A binary cluster structure optimization method dynamically adjusting optimization strategy

Abstract

The application discloses a binary cluster structure optimization method of dynamically adjusting optimization strategy, and belongs to the field of computational chemistry simulation. The method comprises the following steps: generating a plurality of initial cluster structures to form a population structure library; eight mutation operations for generating new geometric structures are designed according to cluster structure characteristics, and the same selection probability is given; and a structure optimization operation is performed, and according to the performance of the eight mutation methods in the optimization process, the selection probability of each method is dynamically adjusted. The application considers the comprehensive effect of a plurality of mutation operations on the optimization algorithm, avoids the shortcomings of relying on a single mutation operation, and can improve the efficiency of the algorithm; and the binary Gupta potential function is used as an evaluation function of the optimization algorithm to obtain the most stable structure.

Description

Technical Field

[0001] This invention relates to the field of computational chemistry simulation, and more specifically to a method for optimizing binary cluster structures by dynamically adjusting optimization strategies. Background Technology

[0002] Nanoclusters possess unique physical and chemical properties, such as optical, electromagnetic, and catalytic properties. These properties are largely determined by their geometric structure. Obtaining optimal structures through computational simulations is a crucial aspect of cluster property research. Compared to single-atom clusters, binary clusters offer greater combinatoriality and selectivity. However, the coexistence of geometric isomers and positional isomers due to differences in the relative positions of different atom types within binary cluster structures makes optimizing their structures a challenging task. Representative binary cluster structure optimization methods developed include genetic algorithms (GA), improved Basin-hopping algorithms (BH), and improved adaptive immune optimization algorithms (AIOA).

[0003] The application of the above-mentioned binary cluster structure optimization method has two problems that need to be solved. First, the structure mutation operation in the existing algorithm is monotonous. Once it gets stuck in the local optima of the geometric configuration during the optimization process, it is difficult to get it out of the local optima energy surface through a single method, resulting in generally low algorithm efficiency. Second, the method of generating new structures is generally a fixed mutation operation method. The merits of the operation are not dynamically evaluated during the optimization process, and it is impossible to make a choice. Summary of the Invention

[0004] The purpose of this invention is to provide an efficient method for optimizing binary cluster structures by dynamically adjusting optimization strategies.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0006] A binary cluster structure optimization method with dynamically adjusted optimization strategy, the specific steps of which are as follows:

[0007] S1: Setting parameters

[0008] k is the number of iterations the algorithm has run. max This represents the maximum number of iterations.

[0009] S2: Constructing the initial cluster structure population library

[0010] M initial A's are randomly generated in the Cartesian coordinate system. n B mCluster structures are defined, where n is the number of type A atoms and m is the number of type B atoms. The energy value of each cluster structure in the population library is calculated based on the potential function describing the cluster. A memory-constrained quasi-Newton method is applied for local optimization to obtain the corresponding more stable structures. A binary dynamic grid search method is used to optimize the geometric configuration of individuals in the population library, and then a first-improved local search algorithm is used to obtain the optimal positional isomers. The structural coordinates of the optimized positional isomers are centered to form the initial cluster structure population library X0. At this point, k = 1;

[0011] S3: Mutation Operation

[0012] Calculate the distance r from the farthest atom in each cluster structure to the center of the structure. max Eight methods for generating new cluster structures are designed, and the eight mutation methods are as follows:

[0013] 1) Along the y-axis of the coordinate system, the y-axis in the structural coordinates i >r max The atoms of / 2 rotate 36 degrees clockwise;

[0014] 2) Along the y-axis of the coordinate system, the y-axis in the structural coordinates... i >r max The atoms of / 2 rotate 180 degrees clockwise;

[0015] 3) Along the y-axis of the coordinate system, the y-axis in the structural coordinates... i Atoms with a value greater than 0.0 rotate 90 degrees clockwise;

[0016] 4) The distance from the atom to the center is less than r max / 3 of the atoms rotate 90 degrees clockwise around the y-axis of the coordinate system;

[0017] 5) In structural coordinates, y i Atoms with a value greater than 0.0 move a distance r0 along the x-axis of the coordinate system;

[0018] 6) Along the y-axis of the coordinate system, change the y... i >2r max / 3 and y i <-2r max / 3 of the atoms move towards the center. distance, The nearest neighbor distance between atoms;

[0019] 7) Randomly move the four atoms with the highest energy values ​​in the structure to a distance r from the center. max Within a sphere with a radius of 3;

[0020] 8) Randomly move the four atoms with the highest energy values ​​in the structure to a distance of radius from the center. Within the sphere;

[0021] S4: Assign the same selection probability P to the above eight mutation operations. h (h = 1-8), which is 12.5% ​​for each. M0 structures are selected from the initial population pool as the objects to be optimized according to their selected probabilities.

[0022] S5: Perform optimization operations

[0023] A binary dynamic lattice search method is used to find the optimal geometric configuration for each of the M0 structures. Then, an improved local search algorithm is employed to find the optimal positional isomers. The selection probabilities of eight operations are adaptively and dynamically adjusted based on the changes in cluster structure energy before and after the optimization operations. If the structure energy decreases after an optimization operation, the selection probability of that operation is increased, specifically: P h =P h (1+15%u), if k / k max If k / k ≤ 0.5, then u is a random number between [0.5, 1]. max >0.5, where u is a random number between [0, 0.5]. At this point, the average probability of choosing the other seven operations is reduced by P. h 15% u / 7;

[0024] S6: Update population database

[0025] A connection table describing the cluster topology is used to perform similarity checks between the optimized individuals and individuals in the gene pool. If the energy value of the optimized individual is lower than that of the most similar individual in the gene pool, then the optimized individual replaces the individual in the gene pool. In this case, k = k + 1;

[0026] S7: If k>k max If the selection probability is correct, proceed to step S8; otherwise, select M0 structures from the current population database according to the adjusted selection probability and proceed to step S5.

[0027] S8: Extract the globally optimal structure, which is the binary A. n B m The optimal structure of a cluster.

[0028] Preferably, in step S1, k max It needs to be set according to the optimization scale, and the value is 30;

[0029] Preferably, step S3 incorporates eight mutation operations to make the algorithm more likely to escape the local extremum of the geometric configuration.

[0030] Preferably, in step S5, the probability of each mutation operation being selected is dynamically adjusted, taking into account the combined effect of multiple mutation operations on the optimization algorithm, avoiding the shortcomings of relying on a single mutation operation, and thus improving the efficiency of the algorithm.

[0031] The beneficial effects of this invention are as follows:

[0032] (1) The eight mutation operation strategies proposed in this invention ensure the global space search capability of the algorithm;

[0033] (2) This invention takes into account the impact of multiple mutation operations on the performance of the optimization algorithm, avoids the insufficient optimization caused by relying on a single mutation operation, and can improve the efficiency of the algorithm. Attached Figure Description

[0034] Figure 1 This is a flowchart of the present invention.

[0035] The present invention will now be described in further detail with reference to specific embodiments. Detailed Implementation

[0036] To make the objectives, technical solutions, and advantages of the present invention clearer, the invention will be described clearly and completely below in conjunction with specific embodiments.

[0037] This embodiment is a binary cluster structure optimization method based on the basic framework of population optimization algorithm, which designs eight cluster structure mutation methods and adopts a dynamic adjustment optimization strategy.

[0038] Cu described by the Gupta potential function n Au m Taking the interatomic interactions of a binary cluster (n+m=30) as an example, the specific implementation steps are as follows:

[0039] S1: Setting parameters

[0040] k is the number of iterations the algorithm has run. max This represents the maximum number of iterations.

[0041] S2: Constructing the initial cluster structure population library

[0042] M initial Cu values ​​are randomly generated in the Cartesian coordinate system. n Au m (n+m=30) cluster structure. The energy values ​​of each Cu-Au cluster structure in the clock group library are calculated based on the Gupta potential function. The calculation formula is as follows:

[0043]

[0044]

[0045]

[0046] Where N is the total number of atoms, r ij V is the distance between atoms i and j. r and V m Representing the many-body gravitational term and the Born-Mayer repulsive term. For the Gupta potential function of Cu-Au clusters, A... ij ξ ij , p ij and q ij Parameter values ​​can be obtained from literature. A memory-constrained quasi-Newton method is applied for local optimization to obtain a relatively stable structure. A binary dynamic grid search method is used for each structure to obtain a more stable configuration, and then a newly improved local search algorithm is used to find the optimal positional isomers. The structure coordinates of the optimized positional isomers are centered to form the initial cluster structure population X0. At this point, k = 1;

[0047] S3: Mutation Operation

[0048] Calculate the distance r from the farthest atom in each cluster structure to the center of the structure. max Eight methods for generating new cluster structures are designed, and the eight mutation methods are as follows:

[0049] 1) Along the y-axis of the coordinate system, the y-axis in the structural coordinates i >r max The atoms of / 2 rotate 36 degrees clockwise;

[0050] 2) Along the y-axis of the coordinate system, the y-axis in the structural coordinates... i >r max The atoms of / 2 rotate 180 degrees clockwise;

[0051] 3) Along the y-axis of the coordinate system, the y-axis in the structural coordinates... i Atoms with a value greater than 0.0 rotate 90 degrees clockwise;

[0052] 4) The distance from the atom to the center is less than r max / 3 of the atoms rotate 90 degrees clockwise around the y-axis of the coordinate system;

[0053] 5) In structural coordinates, y i Atoms with a value greater than 0.0 move a distance r0 along the x-axis of the coordinate system;

[0054] 6) Along the y-axis of the coordinate system, change the y... i >2r max / 3 and y i <-2r max / 3 of the atoms move towards the center. distance, The nearest neighbor distance between atoms;

[0055] 7) Randomly move the four atoms with the highest energy values ​​in the structure to a distance r from the center. max Within a sphere with a radius of 3;

[0056] 8) Randomly move the four atoms with the highest energy values ​​in the structure to a distance of radius from the center. Within the sphere;

[0057] S4: Assign the same selection probability P to the above eight mutation operations. h (h = 1-8), which is 12.5% ​​for each. M0 structures are selected from the initial population pool as the objects to be optimized according to their selected probabilities.

[0058] S5: Perform optimization operations

[0059] A binary dynamic grid search method is used for each of the M0 structures, and then an improved local search algorithm is used to find the optimal positional isomers.

[0060] The selection probabilities of eight operations are adaptively and dynamically adjusted based on the changes in structural energy before and after the optimization operation. If the structural energy decreases after the optimization operation, the selection probability of that operation is increased, specifically: P h =P h (1+15%u), if k / k max If k / k ≤ 0.5, then u is a random number between [0.5, 1]. max >0.5, where u is a random number between [0, 0.5]. At this point, the average probability of choosing the other seven operations is reduced by P. h 15% u / 7;

[0061] S6: Update population database

[0062] A connection table describing the cluster topology is used to perform similarity checks between the optimized individuals and individuals in the gene pool. If the energy value of the optimized individual is lower than that of a similar individual in the gene pool, the optimized individual replaces the individual in the gene pool. In this case, k = k + 1;

[0063] S7: If k>k max If the selection probability is correct, proceed to step S8; otherwise, select M0 structures from the current population database according to the adjusted selection probability and proceed to step S5.

[0064] S8: Outputs the globally optimal structure, which is Cu. n Au m The most stable structure of a binary cluster (n+m=30).

[0065] Cu is composed of individual atoms n Au m The optimization results of the (n+m=30) binary cluster structure are shown in Table 1.

[0066] Table 1

[0067]

[0068] Table 1 shows the optimized Cu in this embodiment. n Au m (n+m=30) Optimization results of the stable cluster structure. The initial population size M is 10, the number of selected individuals is 8, the algorithm is run independently 20 times, and the optimal result is statistically analyzed.

[0069] The embodiments of the present invention described above do not constitute a limitation on the scope of protection of the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the claims of the present invention.

Claims

1. A binary cluster structure optimization method with dynamically adjusted optimization strategies, characterized in that: The specific steps are as follows: S1: Setting parameters k is the number of iterations the algorithm has run. max This represents the maximum number of iterations. S2: Constructing the initial cluster structure population library M initial A's are randomly generated in the Cartesian coordinate system. n B m Cluster structures are defined, where n is the number of type A atoms and m is the number of type B atoms. The energy values ​​of each cluster structure in the population library are calculated based on the potential function describing the cluster, and a memory-constrained quasi-Newton method is applied to perform local optimization operations to obtain the corresponding relatively stable structures. The geometric configuration of individuals in the population pool is optimized by using a binary dynamic grid search method, and then an improved local search algorithm is used to obtain the optimal positional isomers. The structural coordinates of the optimized positional isomers are centered to form the initial cluster structure population pool X0, where k = 1. S3: Mutation Operation Calculate the distance r from the farthest atom in each cluster structure to the center of the structure. max We designed eight methods to generate new cluster structures, which are also known as eight mutation methods. S4: Assign the same selection probability P to the above eight mutation operations. h h = 1-8, which is 12.5%; M0 structures are selected from the initial population pool as the objects to be optimized according to the probability of being selected; S5: Perform optimization operations A binary dynamic lattice search method is used to find the optimal geometric configuration for each of the M0 structures. Then, an improved local search algorithm is employed to find the optimal positional isomers. The selection probabilities of eight operations are adaptively and dynamically adjusted based on the changes in cluster structure energy before and after optimization operations. If the structure energy decreases after an optimization operation, the selection probability of that operation is increased, specifically: P h = P h (1+15% u), if k / k max If k ≤ 0.5, then u is a random number between [0.5, 1]. max > 0.5, where u is a random number between [0, 0.5]; at this point, the average selection probability of the other seven operations is reduced by P. h 15% u / 7; S6: Update the population database The optimized individuals are compared with the individuals in the gene pool using a connection table describing the cluster topology. If the energy value of the optimized individual is lower than that of the most similar individual in the gene pool, the optimized individual is used to replace the individual in the gene pool. In this case, k = k + 1. S7: If k > k max If the selection probability is correct, proceed to step S8; otherwise, select M0 structures from the current population database according to the adjusted selection probability and proceed to step S5. S8: Extract the globally optimal structure, which is the binary A. n B m The optimal structure of a cluster; The eight mutation methods used in step S3 are as follows: 1) Along the y-axis of the coordinate system, the y-axis in the structural coordinate system... i > r max The atoms of / 2 rotate 36 degrees clockwise; 2) Along the y-axis of the coordinate system, the y-axis in the structural coordinates... i > r max The atoms of / 2 rotate 180 degrees clockwise; 3) Along the y-axis of the coordinate system, the y-axis in the structural coordinates... i Atoms with a value greater than 0.0 rotate 90 degrees clockwise. 4) Atoms with a distance of less than r from the center max / 3 of the atoms rotate 90 degrees clockwise around the y-axis of the coordinate system; 5) In structural coordinates, y i Atoms with a length greater than 0.0 move a distance r0 along the x-axis of the coordinate system; 6) Along the y-axis of the coordinate system, change the y... i > 2r max / 3 and y i < -2r max / 3 of the atoms move towards the center. distance, The nearest neighbor distance between atoms; 7) Randomly move the four atoms with the highest energy values ​​in the structure to a distance r from the center. max Within a sphere with a radius of 3; 8) Randomly move the four atoms with the highest energy values ​​in the structure to a distance of [r] from the center. max , r max + Within the sphere.

2. The binary cluster structure optimization method with dynamic adjustment optimization strategy according to claim 1, characterized in that: In step S1, k max It needs to be set according to the optimization scale, and the value is 30.

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