A novel algorithm for source location by utilizing the time difference of arrival (TDOA) measurements of a signal received at spatially separated sensors is proposed. The algorithm is based on quadratic constraint tot...A novel algorithm for source location by utilizing the time difference of arrival (TDOA) measurements of a signal received at spatially separated sensors is proposed. The algorithm is based on quadratic constraint total least-squares (QC-TLS) method and gives an explicit solution. The total least-squares method is a generalized data fitting method that is appropriate for cases when the system model contains error or is not known exactly, and quadratic constraint, which could be realized via Lagrange multipliers technique, could constrain the solution to the location equations to improve location accuracy. Comparisons of performance with ordinary least-squares are made, and Monte Carlo simulations are performed. Simulation results indicate that the proposed algorithm has high location accuracy and achieves accuracy close to the Cramer-Rao lower bound (CRLB) near the small TDOA measurement error region.展开更多
The solution of the grey model(GM(1,1)model)generally involves equal-precision observations,and the(co)variance matrix is established from the prior information.However,the data are generally available with unequal-pr...The solution of the grey model(GM(1,1)model)generally involves equal-precision observations,and the(co)variance matrix is established from the prior information.However,the data are generally available with unequal-precision measurements in reality.To deal with the errors of all observations for GM(1,1)model with errors-in-variables(EIV)structure,we exploit the total least-squares(TLS)algorithm to estimate the parameters of GM(1,1)model in this paper.Ignoring that the effect of the improper prior stochastic model and the homologous observations may degrade the accuracy of parameter estimation,we further present a nonlinear total least-squares variance component estimation approach for GM(1,1)model,which resorts to the minimum norm quadratic unbiased estimation(MINQUE).The practical and simulative experiments indicate that the presented approach has significant merits in improving the predictive accuracy in comparison with control methods.展开更多
The numerical dispersion phenomenon in the finite-difference forward modeling simulations of the wave equation significantly affects the imaging accuracy in acoustic reflection logging.This issue is particularly prono...The numerical dispersion phenomenon in the finite-difference forward modeling simulations of the wave equation significantly affects the imaging accuracy in acoustic reflection logging.This issue is particularly pronounced in the reverse time migration(RTM)method used for shear-wave(S-wave)logging imaging.This not only affects imaging accuracy but also introduces ambiguities in the interpretation of logging results.To address this challenge,this study proposes the use of a least-squares difference coefficient optimization algorithm aiming to suppress the numerical dispersion phenomenon in the RTM of S-wave reflection imaging logging.By optimizing the difference coefficients,the high-precision finite-difference algorithm serves as an effective operator for both forward and backward RTM processes.This approach is instrumental in eliminating migration illusions,which are often caused by numerical dispersion.The effectiveness of this optimized algorithm is demonstrated through numerical results,which indicate that it can achieve more accurate forward imaging results across various conditions,including high-and low-velocity strata,and is effective in both large and small spatial grids.The results of processing real data demonstrate that numerical dispersion optimization effectively reduces migration artifacts and diminishes ambiguities in logging interpretations.This optimization offers crucial technical support to the RTM method,enhancing its capability for accurately modeling and imaging S-wave reflections.展开更多
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 obt...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.展开更多
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 ...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.展开更多
Unlike a traditional flowshop problem where a job is assumed to be indivisible, in the lot-streaming flowshop problem, a job is allowed to overlap its operations between successive machines by splitting it into a numb...Unlike a traditional flowshop problem where a job is assumed to be indivisible, in the lot-streaming flowshop problem, a job is allowed to overlap its operations between successive machines by splitting it into a number of smaller sub-lots and moving the completed portion of the sub-lots to downstream machine. In this way, the production is accelerated. This paper presents a discrete artificial bee colony （DABC） algorithm for a lot-streaming flowshop scheduling problem with total flowtime criterion. Unlike the basic ABC algorithm, the proposed DABC algorithm represents a solution as a discrete job permutation. An efficient initialization scheme based on the extended Nawaz-Enscore-Ham heuristic is utilized to produce an initial population with a certain level of quality and diversity. Employed and onlooker bees generate new solutions in their neighborhood, whereas scout bees generate new solutions by performing insert operator and swap operator to the best solution found so far. Moreover, a simple but effective local search is embedded in the algorithm to enhance local exploitation capability. A comparative experiment is carried out with the existing discrete particle swarm optimization, hybrid genetic algorithm, threshold accepting, simulated annealing and ant colony optimization algorithms based on a total of 160 randomly generated instances. The experimental results show that the proposed DABC algorithm is quite effective for the lot-streaming flowshop with total flowtime criterion in terms of searching quality, robustness and effectiveness. This research provides the references to the optimization research on lot-streaming flowshop.展开更多
A discrete artificial bee colony algorithm is proposed for solving the blocking flow shop scheduling problem with total flow time criterion. Firstly, the solution in the algorithm is represented as job permutation. Se...A discrete artificial bee colony algorithm is proposed for solving the blocking flow shop scheduling problem with total flow time criterion. Firstly, the solution in the algorithm is represented as job permutation. Secondly, an initialization scheme based on a variant of the NEH (Nawaz-Enscore-Ham) heuristic and a local search is designed to construct the initial population with both quality and diversity. Thirdly, based on the idea of iterated greedy algorithm, some newly designed schemes for employed bee, onlooker bee and scout bee are presented. The performance of the proposed algorithm is tested on the well-known Taillard benchmark set, and the computational results demonstrate the effectiveness of the discrete artificial bee colony algorithm. In addition, the best known solutions of the benchmark set are provided for the blocking flow shop scheduling problem with total flow time criterion.展开更多
This paper suggests a group of statistical algorithms for calculating the total absorption coefficients based on in situ data of apparent optical property and inherent optical property collected with strict quality as...This paper suggests a group of statistical algorithms for calculating the total absorption coefficients based on in situ data of apparent optical property and inherent optical property collected with strict quality assurance according to NASA ocean bio-optic protocols in the Yellow Sea and the East China Sea in spring 2003. The band-ratios ofRrs412/Rrs555, Rrs49o/Rrs555 are used in the algorithms to derive the total absorption coefficients （at） at 412, 440, 488, 510, 532 and 555nm bands, respectively. The average relative errors between inversed and measured values are less than 25.8%, with the correlative coefficients （R2） being 0.75-0.85. Error sensitivity analysis shows that the maximum retrieval error is less than 24.0% at ＋5% error in Rrs＇s. So the statistical algorithms of this paper are practicable. In this paper, the relations between the total absorption coefficients at 412, 488, 510, 532, 555 nm and that of 440nm are also studied. The results show that the relations between the total absorption coefficients of 400-600 nm and that of 440 nm are correlated well and all of their correlative coefficients R2 are greater than 0.99. Furthermore, a regression analysis is also done for the slope of the linear relations and wavelengths, and the R2 is also 0.99. Thus it is possible to retrieve other bands＇ total absorption coefficients with only one band absorption value, which significantly reduce the number of unknown parameters in studying other ocean color related problems.展开更多
We present a new algorithm for nesting problems.Many equally spaced points are set on a sheet,and a piece is moved to one of the points and rotated by an angle.Both the point and the rotation angle constitute the pack...We present a new algorithm for nesting problems.Many equally spaced points are set on a sheet,and a piece is moved to one of the points and rotated by an angle.Both the point and the rotation angle constitute the packing attitude of the piece.We propose a new algorithm named HAPE(Heuristic Algorithm based on the principle of minimum total Potential Energy) to find the optimal packing attitude at which the piece has the lowest center of gravity.In addition,a new technique for polygon overlap testing is proposed which avoids the time-consuming calculation of no-fit-polygon(NFP).The detailed implementation of HAPE is presented and two computational experiments are described.The first experiment is based on a real industrial problem and the second on 11 published benchmark problems.Using a hill-climbing(HC) search method,the proposed algorithm performs well in comparison with other published solutions.展开更多
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...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.展开更多
This paper develops a variational model for image noise removal using total curvature(TC), which is a high-order regularizer. The TC has the advantage of preserving image feature. Unfortunately, it also has the charac...This paper develops a variational model for image noise removal using total curvature(TC), which is a high-order regularizer. The TC has the advantage of preserving image feature. Unfortunately, it also has the characteristics of nonlinear, non-convex and non-smooth. Consequently, the numerical computation with the curvature regularization is difficult. In order to conquer the computation problem, the proposed model is transformed into an alternating optimization problem by importing auxiliary variables. Furthermore, based on alternating direction method of multipliers, we design a fast numerical approximation iterative scheme for proposed model. Finally, numerous experiments are implemented to indicate the advantages of the proposed model in image edge preserving, image contrast and corners preserving. Meanwhile, the high computational efficiency of the designed model is verified by comparing with traditional models, including the total variation(TV) and total Laplace(TL) model.展开更多
Ultra-high voltage(UHV)transmission lines are an important part of China’s power grid and are often surrounded by a complex electromagnetic environment.The ground total electric field is considered a main electromagn...Ultra-high voltage(UHV)transmission lines are an important part of China’s power grid and are often surrounded by a complex electromagnetic environment.The ground total electric field is considered a main electromagnetic environment indicator of UHV transmission lines and is currently employed for reliable long-term operation of the power grid.Yet,the accurate prediction of the ground total electric field remains a technical challenge.In this work,we collected the total electric field data from the Ningdong-Zhejiang±800 kV UHVDC transmission project,as of the Ling Shao line,and perform an outlier analysis of the total electric field data.We show that the Local Outlier Factor(LOF)elimination algorithm has a small average difference and overcomes the performance of Density-Based Spatial Clustering of Applications with Noise(DBSCAN)and Isolated Forest elimination algorithms.Moreover,the Stacking algorithm has been found to have superior prediction accuracy than a variety of similar prediction algorithms,including the traditional finite element.The low prediction error of the Stacking algorithm highlights the superior ability to accurately forecast the ground total electric field of UHVDC transmission lines.展开更多
Based on mirror-blocks, a totally coded algorithm （TCA） for switched-current （SI） network analysis in frequency domain is presented. The algorithm is simple, available, and suitable for any swltched-current networ...Based on mirror-blocks, a totally coded algorithm （TCA） for switched-current （SI） network analysis in frequency domain is presented. The algorithm is simple, available, and suitable for any swltched-current networks. A basis of analysis and design for switched-current networks via this algorithm is provided.展开更多
Multi-level inverters(MLIs)have become popular in different applications such as industrial power control systems and distributed generations.There are different forms of MLIs.The cascaded MLIs(CMLIs)have some special...Multi-level inverters(MLIs)have become popular in different applications such as industrial power control systems and distributed generations.There are different forms of MLIs.The cascaded MLIs(CMLIs)have some special advantages among them such as more different output voltage levels using the same number of components and higher power quality.In this paper,a 27-level inverter switching algorithm considering total harmonic distortion(THD)minimization is investigated.Switching angles of the inverter switches are achieved by minimizing a THD-based objective function.In order to minimize the THD-based objective function,the hyper-spherical search(HSS)algorithm,as a novel optimization algorithm,is improved and the results of improved HSS(IHSS)are compared with HSS algorithm and other five evolutionary algorithms to show the advantages of IHSS algorithm.展开更多
文摘A novel algorithm for source location by utilizing the time difference of arrival (TDOA) measurements of a signal received at spatially separated sensors is proposed. The algorithm is based on quadratic constraint total least-squares (QC-TLS) method and gives an explicit solution. The total least-squares method is a generalized data fitting method that is appropriate for cases when the system model contains error or is not known exactly, and quadratic constraint, which could be realized via Lagrange multipliers technique, could constrain the solution to the location equations to improve location accuracy. Comparisons of performance with ordinary least-squares are made, and Monte Carlo simulations are performed. Simulation results indicate that the proposed algorithm has high location accuracy and achieves accuracy close to the Cramer-Rao lower bound (CRLB) near the small TDOA measurement error region.
基金supported by the National Natural Science Foundation of China(No.41874001 and No.41664001)Support Program for Outstanding Youth Talents in Jiangxi Province(No.20162BCB23050)National Key Research and Development Program(No.2016YFB0501405)。
文摘The solution of the grey model(GM(1,1)model)generally involves equal-precision observations,and the(co)variance matrix is established from the prior information.However,the data are generally available with unequal-precision measurements in reality.To deal with the errors of all observations for GM(1,1)model with errors-in-variables(EIV)structure,we exploit the total least-squares(TLS)algorithm to estimate the parameters of GM(1,1)model in this paper.Ignoring that the effect of the improper prior stochastic model and the homologous observations may degrade the accuracy of parameter estimation,we further present a nonlinear total least-squares variance component estimation approach for GM(1,1)model,which resorts to the minimum norm quadratic unbiased estimation(MINQUE).The practical and simulative experiments indicate that the presented approach has significant merits in improving the predictive accuracy in comparison with control methods.
基金supported by Scientific Research and Technology Development Project of CNPC(2021DJ4002,2022DJ3908).
文摘The numerical dispersion phenomenon in the finite-difference forward modeling simulations of the wave equation significantly affects the imaging accuracy in acoustic reflection logging.This issue is particularly pronounced in the reverse time migration(RTM)method used for shear-wave(S-wave)logging imaging.This not only affects imaging accuracy but also introduces ambiguities in the interpretation of logging results.To address this challenge,this study proposes the use of a least-squares difference coefficient optimization algorithm aiming to suppress the numerical dispersion phenomenon in the RTM of S-wave reflection imaging logging.By optimizing the difference coefficients,the high-precision finite-difference algorithm serves as an effective operator for both forward and backward RTM processes.This approach is instrumental in eliminating migration illusions,which are often caused by numerical dispersion.The effectiveness of this optimized algorithm is demonstrated through numerical results,which indicate that it can achieve more accurate forward imaging results across various conditions,including high-and low-velocity strata,and is effective in both large and small spatial grids.The results of processing real data demonstrate that numerical dispersion optimization effectively reduces migration artifacts and diminishes ambiguities in logging interpretations.This optimization offers crucial technical support to the RTM method,enhancing its capability for accurately modeling and imaging S-wave reflections.
基金This project is supported by the National Natural Science Foundation of China
文摘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.
文摘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.
基金supported by National Natural Science Foundation of China (Grant Nos. 60973085, 61174187)National Hi-tech Research and Development Program of China (863 Program, Grant No. 2009AA044601)New Century Excellent Talents in University of China (Grant No. NCET-08-0232)
文摘Unlike a traditional flowshop problem where a job is assumed to be indivisible, in the lot-streaming flowshop problem, a job is allowed to overlap its operations between successive machines by splitting it into a number of smaller sub-lots and moving the completed portion of the sub-lots to downstream machine. In this way, the production is accelerated. This paper presents a discrete artificial bee colony （DABC） algorithm for a lot-streaming flowshop scheduling problem with total flowtime criterion. Unlike the basic ABC algorithm, the proposed DABC algorithm represents a solution as a discrete job permutation. An efficient initialization scheme based on the extended Nawaz-Enscore-Ham heuristic is utilized to produce an initial population with a certain level of quality and diversity. Employed and onlooker bees generate new solutions in their neighborhood, whereas scout bees generate new solutions by performing insert operator and swap operator to the best solution found so far. Moreover, a simple but effective local search is embedded in the algorithm to enhance local exploitation capability. A comparative experiment is carried out with the existing discrete particle swarm optimization, hybrid genetic algorithm, threshold accepting, simulated annealing and ant colony optimization algorithms based on a total of 160 randomly generated instances. The experimental results show that the proposed DABC algorithm is quite effective for the lot-streaming flowshop with total flowtime criterion in terms of searching quality, robustness and effectiveness. This research provides the references to the optimization research on lot-streaming flowshop.
基金Supported by the National Natural Science Foundation of China (61174040, 61104178)the Fundamental Research Funds for the Central Universities
文摘A discrete artificial bee colony algorithm is proposed for solving the blocking flow shop scheduling problem with total flow time criterion. Firstly, the solution in the algorithm is represented as job permutation. Secondly, an initialization scheme based on a variant of the NEH (Nawaz-Enscore-Ham) heuristic and a local search is designed to construct the initial population with both quality and diversity. Thirdly, based on the idea of iterated greedy algorithm, some newly designed schemes for employed bee, onlooker bee and scout bee are presented. The performance of the proposed algorithm is tested on the well-known Taillard benchmark set, and the computational results demonstrate the effectiveness of the discrete artificial bee colony algorithm. In addition, the best known solutions of the benchmark set are provided for the blocking flow shop scheduling problem with total flow time criterion.
基金Supported by the Subsystem of Calibration and Validation, HY-1 Ground Application System, National Satellite Ocean Application Ser-vice (NSOAS). China High-Tech "863" Project (Nos. 2001AA636010, 2002AA639160 and 2002AA639200). The Ocean Science Fund Sponsor Project for the Youth, State Oceanic Administration (No. 2005415). The Director’s Science and Technology Fund Sponsor Project for the Youth, NSOAS.
文摘This paper suggests a group of statistical algorithms for calculating the total absorption coefficients based on in situ data of apparent optical property and inherent optical property collected with strict quality assurance according to NASA ocean bio-optic protocols in the Yellow Sea and the East China Sea in spring 2003. The band-ratios ofRrs412/Rrs555, Rrs49o/Rrs555 are used in the algorithms to derive the total absorption coefficients （at） at 412, 440, 488, 510, 532 and 555nm bands, respectively. The average relative errors between inversed and measured values are less than 25.8%, with the correlative coefficients （R2） being 0.75-0.85. Error sensitivity analysis shows that the maximum retrieval error is less than 24.0% at ＋5% error in Rrs＇s. So the statistical algorithms of this paper are practicable. In this paper, the relations between the total absorption coefficients at 412, 488, 510, 532, 555 nm and that of 440nm are also studied. The results show that the relations between the total absorption coefficients of 400-600 nm and that of 440 nm are correlated well and all of their correlative coefficients R2 are greater than 0.99. Furthermore, a regression analysis is also done for the slope of the linear relations and wavelengths, and the R2 is also 0.99. Thus it is possible to retrieve other bands＇ total absorption coefficients with only one band absorption value, which significantly reduce the number of unknown parameters in studying other ocean color related problems.
文摘We present a new algorithm for nesting problems.Many equally spaced points are set on a sheet,and a piece is moved to one of the points and rotated by an angle.Both the point and the rotation angle constitute the packing attitude of the piece.We propose a new algorithm named HAPE(Heuristic Algorithm based on the principle of minimum total Potential Energy) to find the optimal packing attitude at which the piece has the lowest center of gravity.In addition,a new technique for polygon overlap testing is proposed which avoids the time-consuming calculation of no-fit-polygon(NFP).The detailed implementation of HAPE is presented and two computational experiments are described.The first experiment is based on a real industrial problem and the second on 11 published benchmark problems.Using a hill-climbing(HC) search method,the proposed algorithm performs well in comparison with other published solutions.
基金the National Natural Science Foundation of China (70631003)the Hefei University of Technology Foundation (071102F).
文摘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.
基金supported by the National Natural Science Foundation of China(No.61602269)the China Postdoctoral Science Foundation(No.2015M571993)+1 种基金the Shandong Provincial Natural Science Foundation of China(No.ZR2017MD004)the Qingdao Postdoctoral Application Research Funded Project
文摘This paper develops a variational model for image noise removal using total curvature(TC), which is a high-order regularizer. The TC has the advantage of preserving image feature. Unfortunately, it also has the characteristics of nonlinear, non-convex and non-smooth. Consequently, the numerical computation with the curvature regularization is difficult. In order to conquer the computation problem, the proposed model is transformed into an alternating optimization problem by importing auxiliary variables. Furthermore, based on alternating direction method of multipliers, we design a fast numerical approximation iterative scheme for proposed model. Finally, numerous experiments are implemented to indicate the advantages of the proposed model in image edge preserving, image contrast and corners preserving. Meanwhile, the high computational efficiency of the designed model is verified by comparing with traditional models, including the total variation(TV) and total Laplace(TL) model.
基金funded by a science and technology project of State Grid Corporation of China“Comparative Analysis of Long-Term Measurement and Prediction of the Ground Synthetic Electric Field of±800 kV DC Transmission Line”(GYW11201907738)Paulo R.F.Rocha acknowledges the support and funding from the European Research Council(ERC)under the European Union’s Horizon 2020 Research and Innovation Program(Grant Agreement No.947897).
文摘Ultra-high voltage(UHV)transmission lines are an important part of China’s power grid and are often surrounded by a complex electromagnetic environment.The ground total electric field is considered a main electromagnetic environment indicator of UHV transmission lines and is currently employed for reliable long-term operation of the power grid.Yet,the accurate prediction of the ground total electric field remains a technical challenge.In this work,we collected the total electric field data from the Ningdong-Zhejiang±800 kV UHVDC transmission project,as of the Ling Shao line,and perform an outlier analysis of the total electric field data.We show that the Local Outlier Factor(LOF)elimination algorithm has a small average difference and overcomes the performance of Density-Based Spatial Clustering of Applications with Noise(DBSCAN)and Isolated Forest elimination algorithms.Moreover,the Stacking algorithm has been found to have superior prediction accuracy than a variety of similar prediction algorithms,including the traditional finite element.The low prediction error of the Stacking algorithm highlights the superior ability to accurately forecast the ground total electric field of UHVDC transmission lines.
文摘Based on mirror-blocks, a totally coded algorithm （TCA） for switched-current （SI） network analysis in frequency domain is presented. The algorithm is simple, available, and suitable for any swltched-current networks. A basis of analysis and design for switched-current networks via this algorithm is provided.
文摘Multi-level inverters(MLIs)have become popular in different applications such as industrial power control systems and distributed generations.There are different forms of MLIs.The cascaded MLIs(CMLIs)have some special advantages among them such as more different output voltage levels using the same number of components and higher power quality.In this paper,a 27-level inverter switching algorithm considering total harmonic distortion(THD)minimization is investigated.Switching angles of the inverter switches are achieved by minimizing a THD-based objective function.In order to minimize the THD-based objective function,the hyper-spherical search(HSS)algorithm,as a novel optimization algorithm,is improved and the results of improved HSS(IHSS)are compared with HSS algorithm and other five evolutionary algorithms to show the advantages of IHSS algorithm.
