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.

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.

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.

AN ASSESSMENT OF THE MESHLESS WEIGHTED LEAST-SQUARE METHOD

The meshless weighted least-square (MWLS) method was developed based on the weighted least-square method. The method possesses several advantages, such as high accuracy, high stability and high e?ciency. Moreover, the coe?cient matrix obtained is symmetric and semi- positive de?nite. In this paper, the method is further examined critically. The e?ects of several parameters on the results of MWLS are investigated systematically by using a cantilever beam and an in?nite plate with a central circular hole. The numerical results are compared with those obtained by using the collocation-based meshless method (CBMM) and Galerkin-based meshless method (GBMM). The investigated parameters include the type of approximations, the type of weight functions, the number of neighbors of an evaluation point, as well as the manner in which the neighbors of an evaluation point are determined. This study shows that the displacement accuracy and convergence rate obtained by MWLS is comparable to that of the GBMM while the stress accuracy and convergence rate yielded by MWLS is even higher than that of GBMM. Furthermore, MWLS is much more e?cient than GBMM. This study also shows that the instability of CBMM is mainly due to the neglect of the equi- librium residuals at boundary nodes. In MWLS, the residuals of all the governing equations are minimized in a weighted least-square sense.

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.

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.

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.

PCR ALGORITHM FOR PARALLEL COMPUTING MINIMUM-NORM LEAST-SQUARES SOLUTION OF INCONSISTENT LINEAR EQUATIONS

This paper presents a new highly parallel algorithm for computing the minimum-norm least-squares solution of inconsistent linear equations Ax = b(A∈Rm×n,b∈R (A)). By this algorithm the solution x = A + b is obtained in T = n(log2m + log2(n - r + 1) + 5) + log2m + 1 steps with P=mn processors when m × 2(n - 1) and with P = 2n(n - 1) processors otherwise.

NEW EFFICIENT ORDER-RECURSIVE LEAST-SQUARES ALGORITHMS

Order-recursive least-squares(ORLS)algorithms are applied to the prob-lems of estimation and identification of FIR or ARMA system parameters where a fixedset of input signal samples is available and the desired order of the underlying model isunknown.On the basis of several universal formulae for updating nonsymmetric projec-tion operators,this paper presents three kinds of LS algorithms,called nonsymmetric,symmetric and square root normalized fast ORLS algorithms,respectively.As to the au-thors’ knowledge,the first and the third have not been so far provided,and the second isone of those which have the lowest computational requirement.Several simplified versionsof the algorithms are also considered.

Prediction-Based Distance Weighted Algorithm for Target Tracking in Binary Sensor Network

Binary sensor network(BSN) are becoming more attractive due to the low cost deployment,small size,low energy consumption and simple operation.There are two different ways for target tracking in BSN,the weighted algorithms and particle filtering algorithm.The weighted algorithms have good realtime property,however have poor estimation property and some of them does not suit for target’s variable velocity model.The particle filtering algorithm can estimate target's position more accurately with poor realtime property and is not suitable for target’s constant velocity model.In this paper distance weight is adopted to estimate the target’s position,which is different from the existing distance weight in other papers.On the analysis of principle of distance weight (DW),prediction-based distance weighted(PDW) algorithm for target tracking in BSN is proposed.Simulation results proved PDW fits for target's constant and variable velocity models with accurate estimation and good realtime property.

A new PQ disturbances identification method based on combining neural network with least square weighted fusion algorithm

A new method for power quality (PQ) disturbances identification is brought forward based on combining a neural network with least square (LS) weighted fusion algorithm. The characteristic components of PQ disturbances are distilled through an improved phase-located loop (PLL) system at first, and then five child BP ANNs with different structures are trained and adopted to identify the PQ disturbances respectively. The combining neural network fuses the identification results of these child ANNs with LS weighted fusion algorithm, and identifies PQ disturbances with the fused result finally. Compared with a single neural network, the combining one with LS weighted fusion algorithm can identify the PQ disturbances correctly when noise is strong. However, a single neural network may fail in this case. Furthermore, the combining neural network is more reliable than a single neural network. The simulation results prove the conclusions above.

A Full-Newton Step Feasible Interior-Point Algorithm for the Special Weighted Linear Complementarity Problems Based on a Kernel Function

In this paper,a new full-Newton step primal-dual interior-point algorithm for solving the special weighted linear complementarity problem is designed and analyzed.The algorithm employs a kernel function with a linear growth term to derive the search direction,and by introducing new technical results and selecting suitable parameters,we prove that the iteration bound of the algorithm is as good as best-known polynomial complexity of interior-point methods.Furthermore,numerical results illustrate the efficiency of the proposed method.

Prediction of earth rotation parameters based on improved weighted least squares and autoregressive model

In this paper, an improved weighted least squares （WLS）, together with autoregressive （AR） model, is proposed to improve prediction accuracy of earth rotation parameters（ERP）. Four weighting schemes are developed and the optimal power e for determination of the weight elements is studied. The results show that the improved WLS-AR model can improve the ERP prediction accuracy effectively, and for different prediction intervals of ERP, different weight scheme should be chosen.

Fault Diagnosis Model Based on Fuzzy Support Vector Machine Combined with Weighted Fuzzy Clustering

A fault diagnosis model is proposed based on fuzzy support vector machine (FSVM) combined with fuzzy clustering (FC).Considering the relationship between the sample point and non-self class,FC algorithm is applied to generate fuzzy memberships.In the algorithm,sample weights based on a distribution density function of data point and genetic algorithm (GA) are introduced to enhance the performance of FC.Then a multi-class FSVM with radial basis function kernel is established according to directed acyclic graph algorithm,the penalty factor and kernel parameter of which are optimized by GA.Finally,the model is executed for multi-class fault diagnosis of rolling element bearings.The results show that the presented model achieves high performances both in identifying fault types and fault degrees.The performance comparisons of the presented model with SVM and distance-based FSVM for noisy case demonstrate the capacity of dealing with noise and generalization.