power cycle integrated with a small modular reactor

In recent years, various types of surrogate optimization models have been proposed to reduce the computational time and to improve the emulation accuracy. In this study, by leveraging an ANN surrogate model developed earlier, a comprehensive and efficient optimization algorithm is conceived for the global optimal design of an integrated regenerative methanol transcritical cycle. It combines a unique converging/diverging classifier model into the surrogate model to form a surrogate-based model, which significantly improves the prediction accuracy of the objective function. Six binary classifiers are explored and the multi-layer feed-forward (MLF) neural network classifier is selected. In addition, within the five global optimizers being explored, the basin-hopping (BH) and dual-annealing (DA) are selected. The optimal surrogate-based model and global optimizers are then combined to form a unique surrogate-optimizer model. The surrogate-optimizer model is slightly outperformed by the physics-based model in terms of the optimization results, the time consumption of the surrogate-optimizer model during the optimization searching process is 99% less than that of the physics-based model. As the results, the surrogate-optimizer model is slightly outperformed by the physics-based model in terms of the optimization results, where the Levelized Cost of Energy (LCOE) of the Surrogate-DA and Surrogate-BH models are 77.912 and 78.876 $/MWh, respectively, compared to the 77.190 $/MWh of the Baseline model with fairly close penalties between them. In the meantime, the time consumption of the surrogate-optimizer model during the optimization searching process is 99% less than that of the physics-based model.

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.

Analysis of Preliminary Impulsive Trajectory Design for Near-Earth Asteroid Missions under Approaching Phase Constraints

This study investigates the preliminary trajectory design for high-thrust missions to near-Earth asteroids (NEAs), considering distance and phase angle constraints during the approaching phase to enable pre-rendezvous optical navigation and the scientific identification of asteroids. A global optimization algorithm called monotonic basin hopping is used to design -optimal impulsive trajectories both with and without constraints. Comparisons reveal that extending the final leg of the unconstrained reference trajectory and incorporating a few deep-space maneuvers in that final leg can yield a constrained trajectory with a increase of only a few percent. The effects of the phase angle and minimum distance constraint on are also examined. The results indicate that in -optimal constrained trajectories, an additional deep-space maneuver enables the redistribution of maneuvers in the last leg to ideally insert the spacecraft into the constraint cone. However, additional small maneuvers may be necessary at times to ensure that the spacecraft remains within the cone. Based on these findings, we present a two-step approach for the preliminary design of constrained trajectories for NEA missions based on global optimization algorithms. This approach serves as a valuable tool for initial mission design and trade-off analyses involving constraints, fuel usage, and transfer durations.

Structure search method for atomic clusters based on the dividing rectangles algorithm.

The Dividing Rectangles (DIRECT) algorithm is a deterministic optimization method to explore optimal solutions by repeatedly dividing a given hyperrectangle search space into subhyperrectangles. Herein, we propose a structure search method for atomic clusters based on the DIRECT algorithm in combination with a gradient-based local optimizer to enable an efficient structure search in high-dimensional search spaces. We use the Z-matrix representation for defining the hyperrectangle search space, in which the bond lengths, bond angles, and dihedral angles specify a cluster structure. To evaluate its performance, we applied the proposed method to the Lennard-Jones clusters and two kinds of real atomic clusters with many metastable structures, i.e., phosphorus and sulfur clusters, and compared the results with those of conventional methods. The proposed method exhibits a higher efficiency than random search and a comparable efficiency to basin hopping.

Self-Determined Shot Geometry for Open-Configuration Portable X-Ray CT

Open-configuration portable x-ray computed tomography (CT) is a technology that enables the volumetric inspections of regions of interest on large parts. The open-configuration aspect of x-ray CT allows it to be portable and applicable to large and irregular parts that are not conducive to conventional CT booth setups or ring geometry. The inherent problem with the open-configuration setup is lack of mechanical controls that determine the geometry between the x-ray source, detector, and part. As a result, the focus of this paper is a prerequisite technique to self-determine the x-ray shot geometry from the x-ray shot itself. Additional difficulties pertaining to self-determined shot geometry is that there are nine system unknowns for every x-ray shot as compared to conventional CT that has nine system unknowns total. To address these problems, the technique presented here has three unique features: 1) it consists of only a few known constellation markers, 2) it exploits geometry to break the problem into many to find the global optimum solution, and 3) it reprojects a 3D model of the reference constellation for final geometry refinement. A comparison study is provided to demonstrate the advantages of this solution over random basin hopping, a general purpose global optimization technique. After performing this process for every shot, results show that the geometric error is satisfactorily low for successful CT reconstruction.

Atomistic structure search using local surrogate model.

We describe a local surrogate model for use in conjunction with global structure search methods. The model follows the Gaussian approximation potential formalism and is based on the smooth overlap of atomic positions descriptor with sparsification in terms of a reduced number of local environments using mini-batch k-means. The model is implemented in the Atomistic Global Optimization X framework and used as a partial replacement of the local relaxations in basin hopping structure search. The approach is shown to be robust for a wide range of atomistic systems, including molecules, nanoparticles, surface supported clusters, and surface thin films. The benefits in a structure search context of a local surrogate model are demonstrated. This includes the ability to benefit from transfer learning from smaller systems as well as the possibility to perform concurrent multi-stoichiometry searches.

DFT study of small Re-Pt clusters supported on γ-Al2O3

The scarcity and high cost of raw materials such as platinum to synthesize catalysts, makes it desirable to reduce the amount of precious metal used preserving their overall catalytic performance. A promising solution to this is for example, using highly dispersed and catalytically active transition metal clusters supported on metal oxides, such as TiO2, CeO2, and γ-Al2O3. Thus, bimetallic clusters can potentially offer additional catalytic enhancement due to a synergy between the involved metal atoms. We focus our attention on a computational, DFT study of small bimetallic Re-Pt clusters supported on γ-Al2O3. We aim to determine global minima configurations of Re-Pt clusters (up to 5 atoms) on the γ-Al2O3 (100) surface by using a Basin Hopping global optimization scheme. The adsorption and mixing energies are calculated as a function of clusters size and composition, thus providing a quantifiable picture of the stability of such bimetallic clusters. Our results show that bimetallic Re-Pt supported clusters exhibit higher stability compared to monometallic Re or Pt clusters. Regarding the bonding mechanism between metal clusters and the oxide substrate, our calculations indicate that the contribution to the PDOS of the 6-s states of both Re and Pt atoms is negligible, compared to that of the 5s-states. Furthermore, projected density of states (PDOS) analysis indicate that no bond is formed between the surface Al atoms and clusters. A Bader charge transfer analysis reveals that Re-rich clusters transfer electrons to the γ-Al2O3 substrate, while the opposite is true for their Pt-rich counterparts. Finally, various cluster nucleation pathways are investigated finding that the most favorable nucleation routes lead to the Re3Pt2 and Re5 clusters, while the coalescence of Pt atoms into Pt clusters is energetically unfavorable.

Fast atomic structure optimization with on-the-fly sparse Gaussian process potentials *

We apply on-the-fly machine learning potentials (MLPs) using the sparse Gaussian process regression (SGPR) algorithm for fast optimization of atomic structures. Great acceleration is achieved even in the context of a single local optimization. Although for finding the exact local minimum, due to limited accuracy of MLPs, switching to another algorithm may be needed. For random gold clusters, the forces are reduced to ∼0.1 eV Å−1 within less than ten first-principles (FP) calculations. Because of highly transferable MLPs, this algorithm is specially suitable for global optimization methods such as random or evolutionary structure searching or basin hopping. This is demonstrated by sequential optimization of random gold clusters for which, after only a few optimizations, FP calculations were rarely needed.

An Improved Self-Adaptive Differential Evolution with the Neighborhood Search Algorithm for Global Optimization of Bimetallic Clusters.

Global optimization of multicomponent cluster structures is considerably time-consuming due to the existence of a vast number of isomers. In this work, we proposed an improved self-adaptive differential evolution with the neighborhood search (SaNSDE) algorithm and applied it to the global optimization of bimetallic cluster structures. The cross operation was optimized, and an improved basin hopping module was introduced to enhance the searching efficiency of SaNSDE optimization. Taking (PtNi)N (N = 38 or 55) bimetallic clusters as examples, their structures were predicted by using this algorithm. The traditional SaNSDE algorithm was carried out for comparison with the improved SaNSDE algorithm. For all the optimized clusters, the excess energy and the second difference of the energy were calculated to examine their relative stabilities. Meanwhile, the bond order parameters were adopted to quantitatively characterize the cluster structures. The results reveal that the improved SaNSDE algorithm possessed significantly higher searching capability and faster convergence speed than the traditional SaNSDE algorithm. Furthermore, the lowest-energy configurations of (PtNi)38 clusters could be classified as the truncated octahedral and disordered structures. In contrast, all the optimal (PtNi)55 clusters were approximately icosahedral. Our work fully demonstrates the high efficiency of the improved algorithm and advances the development of global optimization algorithms and the structural prediction of multicomponent clusters.

Systematic Comparison of Genetic Algorithm and Basin Hopping Approaches to the Global Optimization of Si(111) Surface Reconstructions.

We present a systematic study of two widely used material structure prediction methods, the Genetic Algorithm and Basin Hopping approaches to global optimization, in a search for the 3 × 3, 5 × 5, and 7 × 7 reconstructions of the Si(111) surface. The Si(111) 7 × 7 reconstruction is the largest and most complex surface reconstruction known, and finding it is a very exacting test for global optimization methods. In this paper, we introduce a modification to previous Genetic Algorithm work on structure search for periodic systems, to allow the efficient search for surface reconstructions, and present a rigorous study of the effect of the different parameters of the algorithm. We also perform a detailed comparison with the recently improved Basin Hopping algorithm using Delocalized Internal Coordinates. Both algorithms succeeded in either resolving the 3 × 3, 5 × 5, and 7 × 7 DAS surface reconstructions or getting “sufficiently close”, i.e., identifying structures that only differ for the positions of a few atoms as well as thermally accessible structures within kBT/unit area of the global minimum, with T = 300 K. Overall, the Genetic Algorithm is more robust with respect to parameter choice and in success rate, while the Basin Hopping method occasionally exhibits some advantages in speed of convergence. In line with previous studies, the results confirm that robustness, success, and speed of convergence of either approach are strongly influenced by how much the trial moves tend to preserve favorable bonding patterns once these appear.

Hopping between distant basins

We present and numerically analyse the Basin Hopping with Skipping (BH-S) algorithm for stochastic optimisation. This algorithm replaces the perturbation step of basin hopping (BH) with a so-called skipping mechanism from rare-event sampling. Empirical results on benchmark optimisation surfaces demonstrate that BH-S can improve performance relative to BH by encouraging non-local exploration, that is, by hopping between distant basins.

Improved penalty algorithm for mixed integer PDE constrained optimization problems

Optimal control problems including partial differential equation (PDE) as well as integer constraints merge the combinatorial difficulties of integer programming and the challenges related to large-scale systems resulting from discretized PDEs. So far, the branch-and-bound framework has been the most common solution strategy for such problems. In order to provide an alternative solution approach, especially in a large-scale context, this article investigates penalization techniques. Taking inspiration from a well-known family of existing exact penalty algorithms, a novel improved penalty algorithm is derived, whose key ingredients are a basin hopping strategy and an interior point method, both of which are specialized for the problem class. A thorough numerical investigation is carried out for a standard stationary test problem. Extensions to a convection-diffusion as well as a nonlinear test problem finally demonstrate the versatility of the approach.

Optimization of SiO2 with GHA and basin hopping

In this paper we continue to develop our structural optimization algorithm built earlier on a numerical platform, the Genetic Hybrid Algorithm (GHA). Our goal now is to extend our algorithm to oxides, find an effective way to search for the known global minimum, alpha-quartz as a test case, and report our results and findings for this system. We studied unit cells of different sizes: 18, 36 and 72 atoms, but most of the presented results are for cases with 18 and 36 atoms. The algorithm makes heavy use of the basin hopping method for searching for the global minimum of the system. We show how we were able to apply basin hopping most effectively in this case and which variables were of importance.We identify three other low energy structures near the global minimum structure, that trap the search. We show that the energy guided basin hopping can be detrimental to the search and structure-based guiding works more reliably. Two different structure based guides were used, one that tries to maximize the shortest silicon–silicon bond in the cell, while the other tries to maximize the calculated order parameter. The guiding was implemented by generating multiple different options for the basin hopping jumps, and doing weighted choosing on those options based on their properties.