Global Minimum Structures of Morse Clusters as a Function of the Range of the Potential:  81 ≤ <i>N</i> ≤ 160

Cheng, Longjiu; Yang, Jinlong

doi:10.1021/jp072238g

Cited by 40 publications

(52 citation statements)

References 59 publications

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“…Global minima search is especially challenging for short-range potentials, since they have a large number of local minima and the search landscape defined by the PES is extremely rough [10]. Furthermore, the global minima for instances with a different number of atoms correspond to a variety of structural geometries [6,11], preventing the application of biased methods and making Morse clusters an excellent benchmark to access the efficacy of global optimization techniques.…”

Section: Morse Clustersmentioning

confidence: 99%

A study on diversity for cluster geometry optimization

Pereira

Marques

2009

Evol. Intel.

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Diversity is a key issue to consider when designing evolutionary approaches for difficult optimization problems. In this paper, we address the development of an effective hybrid algorithm for cluster geometry optimization. The proposed approach combines a steady-state evolutionary algorithm and a straightforward local method that uses derivative information to guide search into the nearest local optimum. The optimization method incorporates a mechanism to ensure that the diversity of the population does not drop below a pre-specified threshold. Three alternative distance measures to estimate the dissimilarity between solutions are evaluated. Results show that diversity is crucial to increase the effectiveness of the hybrid evolutionary algorithm, as it enables it to discover all putative global optima for Morse clusters up to 80 atoms. A comprehensive analysis is presented to gain insight about the most important strengths and weaknesses of the proposed approach. The study shows why distance measures that consider structural information for estimating the dissimilarity between solutions are more suited to this problem than those that take into account fitness values. A detailed explanation for this differentiation is provided.

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Section: Morse Clustersmentioning

confidence: 99%

A study on diversity for cluster geometry optimization

Pereira

Marques

2009

Evol. Intel.

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“…While for β = 6 the structural behaviour of the Morse potential is very similar to that of Lennard-Jones clusters, the global optimization of Morse clusters for β = 10 or β = 14, which correspond to short range interactions, is regarded as a specially tough task, one that is orders of magnitude harder than Lennard-Jones clusters [21,22]. In this study, following previous works [13,14,[60][61][62], we have set β = 14 leaving r i j as the only variable in Eq. 1, resulting on a Morse potential model that depends only on the interactions between particles.…”

Section: Morse Clustersmentioning

confidence: 65%

“…This method was applied to the optimization of short-ranged Morse clusters and obtained good quality results, as it established several new upper bounds on the potential energy for instances until 240 atoms [13,14,25]. DLS creates a dynamic lattice that is formed by all possible locations (in general, sites on the surface of the cluster) for atoms around an initial random minimum structure.…”

Section: Related Workmentioning

confidence: 99%

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Island models for cluster geometry optimization: how design options impact effectiveness and diversity

2015

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Designing island models is a challenging task for researchers. A number of decisions is required regarding the structure of the islands, how they are connected, how many individuals are migrated, which ones and how often. The impact of these choices is yet to be fully understood, specially since it may change between different problems and contexts. Cluster geometry optimization is a widely known and complex problem that provides a set of hard instances to assess and test optimization algorithms. The analysis presented in this paper reveals how design options for island models impact search effectiveness and population diversity, when seeking for the global optima of short-ranged Morse clusters. These outcomes support the definition of a robust and scalable island-based framework for cluster geometry optimization problems.

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“…The DLS method has been successfully applied to LJ clusters [20], Morse clusters [33], C 60 molecular clusters [34], and Ag clusters [35]. The computational results have shown that the DLS method is highly efficient and unbiased.…”

Section: Dynamic Lattice Searching Methodsmentioning

confidence: 99%

Prediction of the lowest energy configuration for Lennard-Jones clusters

Lai

Huang

2011

Sci. China Chem.

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Based on the work of previous researchers, a new unbiased optimization algorithm-the dynamic lattice searching method with two-phase local search and interior operation (DLS-TPIO) -is proposed in this paper. This algorithm is applied to the optimization of Lennard-Jones (LJ) clusters with N = 2-650, 660, and 665-680. For each case, the putative global minimum reported in the Cambridge Cluster Database (CCD) is successfully found. Furthermore, for LJ 533 and LJ 536 , the potential energies obtained in this study are superior to the previous best results. In DLS-TPIO, a combination of the interior operation, two-phase local search method and dynamic lattice searching method is adopted. At the initial stage of the optimization, the interior operation reduces the energy of the cluster, and gradually makes the configuration ordered by moving some surface atoms with high potential energy to the interior of the cluster. Meanwhile, the two-phase local search method guides the search to the more promising region of the configuration space. In this way the success rate of the algorithm is significantly increased. At the final stage of the optimization, in order to decrease energy of the cluster further, the positions of surface atoms are further optimized by using the dynamic lattice searching method. In addition, a simple new method to identify the central atom of icosahedral configurations is also presented. DLS-TPIO has higher computing speed and success rates than some well-known unbiased optimization methods in the literature. global optimization, Lennard-Jones clusters, interior operation, two-phase local search, dynamic lattice searching

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Global Minimum Structures of Morse Clusters as a Function of the Range of the Potential: 81 ≤ N ≤ 160

Abstract: We have attempted to find the putative global minimum structures of Morse clusters for cluster size N=81-160 as a function of the range of the potential (with potential range rho0>or=3.0). Moreover, compared to the results for N Show more

Cited by 40 publications

References 59 publications

A study on diversity for cluster geometry optimization

A study on diversity for cluster geometry optimization

Island models for cluster geometry optimization: how design options impact effectiveness and diversity

Prediction of the lowest energy configuration for Lennard-Jones clusters

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