Large-Scale Multi-Objective Optimization Algorithm Based on Weighted Overlapping Grouping of Decision Variables

The large-scale multi-objective optimization algorithm(LSMOA),based on the grouping of decision variables,is an advanced method for handling high-dimensional decision variables.However,in practical problems,the interaction among decision variables is intricate,leading to large group sizes and suboptimal optimization effects;hence a large-scale multi-objective optimization algorithm based on weighted overlapping grouping of decision variables(MOEAWOD)is proposed in this paper.Initially,the decision variables are perturbed and categorized into convergence and diversity variables;subsequently,the convergence variables are subdivided into groups based on the interactions among different decision variables.If the size of a group surpasses the set threshold,that group undergoes a process of weighting and overlapping grouping.Specifically,the interaction strength is evaluated based on the interaction frequency and number of objectives among various decision variables.The decision variable with the highest interaction in the group is identified and disregarded,and the remaining variables are then reclassified into subgroups.Finally,the decision variable with the strongest interaction is added to each subgroup.MOEAWOD minimizes the interactivity between different groups and maximizes the interactivity of decision variables within groups,which contributed to the optimized direction of convergence and diversity exploration with different groups.MOEAWOD was subjected to testing on 18 benchmark large-scale optimization problems,and the experimental results demonstrate the effectiveness of our methods.Compared with the other algorithms,our method is still at an advantage.

基于K-Means聚类与熵权TOPSIS法的岩石可爆性评价研究

露天矿山的爆破块度分布,直接影响到后续的采装、运输和破碎工作。为了控制石墨矿山不同区域爆破块度分布,基于K-means无监督聚类学习法与熵权TOPSIS评价法建立了一种新的岩石可爆性评价模型,选取岩石密度、动力能量耗散率、动态抗压强度、平均应变率、脆性指数作为评价指标,通过熵权计算,发现岩石破碎程度受脆性指数影响最大,受平均应变率影响最小。将此模型应用于实际石墨矿山,可爆性分为10个等级,统计不同分级下的岩石平均破碎粒径,发现可爆性分级等级越高平均粒径越大,有明显的分级特征,验证了模型的有效性。从爆破石墨矿石岩体类型看,岩石可爆性从易到难排序为:片岩、片麻岩、变粒岩、混合岩。结合石墨矿石微观观测结果分析可知:岩性从片岩向混合岩转变,岩石内部石墨晶质呈下降趋势,石墨矿石可爆性等级也随之越来越高。岩石密度、能量耗散率、动态抗压强度之间呈线性正相关,岩石可爆性与平均应变率、脆性指数存在负相关性。研究成果为矿山矿岩可爆性评价提供了一条新思路,对露天矿山爆破块度优化具有一定的理论和实践指导意义。

Analysis of the COVID-19, Outbreak in Brazil Using Topological Weighted Centroid: An Intelligent Geographic Information System Approach

This study used Topological Weighted Centroid (TWC) to analyze the Coronavirus outbreak in Brazil. This analysis only uses latitude and longitude in formation of the capitals with the confirmed cases on May 24, 2020 to illustrate the usefulness of TWC though any date could have been used. There are three types of TWC analyses, each type having five associated algorithms that produce fifteen maps, TWC-Original, TWC-Frequency and TWC-Windowing. We focus on TWC-Original to illustrate our approach. The TWC method without using the transportation information predicts the network for COVID-19 outbreak that matches very well with the main radial transportation routes network in Brazil.

Plant Leaf Diseases Classification Using Improved K-Means Clustering and SVM Algorithm for Segmentation

Several pests feed on leaves,stems,bases,and the entire plant,causing plant illnesses.As a result,it is vital to identify and eliminate the disease before causing any damage to plants.Manually detecting plant disease and treating it is pretty challenging in this period.Image processing is employed to detect plant disease since it requires much effort and an extended processing period.The main goal of this study is to discover the disease that affects the plants by creating an image processing system that can recognize and classify four different forms of plant diseases,including Phytophthora infestans,Fusarium graminearum,Puccinia graminis,tomato yellow leaf curl.Therefore,this work uses the Support vector machine(SVM)classifier to detect and classify the plant disease using various steps like image acquisition,Pre-processing,Segmentation,feature extraction,and classification.The gray level co-occurrence matrix(GLCM)and the local binary pattern features(LBP)are used to identify the disease-affected portion of the plant leaf.According to experimental data,the proposed technology can correctly detect and diagnose plant sickness with a 97.2 percent accuracy.

Genetic Algorithm Combined with the K-Means Algorithm:A Hybrid Technique for Unsupervised Feature Selection

The dimensionality of data is increasing very rapidly,which creates challenges for most of the current mining and learning algorithms,such as large memory requirements and high computational costs.The literature includes much research on feature selection for supervised learning.However,feature selection for unsupervised learning has only recently been studied.Finding the subset of features in unsupervised learning that enhances the performance is challenging since the clusters are indeterminate.This work proposes a hybrid technique for unsupervised feature selection called GAk-MEANS,which combines the genetic algorithm(GA)approach with the classical k-Means algorithm.In the proposed algorithm,a new fitness func-tion is designed in addition to new smart crossover and mutation operators.The effectiveness of this algorithm is demonstrated on various datasets.Fur-thermore,the performance of GAk-MEANS has been compared with other genetic algorithms,such as the genetic algorithm using the Sammon Error Function and the genetic algorithm using the Sum of Squared Error Function.Additionally,the performance of GAk-MEANS is compared with the state-of-the-art statistical unsupervised feature selection techniques.Experimental results show that GAk-MEANS consistently selects subsets of features that result in better classification accuracy compared to others.In particular,GAk-MEANS is able to significantly reduce the size of the subset of selected features by an average of 86.35%(72%–96.14%),which leads to an increase of the accuracy by an average of 3.78%(1.05%–6.32%)compared to using all features.When compared with the genetic algorithm using the Sammon Error Function,GAk-MEANS is able to reduce the size of the subset of selected features by 41.29%on average,improve the accuracy by 5.37%,and reduce the time by 70.71%.When compared with the genetic algorithm using the Sum of Squared Error Function,GAk-MEANS on average is able to reduce the size of the subset of selected features by 15.91%,and improve the accuracy by 9.81%,but the time is increased by a factor of 3.When compared with the machine-learning based methods,we observed that GAk-MEANS is able to increase the accuracy by 13.67%on average with an 88.76%average increase in time.

Weighted PageRank Algorithm Search Engine Ranking Model for Web Pages

As data grows in size,search engines face new challenges in extracting more relevant content for users’searches.As a result,a number of retrieval and ranking algorithms have been employed to ensure that the results are relevant to the user’s requirements.Unfortunately,most existing indexes and ranking algo-rithms crawl documents and web pages based on a limited set of criteria designed to meet user expectations,making it impossible to deliver exceptionally accurate results.As a result,this study investigates and analyses how search engines work,as well as the elements that contribute to higher ranks.This paper addresses the issue of bias by proposing a new ranking algorithm based on the PageRank(PR)algorithm,which is one of the most widely used page ranking algorithms We pro-pose weighted PageRank(WPR)algorithms to test the relationship between these various measures.The Weighted Page Rank(WPR)model was used in three dis-tinct trials to compare the rankings of documents and pages based on one or more user preferences criteria.Thefindings of utilizing the Weighted Page Rank model showed that using multiple criteria to rankfinal pages is better than using only one,and that some criteria had a greater impact on ranking results than others.

基于改进K-means算法的电力营销档案信息管理系统

为满足档案管理用户需求,实现不同营销档案管理信息分类,提出改进K-means算法的电力营销档案信息管理系统。设计电能信息收编、客户缴费管理、营销报表管理及系统开发等子系统功能;利用改进的K-means方法定义系统算法,引入权重概念,将元素分配到和中心点距离最近的簇中,实现档案分类统计。仿真实验证明,该系统可实现不同营销档案的准确分类,减少响应延时,提高系统吞吐量,满足电力营销档案管理用户需求。

Blind source separation by weighted K-means clustering

Blind separation of sparse sources （BSSS） is discussed. The BSSS method based on the conventional K-means clustering is very fast and is also easy to implement. However, the accuracy of this method is generally not satisfactory. The contribution of the vector x（t） with different modules is theoretically proved to be unequal, and a weighted K-means clustering method is proposed on this grounds. The proposed algorithm is not only as fast as the conventional K-means clustering method, but can also achieve considerably accurate results, which is demonstrated by numerical experiments.

基于改进的Weighted K-Means聚类的外卖员接单区域划分问题研究

外卖行业蓬勃发展,人们对于外卖服务质量的要求也不断提升。因外卖员接单区域基本固定,合理划分外卖员负责区域并分配每个区域外卖员人数成为提升效率的关键。本项目基于查询算法模型,分析上海市2017年某时段的外卖数据,试图得到一个对于外卖接单区域的较为合理的划分标准并给出该划分。K-Means是一种常见的划分聚类算法,是在集中式系统框架无法对海量数据进行处理分析的基础上提出的。然而对于有权重的二维点集无法使用K-Means聚类算法,因此研究一种改进的Weighted K-Means算法显得尤为必要。本项目定义带权质心和带权距离,提出了新的Weighted K-Means算法,并使用改进前后的两种方法处理上海市外卖接单信息,给出合理可行的外卖员接单区域划分。对比两种方法的结果,改进的Weighted K-Means不仅方法可行,区域划分表现也更优秀。与此同时,使用该方法对外卖接单区域进行新的划分,有助于优化现有外卖模式、提升外卖效率以及顾客满意度。

An Improved Bald Eagle Search Algorithm with Cauchy Mutation and Adaptive Weight Factor for Engineering Optimization

The Bald Eagle Search algorithm(BES)is an emerging meta-heuristic algorithm.The algorithm simulates the hunting behavior of eagles,and obtains an optimal solution through three stages,namely selection stage,search stage and swooping stage.However,BES tends to drop-in local optimization and the maximum value of search space needs to be improved.To fill this research gap,we propose an improved bald eagle algorithm(CABES)that integrates Cauchy mutation and adaptive optimization to improve the performance of BES from local optima.Firstly,CABES introduces the Cauchy mutation strategy to adjust the step size of the selection stage,to select a better search range.Secondly,in the search stage,CABES updates the search position update formula by an adaptive weight factor to further promote the local optimization capability of BES.To verify the performance of CABES,the benchmark function of CEC2017 is used to simulate the algorithm.The findings of the tests are compared to those of the Particle Swarm Optimization algorithm(PSO),Whale Optimization Algorithm(WOA)and Archimedes Algorithm(AOA).The experimental results show that CABES can provide good exploration and development capabilities,and it has strong competitiveness in testing algorithms.Finally,CABES is applied to four constrained engineering problems and a groundwater engineeringmodel,which further verifies the effectiveness and efficiency of CABES in practical engineering problems.

基于加权密度Canopy的K-means文本聚类

针对现有文本聚类性能不高的问题,提出了一种改进质心初始化的K-means文本聚类算法.该算法首先利用Canopy算法进行文本预聚类,并且对Canopy算法的阈值选取策略进行改进,定义加权密度进行Canopy中心的选取,得到更准确的聚类数以及初始聚类中心;然后将所得结果作为K-means算法的初始化参数进行后续迭代聚类,有效解决了传统算法因随机选取初始聚类中心而陷入局部最优解的问题,减少了算法的迭代次数,提高了聚类准确性.实验结果表明:与其他同类型算法相比,该算法在文本聚类分析中更具优势.

A Weighted Algorithm for Watermarking Relational Databases

A weighted algorithm for watermarking relational databases for copyright protection is presented. The possibility of watermarking an attribute is assigned according to its weight decided by the owner of the database. A one-way hash function and a secret key known only to the owner of the data are used to select tuples and bits to mark. By assigning high weight to significant attributes, the scheme ensures that important attributes take more chance to be marked than less important ones. Experimental results show that the proposed scheme is robust against various forms of attacks, and has perfect immunity to subset attack.

Estimating wheat fractional vegetation cover using a density peak k-means algorithm based on hyperspectral image data

Fractional vegetation cover(FVC)is an important parameter to measure crop growth.In studies of crop growth monitoring,it is very important to extract FVC quickly and accurately.As the most widely used FVC extraction method,the photographic method has the advantages of simple operation and high extraction accuracy.However,when soil moisture and acquisition times vary,the extraction results are less accurate.To accommodate various conditions of FVC extraction,this study proposes a new FVC extraction method that extracts FVC from a normalized difference vegetation index(NDVI)greyscale image of wheat by using a density peak k-means(DPK-means)algorithm.In this study,Yangfumai 4(YF4)planted in pots and Yangmai 16(Y16)planted in the field were used as the research materials.With a hyperspectral imaging camera mounted on a tripod,ground hyperspectral images of winter wheat under different soil conditions(dry and wet)were collected at 1 m above the potted wheat canopy.Unmanned aerial vehicle(UAV)hyperspectral images of winter wheat at various stages were collected at 50 m above the field wheat canopy by a UAV equipped with a hyperspectral camera.The pixel dichotomy method and DPK-means algorithm were used to classify vegetation pixels and non-vegetation pixels in NDVI greyscale images of wheat,and the extraction effects of the two methods were compared and analysed.The results showed that extraction by pixel dichotomy was influenced by the acquisition conditions and its error distribution was relatively scattered,while the extraction effect of the DPK-means algorithm was less affected by the acquisition conditions and its error distribution was concentrated.The absolute values of error were 0.042 and 0.044,the root mean square errors(RMSE)were 0.028 and 0.030,and the fitting accuracy R2 of the FVC was 0.87 and 0.93,under dry and wet soil conditions and under various time conditions,respectively.This study found that the DPK-means algorithm was capable of achieving more accurate results than the pixel dichotomy method in various soil and time conditions and was an accurate and robust method for FVC extraction.

Concise review of relaxations and approximation algorithms for nonidentical parallel-machine scheduling to minimize total weighted completion times

A class of nonidentical parallel machine scheduling problems are considered in which the goal is to minimize the total weighted completion time. Models and relaxations are collected. Most of these problems are NP-hard, in the strong sense, or open problems, therefore approximation algorithms are studied. The review reveals that there exist some potential areas worthy of further research.

Grover quantum searching algorithm based on weighted targets

The current Grover quantum searching algorithm cannot identify the difference in importance of the search targets when it is applied to an unsorted quantum database, and the probability for each search target is equal. To solve this problem, a Grover searching algorithm based on weighted targets is proposed. First, each target is endowed a weight coefficient according to its importance. Applying these different weight coefficients, the targets are represented as quantum superposition states. Second, the novel Grover searching algorithm based on the quantum superposition of the weighted targets is constructed. Using this algorithm, the probability of getting each target can be approximated to the corresponding weight coefficient, which shows the flexibility of this algorithm. Finally, the validity of the algorithm is proved by a simple searching example.

Assessing Criteria Weights by the Symmetry Point of Criterion (Novel SPC Method)–Application in the Efficiency Evaluation of the Mineral Deposit Multi-Criteria Partitioning Algorithm

Information about the relative importance of each criterion or theweights of criteria can have a significant influence on the ultimate rank of alternatives.Accordingly,assessing the weights of criteria is a very important task in solving multi-criteria decision-making problems.Three methods are commonly used for assessing the weights of criteria:objective,subjective,and integrated methods.In this study,an objective approach is proposed to assess the weights of criteria,called SPCmethod(Symmetry Point of Criterion).This point enriches the criterion so that it is balanced and easy to implement in the process of the evaluation of its influence on decision-making.The SPC methodology is systematically presented and supported by detailed calculations related to an artificial example.To validate the developed method,we used our numerical example and calculated the weights of criteria by CRITIC,Entropy,Standard Deviation and MEREC methods.Comparative analysis between these methods and the SPC method reveals that the developedmethod is a very reliable objective way to determine the weights of criteria.Additionally,in this study,we proposed the application of SPCmethod to evaluate the efficiency of themulti-criteria partitioning algorithm.The main idea of the evaluation is based on the following fact:the greater the uniformity of the weights of criteria,the higher the efficiency of the partitioning algorithm.The research demonstrates that the SPC method can be applied to solving different multi-criteria problems.

Optimizing Polynomial-Time Solutions to a Network Weighted Vertex Cover Game

Weighted vertex cover(WVC)is one of the most important combinatorial optimization problems.In this paper,we provide a new game optimization to achieve efficiency and time of solutions for the WVC problem of weighted networks.We first model the WVC problem as a general game on weighted networks.Under the framework of a game,we newly define several cover states to describe the WVC problem.Moreover,we reveal the relationship among these cover states of the weighted network and the strict Nash equilibriums(SNEs)of the game.Then,we propose a game-based asynchronous algorithm(GAA),which can theoretically guarantee that all cover states of vertices converging in an SNE with polynomial time.Subsequently,we improve the GAA by adding 2-hop and 3-hop adjustment mechanisms,termed the improved game-based asynchronous algorithm(IGAA),in which we prove that it can obtain a better solution to the WVC problem than using a the GAA.Finally,numerical simulations demonstrate that the proposed IGAA can obtain a better approximate solution in promising computation time compared with the existing representative algorithms.

Identification of key genes underlying clinical features of hepatocellular carcinoma based on weighted gene co‑expression network analysis and bioinformatics analysis

Objective: To identify module genes that are closely related to clinical features of hepatocellular carcinoma (HCC) by weighted gene co‑expression network analysis, and to provide a reference for early clinical diagnosis and treatment. Methods: GSE84598 chip data were downloaded from the GEO database, and module genes closely related to the clinical features of HCC were extracted by comprehensive weighted gene co‑expression network analysis. Hub genes were identified through protein interaction network analysis by the maximum clique centrality (MCC) algorithm;Finally, the expression of hub genes was validated by TCGA database and the Kaplan Meier plotter online database was used to evaluate the prognostic relationship between hub genes and HCC patients. Results: By comparing the gene expression data between HCC tissue samples and normal liver tissue samples, a total of 6 262 differentially expressed genes were obtained, of which 2 207 were upregulated and 4 055 were downregulated. Weighted gene co‑expression network analysis was applied to identify 120 genes of key modules. By intersecting with the differentially expressed genes, 115 candidate hub genes were obtained. The results of enrichment analysis showed that the candidate hub genes were closely related to cell mitosis, p53 signaling pathway and so on. Further application of the MCC algorithm to the protein interaction network of 115 candidate hub genes identified five hub genes, namely NUF2, RRM2, UBE2C, CDC20 and MAD2L1. Validation of hub genes by TCGA database revealed that all five hub genes were significantly upregulated in HCC tissues compared to normal liver tissues;Moreover, survival analysis revealed that high expression of hub genes was closely associated with poor prognosis in HCC patients. Conclusions: This study identifies five hub genes by combining multiple databases, which may provide directions for the clinical diagnosis and treatment of HCC.

Photovoltaic Models Parameters Estimation Based on Weighted Mean of Vectors

Renewable energy sources are gaining popularity,particularly photovoltaic energy as a clean energy source.This is evident in the advancement of scientific research aimed at improving solar cell performance.Due to the non-linear nature of the photovoltaic cell,modeling solar cells and extracting their parameters is one of the most important challenges in this discipline.As a result,the use of optimization algorithms to solve this problem is expanding and evolving at a rapid rate.In this paper,a weIghted meaN oF vectOrs algorithm(INFO)that calculates the weighted mean for a set of vectors in the search space has been applied to estimate the parameters of solar cells in an efficient and precise way.In each generation,the INFO utilizes three operations to update the vectors’locations:updating rules,vector merging,and local search.The INFO is applied to estimate the parameters of static models such as single and double diodes,as well as dynamic models such as integral and fractional models.The outcomes of all applications are examined and compared to several recent algorithms.As well as the results are evaluated through statistical analysis.The results analyzed supported the proposed algorithm’s efficiency,accuracy,and durability when compared to recent optimization algorithms.

A Novel Symbolic Algorithm for Maximum Weighted Matching in Bipartite Graphs

The maximum weighted matching problem in bipartite graphs is one of the classic combinatorial optimization problems, and arises in many different applications. Ordered binary decision diagram (OBDD) or algebraic decision diagram (ADD) or variants thereof provides canonical forms to represent and manipulate Boolean functions and pseudo-Boolean functions efficiently. ADD and OBDD-based symbolic algorithms give improved results for large-scale combinatorial optimization problems by searching nodes and edges implicitly. We present novel symbolic ADD formulation and algorithm for maximum weighted matching in bipartite graphs. The symbolic algorithm implements the Hungarian algorithm in the context of ADD and OBDD formulation and manipulations. It begins by setting feasible labelings of nodes and then iterates through a sequence of phases. Each phase is divided into two stages. The first stage is building equality bipartite graphs, and the second one is finding maximum cardinality matching in equality bipartite graph. The second stage iterates through the following steps: greedily searching initial matching, building layered network, backward traversing node-disjoint augmenting paths, updating cardinality matching and building residual network. The symbolic algorithm does not require explicit enumeration of the nodes and edges, and therefore can handle many complex executions in each step. Simulation experiments indicate that symbolic algorithm is competitive with traditional algorithms.