Comparison of debris flow susceptibility assessment methods:support vector machine,particle swarm optimization,and feature selection techniques

The selection of important factors in machine learning-based susceptibility assessments is crucial to obtain reliable susceptibility results.In this study,metaheuristic optimization and feature selection techniques were applied to identify the most important input parameters for mapping debris flow susceptibility in the southern mountain area of Chengde City in Hebei Province,China,by using machine learning algorithms.In total,133 historical debris flow records and 16 related factors were selected.The support vector machine(SVM)was first used as the base classifier,and then a hybrid model was introduced by a two-step process.First,the particle swarm optimization(PSO)algorithm was employed to select the SVM model hyperparameters.Second,two feature selection algorithms,namely principal component analysis(PCA)and PSO,were integrated into the PSO-based SVM model,which generated the PCA-PSO-SVM and FS-PSO-SVM models,respectively.Three statistical metrics(accuracy,recall,and specificity)and the area under the receiver operating characteristic curve(AUC)were employed to evaluate and validate the performance of the models.The results indicated that the feature selection-based models exhibited the best performance,followed by the PSO-based SVM and SVM models.Moreover,the performance of the FS-PSO-SVM model was better than that of the PCA-PSO-SVM model,showing the highest AUC,accuracy,recall,and specificity values in both the training and testing processes.It was found that the selection of optimal features is crucial to improving the reliability of debris flow susceptibility assessment results.Moreover,the PSO algorithm was found to be not only an effective tool for hyperparameter optimization,but also a useful feature selection algorithm to improve prediction accuracies of debris flow susceptibility by using machine learning algorithms.The high and very high debris flow susceptibility zone appropriately covers 38.01%of the study area,where debris flow may occur under intensive human activities and heavy rainfall events.

A Reference Vector-Assisted Many-Objective Optimization Algorithm with Adaptive Niche Dominance Relation

It is still a huge challenge for traditional Pareto-dominatedmany-objective optimization algorithms to solve manyobjective optimization problems because these algorithms hardly maintain the balance between convergence and diversity and can only find a group of solutions focused on a small area on the Pareto front,resulting in poor performance of those algorithms.For this reason,we propose a reference vector-assisted algorithmwith an adaptive niche dominance relation,for short MaOEA-AR.The new dominance relation forms a niche based on the angle between candidate solutions.By comparing these solutions,the solutionwith the best convergence is found to be the non-dominated solution to improve the selection pressure.In reproduction,a mutation strategy of k-bit crossover and hybrid mutation is used to generate high-quality offspring.On 23 test problems with up to 15-objective,we compared the proposed algorithm with five state-of-the-art algorithms.The experimental results verified that the proposed algorithm is competitive.

Feature Extraction of Stored-grain Insects Based on Ant Colony Optimization and Support Vector Machine Algorithm

[Objective] The aim was to study the feature extraction of stored-grain insects based on ant colony optimization and support vector machine algorithm, and to explore the feasibility of the feature extraction of stored-grain insects. [Method] Through the analysis of feature extraction in the image recognition of the stored-grain insects, the recognition accuracy of the cross-validation training model in support vector machine （SVM） algorithm was taken as an important factor of the evaluation principle of feature extraction of stored-grain insects. The ant colony optimization （ACO） algorithm was applied to the automatic feature extraction of stored-grain insects. [Result] The algorithm extracted the optimal feature subspace of seven features from the 17 morphological features, including area and perimeter. The ninety image samples of the stored-grain insects were automatically recognized by the optimized SVM classifier, and the recognition accuracy was over 95%. [Conclusion] The experiment shows that the application of ant colony optimization to the feature extraction of grain insects is practical and feasible.

ε-strongly Efficient Solutions for Vector Optimization with Set-valued Maps

In locally convex Hausdorff topological vector spaces,ε-strongly efficient solutions for vector optimization with set-valued maps are discussed.Firstly,ε-strongly efficient point of set is introduced.Secondly,under the nearly cone-subconvexlike set-valued maps,the theorem of scalarization for vector optimization is obtained.Finally,optimality conditions of ε-strongly efficient solutions for vector optimization with generalized inequality constraints and equality constraints are obtained.

Parameter selection of support vector machine for function approximation based on chaos optimization

The support vector machine （SVM） is a novel machine learning method, which has the ability to approximate nonlinear functions with arbitrary accuracy. Setting parameters well is very crucial for SVM learning results and generalization ability, and now there is no systematic, general method for parameter selection. In this article, the SVM parameter selection for function approximation is regarded as a compound optimization problem and a mutative scale chaos optimization algorithm is employed to search for optimal paraxneter values. The chaos optimization algorithm is an effective way for global optimal and the mutative scale chaos algorithm could improve the search efficiency and accuracy. Several simulation examples show the sensitivity of the SVM parameters and demonstrate the superiority of this proposed method for nonlinear function approximation.

Identifcation of large-scale goaf instability in underground mine using particle swarm optimization and support vector machine

An approach which combines particle swarm optimization and support vector machine(PSO–SVM)is proposed to forecast large-scale goaf instability(LSGI).Firstly,influencing factors of goaf safety are analyzed,and following parameters were selected as evaluation indexes in the LSGI:uniaxial compressive strength(UCS)of rock,elastic modulus(E)of rock,rock quality designation(RQD),area ration of pillar(Sp),the ratio of width to height of the pillar(w/h),depth of ore body(H),volume of goaf(V),dip of ore body(a)and area of goaf(Sg).Then LSGI forecasting model by PSO-SVM was established according to the influencing factors.The performance of hybrid model(PSO+SVM=PSO–SVM)has been compared with the grid search method of support vector machine(GSM–SVM)model.The actual data of 40 goafs are applied to research the forecasting ability of the proposed method,and two cases of underground mine are also validated by the proposed model.The results indicated that the heuristic algorithm of PSO can speed up the SVM parameter optimization search,and the predictive ability of the PSO–SVM model with the RBF kernel function is acceptable and robust,which might hold a high potential to become a useful tool in goaf risky prediction research.

Reliability-based multidisciplinary design optimization using incremental shifting vector strategy and its application in electronic product design

Use of multidisciplinary analysis in reliabilitybased design optimization(RBDO) results in the emergence of the important method of reliability-based multidisciplinary design optimization(RBMDO). To enhance the efficiency and convergence of the overall solution process,a decoupling algorithm for RBMDO is proposed herein.Firstly, to decouple the multidisciplinary analysis using the individual disciplinary feasible(IDF) approach, the RBMDO is converted into a conventional form of RBDO. Secondly,the incremental shifting vector(ISV) strategy is adopted to decouple the nested optimization of RBDO into a sequential iteration process composed of design optimization and reliability analysis, thereby improving the efficiency significantly. Finally, the proposed RBMDO method is applied to the design of two actual electronic products: an aerial camera and a car pad. For these two applications, two RBMDO models are created, each containing several finite element models(FEMs) and relatively strong coupling between the involved disciplines. The computational results demonstrate the effectiveness of the proposed method.

Parameter selection of support vector regression based on hybrid optimization algorithm and its application

Choosing optimal parameters for support vector regression （SVR） is an important step in SVR. design, which strongly affects the pefformance of SVR. In this paper, based on the analysis of influence of SVR parameters on generalization error, a new approach with two steps is proposed for selecting SVR parameters, First the kernel function and SVM parameters are optimized roughly through genetic algorithm, then the kernel parameter is finely adjusted by local linear search, This approach has been successfully applied to the prediction model of the sulfur content in hot metal. The experiment results show that the proposed approach can yield better generalization performance of SVR than other methods,

A Metamodeling Method Based on Support Vector Regression for Robust Optimization

Metamodeling techniques have been used in robust optimization to reduce the high computational cost of the uncertainty analysis and improve the performance of robust optimization problems with computationally expensive simulation models. Existing metamodels main focus on polynomial regression（PR）, neural networks（NN） and Kriging models, these metamodels are not well suited for large-scale robust optimization problems with small size training sets and high nonlinearity. To address the problem, a reduced approximation model technique based on support vector regression（SVR） is introduced in order to improve the accuracy of metamodels. A robust optimization method based on SVR is presented for problems that involve high dimension and nonlinear. First appropriate design parameter samples are selected by experimental design theories, then the response samples are obtained from the simulations such as finite element analysis, the SVR metamodel is constructed and treated as the mean and the variance of the objective performance functions. Combining other constraints, the robust optimization model is formed which can be solved by genetic algorithm （GA）. The applicability of the method developed is demonstrated using a case of two-bar structure system study. The performances of SVR were compared with those of PR, Kriging and back-propagation neural networks（BPNN）, the comparison results show that the prediction accuracy of the SVR metamodel was higher than those of other metamodels under uncertainty. The robust optimization solutions are near to the real result, and the proposed method is found to be accurate and efficient for robust optimization. This reaserch provides an efficient method for robust optimization problems with complex structure.

Nonlinear Optimization Method of Ship Floating Condition Calculation in Wave Based on Vector

Ship floating condition in regular waves is calculated. New equations controlling any ship＇s floating condition are proposed by use of the vector operation. This form is a nonlinear optimization problem which can be solved using the penalty function method with constant coefficients. And the solving process is accelerated by dichotomy. During the solving process, the ship＇s displacement and buoyant centre have been calculated by the integration of the ship surface according to the waterline. The ship surface is described using an accumulative chord length theory in order to determine the displacement, the buoyancy center and the waterline. The draught forming the waterline at each station can be found out by calculating the intersection of the ship surface and the wave surface. The results of an example indicate that this method is exact and efficient. It can calculate the ship floating condition in regular waves as well as simplify the calculation and improve the computational efficiency and the precision of results.

On vector variational-like inequalities and vector optimization problems with (G, α)-invexity

The aim of this paper is to study the relationship among Minty vector variational-like inequality problem, Stampacchia vector variational-like inequality problem and vector optimization problem involving (G, α)-invex functions. Furthermore, we establish equivalence among the solutions of weak formulations of Minty vector variational-like inequality problem, Stampacchia vector variational-like inequality problem and weak efficient solution of vector optimization problem under the assumption of (G, α)-invex functions. Examples are provided to elucidate our results.

Generalized cone-subconvexlike set-valued maps and applications to vector optimization

The definitions of cone-subconvexlike set-valued maps and generalized cone-subconvexlike set-valued maps in topological vector spaces are defined by using the relative interiors of ordering cone. The relationships between the two classes of set-valued maps are investigated, and some properties of them are shown. A Gordan type alternative theorem under the assumption of generalized cone-subconvexlikeness of set-valued maps is proved by applying convex separation theorems involving the relative interiors in infinite dimensional spaces. Finally a necessary optimality condition theorem is shown for a general kind of set-valued vector optimization in a sense of weak E-minimizer.

Optimality of Vector Optimization Involving Generalized Type-I Functions in Banach

In this note,new classes of generalized type-I functions are introduced for functions between Banach spaces.These generalized type-I functions are then utilized to establish sufficient optimality conditions and duality results for a vector optimization problem with functions defined on a Banach space.

Support vector machine forecasting method improved by chaotic particle swarm optimization and its application

By adopting the chaotic searching to improve the global searching performance of the particle swarm optimization (PSO), and using the improved PSO to optimize the key parameters of the support vector machine (SVM) forecasting model, an improved SVM model named CPSO-SVM model was proposed. The new model was applied to predicting the short term load, and the improved effect of the new model was proved. The simulation results of the South China Power Market’s actual data show that the new method can effectively improve the forecast accuracy by 2.23% and 3.87%, respectively, compared with the PSO-SVM and SVM methods. Compared with that of the PSO-SVM and SVM methods, the time cost of the new model is only increased by 3.15 and 4.61 s, respectively, which indicates that the CPSO-SVM model gains significant improved effects.

Particle Swarm Optimization-Support Vector Machine Model for Machinery Fault Diagnoses in High-Voltage Circuit Breakers

According to statistic data,machinery faults contribute to largest proportion of High-voltage circuit breaker failures,and traditional maintenance methods exist some disadvantages for that issue.Therefore,based on the wavelet packet decomposition approach and support vector machines,a new diagnosis model is proposed for such fault diagnoses in this study.The vibration eigenvalue extraction is analyzed through wavelet packet decomposition,and a four-layer support vector machine is constituted as a fault classifier.The Gaussian radial basis function is employed as the kernel function for the classifier.The penalty parameter c and kernel parameterδof the support vector machine are vital for the diagnostic accuracy,and these parameters must be carefully predetermined.Thus,a particle swarm optimizationsupport vector machine model is developed in which the optimal parameters c andδfor the support vector machine in each layer are determined by the particle swarm algorithm.The validity of this fault diagnosis model is determined with a real dataset from the operation experiment.Moreover,comparative investigations of fault diagnosis experiments with a normal support vector machine and a particle swarm optimization back-propagation neural network are also implemented.The results indicate that the proposed fault diagnosis model yields better accuracy and e-ciency than these other models.

Intelligent Optimization Methods for High-Dimensional Data Classification for Support Vector Machines

Support vector machine (SVM) is a popular pattern classification method with many application areas. SVM shows its outstanding performance in high-dimensional data classification. In the process of classification, SVM kernel parameter setting during the SVM training procedure, along with the feature selection significantly influences the classification accuracy. This paper proposes two novel intelligent optimization methods, which simultaneously determines the parameter values while discovering a subset of features to increase SVM classification accuracy. The study focuses on two evolutionary computing approaches to optimize the parameters of SVM: particle swarm optimization (PSO) and genetic algorithm (GA). And we combine above the two intelligent optimization methods with SVM to choose appropriate subset features and SVM parameters, which are termed GA-FSSVM (Genetic Algorithm-Feature Selection Support Vector Machines) and PSO-FSSVM(Particle Swarm Optimization-Feature Selection Support Vector Machines) models. Experimental results demonstrate that the classification accuracy by our proposed methods outperforms traditional grid search approach and many other approaches. Moreover, the result indicates that PSO-FSSVM can obtain higher classification accuracy than GA-FSSVM classification for hyperspectral data.

Novel Control Vector Parameterization Method with Differential Evolution Algorithm and Its Application in Dynamic Optimization of Chemical Processes

Two general approaches are adopted in solving dynamic optimization problems in chemical processes, namely, the analytical and numerical methods. The numerical method, which is based on heuristic algorithms, has been widely used. An approach that combines differential evolution （DE） algorithm and control vector parameteri- zation （CVP） is proposed in this paper. In the proposed CVP, control variables are approximated with polynomials based on state variables and time in the entire time interval. Region reduction strategy is used in DE to reduce the width of the search region, which improves the computing efficiency. The results of the case studies demonstrate the feasibility and efficiency of the oroposed methods.

A new support vector machine optimized by improved particle swarm optimization and its application

A new support vector machine （SVM） optimized by an improved particle swarm optimization （PSO） combined with simulated annealing algorithm （SA） was proposed. By incorporating with the simulated annealing method, the global searching capacity of the particle swarm optimization（SAPSO） was enchanced, and the searching capacity of the particle swarm optimization was studied. Then, the improyed particle swarm optimization algorithm was used to optimize the parameters of SVM （c,σ and ε）. Based on the operational data provided by a regional power grid in north China, the method was used in the actual short term load forecasting. The results show that compared to the PSO-SVM and the traditional SVM, the average time of the proposed method in the experimental process reduces by 11.6 s and 31.1 s, and the precision of the proposed method increases by 1.24% and 3.18%, respectively. So, the improved method is better than the PSO-SVM and the traditional SVM.

Fast Training of Support Vector Machines Using Error-Center-Based Optimization

This paper presents a new algorithm for Support Vector Machine (SVM) training, which trains a machine based on the cluster centers of errors caused by the current machine. Experiments with various training sets show that the computation time of this new algorithm scales almost linear with training set size and thus may be applied to much larger training sets, in comparison to standard quadratic programming (QP) techniques.

Prediction of blasting mean fragment size using support vector regression combined with five optimization algorithms

The main purpose of blasting operation is to produce desired and optimum mean size rock fragments.Smaller or fine fragments cause the loss of ore during loading and transportation,whereas large or coarser fragments need to be further processed,which enhances production cost.Therefore,accurate prediction of rock fragmentation is crucial in blasting operations.Mean fragment size(MFS) is a crucial index that measures the goodness of blasting designs.Over the past decades,various models have been proposed to evaluate and predict blasting fragmentation.Among these models,artificial intelligence(AI)-based models are becoming more popular due to their outstanding prediction results for multiinfluential factors.In this study,support vector regression(SVR) techniques are adopted as the basic prediction tools,and five types of optimization algorithms,i.e.grid search(GS),grey wolf optimization(GWO),particle swarm optimization(PSO),genetic algorithm(GA) and salp swarm algorithm(SSA),are implemented to improve the prediction performance and optimize the hyper-parameters.The prediction model involves 19 influential factors that constitute a comprehensive blasting MFS evaluation system based on AI techniques.Among all the models,the GWO-v-SVR-based model shows the best comprehensive performance in predicting MFS in blasting operation.Three types of mathematical indices,i.e.mean square error(MSE),coefficient of determination(R^(2)) and variance accounted for(VAF),are utilized for evaluating the performance of different prediction models.The R^(2),MSE and VAF values for the training set are 0.8355,0.00138 and 80.98,respectively,whereas 0.8353,0.00348 and 82.41,respectively for the testing set.Finally,sensitivity analysis is performed to understand the influence of input parameters on MFS.It shows that the most sensitive factor in blasting MFS is the uniaxial compressive strength.