AN ANALYSIS ABOUT BEHAVIOR OF EVOLUTIONARY ALGORITHMS:A KIND OF THEORETICAL DESCRIPTION BASED ON GLOBAL RANDOM SEARCH METHODS

Evolutionary computation is a kind of adaptive non--numerical computation method which is designed tosimulate evolution of nature. In this paper, evolutionary algorithm behavior is described in terms of theconstruction and evolution of the sampling distributions over the space of candidate solutions. Iterativeconstruction of the sampling distributions is based on the idea of the global random search of generationalmethods. Under this frame, propontional selection is characterized as a gobal search operator, and recombination is characerized as the search process that exploits similarities. It is shown-that by properly constraining the search breadth of recombination operators, weak convergence of evolutionary algorithms to aglobal optimum can be ensured.

Multiobjective particle swarm inversion algorithm for two-dimensional magnetic data

Regularization inversion uses constraints and a regularization factor to solve ill- posed inversion problems in geophysics. The choice of the regularization factor and of the initial model is critical in regularization inversion. To deal with these problems, we propose a multiobjective particle swarm inversion （MOPSOI） algorithm to simultaneously minimize the data misfit and model constraints, and obtain a multiobjective inversion solution set without the gradient information of the objective function and the regularization factor. We then choose the optimum solution from the solution set based on the trade-off between data misfit and constraints that substitute for the regularization factor. The inversion of synthetic two-dimensional magnetic data suggests that the MOPSOI algorithm can obtain as many feasible solutions as possible; thus, deeper insights of the inversion process can be gained and more reasonable solutions can be obtained by balancing the data misfit and constraints. The proposed MOPSOI algorithm can deal with the problems of choosing the right regularization factor and the initial model.

Clonal Selection Based Memetic Algorithm for Job Shop Scheduling Problems

A clonal selection based memetic algorithm is proposed for solving job shop scheduling problems in this paper. In the proposed algorithm, the clonal selection and the local search mechanism are designed to enhance exploration and exploitation. In the clonal selection mechanism, clonal selection, hypermutation and receptor edit theories are presented to construct an evolutionary searching mechanism which is used for exploration. In the local search mechanism, a simulated annealing local search algorithm based on Nowicki and Smutnicki＇s neighborhood is presented to exploit local optima. The proposed algorithm is examined using some well-known benchmark problems. Numerical results validate the effectiveness of the proposed algorithm.

Improvement of a new rotation function for molecular replacement by designing new scoring functions and dynamic correlation coefficient

A previously published new rotation function has been improved by using a dynamic correlation coefficient as well as two new scoring functions of relative entropy and mean-square-residues to make the rotation function more robust and independent of a specific set of weights for scoring and ranking. The previously described new rotation function calculates the rotation function of molecular replacement by matching the search model directly with the Patterson vector map. The signal-to-noise ratio for the correct match was increased by averaging all the matching peaks. Several matching scores were employed to evaluate the goodness of matching. These matching scores were then combined into a single total score by optimizing a set of weights using the linear regression method. It was found that there exists an optimal set of weights that can be applied to the global rotation search and the correct solution can be ranked in the top 100 or less. However, this set of optimal weights in general is dependent on the search models and the crystal structures with different space groups and cell parameters. In this work, we try to solve this problem by designing a dynamic correlation coefficient. It is shown that the dynamic correlation coefficient works for a variety of space groups and cell parameters in the global search of rotation function. We also introduce two new matching scores： relative entropy and mean-square-residues. Last but not least, we discussed a valid method for the optimization of the adjustable parameters for matching vectors.

The May 23 and 24, 1994 Taiwan earth quakes: comparison of source process between the two events

Inversion for the seismic fault rupture history is an important way to study the nature of the earthquake source. Inthis paper, we have selected two Taiwan earthquakes that occurred closely in time and located in the same region,inversed the distribution of the slip amplitudes, rakes, risetimes and the rupture times on the fault planes by usingGDSN broad-band and long-period records and the adaptive hybrid global search algorithm, and compared the twoevents. The slip rate of every subfault calculated provides information about the distribution of tectonic stress andfault strength. To the former event (Ms=6.0), the maximum slip amplitude 2.4 m and the minimum risetime 1.2 sare both located at the hypocentre. The latter earthquake (Ms=6.6) consisted of two subevents and the second source has 4 s delay. The maximum slip amplitUde 0.9 m located near hypocentre is corresponding to the minimumrisetime l.4 s, and the corresponding maximum slip rate 0.7 m.s~-1 is similar to the peak value of other large sliprate areas. We consider that the latter event has more complicated temporal-spatial distribution than the former.

An Advanced Stochastic Numerical Approach for Host-Vector-Predator Nonlinear Model

A novel design of the computational intelligent framework is presented to solve a class of host-vector-predator nonlinear model governed with set of ordinary differential equations.The host-vector-predator nonlinear model depends upon five groups or classes,host plant susceptible and infected populations,vectors population of susceptible and infected individuals and the predator population.An unsupervised artificial neural network is designed using the computational framework of local and global search competencies of interior-point algorithm and genetic algorithms.For solving the hostvector-predator nonlinear model,a merit function is constructed using the differential model and its associated boundary conditions.The optimization of this merit function is performed using the computational strength of designed integrated heuristics based on interior point method and genetic algorithms.For the comparison,the obtained numerical solutions of networks models optimized with efficacy of global search of genetic algorithm and local search with interior point method have been compared with the Adams numerical solver based results or outcomes.Moreover,the statistical analysis will be performed to check the reliability,robustness,viability,correctness and competency of the designed integrated heuristics of unsupervised networks trained with genetic algorithm aid with interior point algorithm for solving the biological based host-vector-predator nonlinear model for sundry scenarios of paramount interest.

A CLASSOF NONMONOTONE CONJUGATE GRADIENT METHODSFOR NONCONVEX FUNCTIONS

This paper discusses the global convergence of a class of nonmonotone conjugate gra- dient methods(NM methods) for nonconvex object functions.This class of methods includes the nonmonotone counterpart of modified Polak- Ribière method and modified Hestenes- Stiefel method as special cases

Hybrid Improved Self-adaptive Differential Evolution and Nelder-Mead Simplex Method for Solving Constrained Real-Parameters

In this paper, a new hybrid algorithm based on exploration power of a new improvement self-adaptive strategy for controlling parameters in DE （differential evolution） algorithm and exploitation capability of Nelder-Mead simplex method is presented （HISADE-NMS）. The DE has been used in many practical cases and has demonstrated good convergence properties. It has only a few control parameters as number of particles （NP）, scaling factor （F） and crossover control （CR）, which are kept fixed throughout the entire evolutionary process. However, these control parameters are very sensitive to the setting of the control parameters based on their experiments. The value of control parameters depends on the characteristics of each objective function, therefore, we have to tune their value in each problem that mean it will take too long time to perform. In the new manner, we present a new version of the DE algorithm for obtaining self-adaptive control parameter settings. Some modifications are imposed on DE to improve its capability and efficiency while being hybridized with Nelder-Mead simplex method. To valid the robustness of new hybrid algorithm, we apply it to solve some examples of structural optimization constraints.

Graph attention network for global search of atomic clusters:A case study of Ag_(n)(n=14-26)clusters

Due to coexistence of huge number of structural isomers,global search for the ground-state structures of atomic clusters is a challenging issue.The difficulty also originates from the computational cost of ab initio methods for describing the potential energy surface.Recently,machine learning techniques have been widely utilized to accelerate materials discovery and molecular simulation.Compared to the commonly used artificial neural network,graph network is naturally suitable for clusters with flexible geometric environment of each atom.Herein we develop a cluster graph attention network(CGANet)by aggregating information of neighboring vertices and edges using attention mechanism,which can precisely predict the binding energy and force of silver clusters with root mean square error of 5.4 meV/atom and mean absolute error of 42.3 meV/Å,respectively.As a proof-of-concept,we have performed global optimization of mediumsized Agn clusters(n=14–26)by combining CGANet and genetic algorithm.The reported ground-state structures for n=14–21,have been successfully reproduced,while entirely new lowest-energy structures are obtained for n=22–26.In addition to the description of potential energy surface,the CGANet is also applied to predict the electronic properties of clusters,such as HOMO energy and HOMO-LUMO gap.With accuracy comparable to ab initio methods and acceleration by at least two orders of magnitude,CGANet holds great promise in global search of lowest-energy structures of large clusters and inverse design of functional clusters.

TGMin： A global-minimum structure search program based on a constrained basin-hopping algorithm

In this article, we introduce Tsinghua Global Minimum （TGMin） as a new program for the global minimum searching of geometric structures of gas-phase or surface-supported atomic clusters, and the constrained basin-hopping （BH） algorithm implemented in this program. To improve the efficiency of the BH algorithm, several types of constraints are introduced to reduce the vast search space, including constraints on the random displacement step size, displacement of low-coordination atoms, and geometrical structure adjustment after displacement. The ultrafast shape-recognition （USR） algorithm and its variants are implemented to identify duplicate structures during the global minimum search. In addition to the Metropolis acceptance criterion, we also implemented a morphology-based constraint that confines the global minimum search to a specific type of morphology, such as planar or non-planar structures, which offers a strict divide-and-conquer strategy for the BH algorithm. These improvements are implemented in the TGMin program, which was developed over the past decade and has been used in a number of publications. We tested our TGMin program on global minimum structural searches for a number of metal and main-group clusters including C60, Au20 and B20 clusters. Over the past five years, the TGMin program has been used to determine the global minimum structures of a series of boron atomic clusters （such as [B26]^-, [B28]^-, [B30]^-, [B35]^-, [B36]^-, [B39]^-, [B40]^-, [MnB16]^-, [COB18]^-, [RhB18]^-, and [TaB20]^-）, metal-containing clusters Lin （n = 3-20）, Aug（CO）8^＋ and [Cr6O19]^2-. and the oxide-supported metal catalyst Au7/γ-Al2O3, as well as other isolated and surface-supported atomic clusters. In this article we present the major features of TGMin program and show that it is highly efficient at searching for global-minimum structures of atomic clusters in the gas phase and on various surface supports.

Two dimensional GeO_(2)/MoSi_(2)N_(4)van der Waals heterostructures with robust type-Ⅱ band alignment

Constructing two-dimensional(2D)van der Waals heterostructures(vdWHs)can expand the electronic and optoelectronic applications of 2D semiconductors.However,the work on the 2D vdWHs with robust band alignment is still scarce.Here,we employ a global structure search approach to construct the vdWHs with monolayer MoSi_(2)N_(4)and widebandgap GeO_(2).The studies show that the GeO_(2)/MoSi_(2)N_(4)vdWHs have the characteristics of direct structures with the band gap of 0.946 eV and typeII band alignment with GeO_(2)and MoSi_(2)N_(4)layers as the conduction band minimum(CBM)and valence band maximum(VBM),respectively.Also,the direct-to-indirect band gap transition can be achieved by applying biaxial strain.In particular,the 2D GeO_(2)/MoSi_(2)N_(4)vdWHs show a robust type-II band alignment under the effects of biaxial strain,interlayer distance and external electric field.The results provide a route to realize the robust type-II band alignment vdWHs,which is helpful for the implementation of optoelectronic nanodevices with stable characteristics.

A modified simulated annealing algorithm and an excessive area model for floorplanning using fixed-outline constraints

Outline-free floorplanning focuses on area and wirelength reductions, which are usually meaningless, since they can hardly satisfy modern design requirements. We concentrate on a more difficult and useful issue, fixed-outline floorplanning. This issue imposes fixed-outline constraints on the outline-free floorplanning, making the physical design more interesting and challenging. The contributions of this paper are primarily twofold. First, a modified simulated annealing(MSA) algorithm is proposed. In the beginning of the evolutionary process, a new attenuation formula is used to decrease the temperature slowly, to enhance MSA's global searching capacity. After a period of time, the traditional attenuation formula is employed to decrease the temperature rapidly, to maintain MSA's local searching capacity. Second, an excessive area model is designed to guide MSA to find feasible solutions readily. This can save much time for refining feasible solutions. Additionally, B*-tree representation is known as a very useful method for characterizing floorplanning. Therefore, it is employed to perform a perturbing operation for MSA. Finally, six groups of benchmark instances with different dead spaces and aspect ratios—circuits n10, n30, n50, n100, n200, and n300—are chosen to demonstrate the efficiency of our proposed method on fixed-outline floorplanning. Compared to several existing methods, the proposed method is more efficient in obtaining desirable objective function values associated with the chip area, wirelength, and fixed-outline constraints.

Glass-like energy and property landscape of Pt nanoclusters

Pt nanoclusters play an important role in catalysis-related applications. Essential to their activities are their geometries and energy landscapes. In this work, we studied the energy landscapes of Pt clusters using a parallel differential evolution optimization algorithm and an accelerated ab initio atomic relaxation method, which allowed us to explore unprecedentedly large numbers of geometry local minima at ab initio level. We found many lower-energy isomers with low symmetry in their geometry. The energy landscapes were demonstrated to be glass-like with a large number of local minimum structures close to the global minimum. The electronic and magnetic properties of most glass-like local minima were dramatically different from the global minimum, and they should be observed in the experimental measurements. The connections between these local minima were further analyzed using data mining techniques.

Heilbronn's Problem of Eight Points in the Square

In this work the authors consider the problem of optimally distributing 8 points inside a unit square so that the smallest area of the(38)triangles formed by them is maximal.Symbolic computations are employed to reduce the problem into a nonlinear programming problem and find its optimal solution.All computations are done using Maple.