利用粒子滤波方法求解数据包络分析问题

doi:10.11896/jsjkx.210600110

摘要/Abstract

摘要： 数据包络分析法是一种对多投入/多产出的决策单元的生产效率进行评价的方法。数据包络分析方法被广泛应用于各个领域的效率分析问题,然而目前用于求解数据包络分析问题的方法主要是利用一些专业化的软件进行求解,整体过程专业化要求程度高。为了能够方便地求解数据包络分析问题,利用优化的思想求解数据包络分析问题。针对数据包络分析问题的优化求解,提出了一种基于粒子滤波的优化方法。系统地介绍了粒子滤波方法的基本原理,然后将优化问题转化粒子滤波的状态估计问题,从而利用粒子滤波的基本原理求解数据包络分析的优化问题,以得到一个全局最优解。最后,通过仿真实例验证了所提方法的有效性。实验结果表明,基于粒子滤波的优化方法能够准确、有效地解决数据包络分析的问题。

关键词: 粒子滤波, 滤波问题, 数据包络分析, 线性规划, 优化算法, 优化问题

Abstract: Data envelopment analysis is a method to evaluate the production efficiency of multi-input&multi-output decision ma-king units.The data envelopment analysis method is widely used to solve efficiency analysis problems in various fields.However,the current methods for solving data envelopment analysis problems mainly use some specialized software to solve the problem,and the entire process requires a high specialization.In order to solve the data envelopment analysis problem conveniently,the optimization philosophy is used to solve the data envelopment analysis problem.In this paper,an optimization method based on particle filter is proposed for solving the data envelopment analysis problem.Firstly,the basic principles of the particle filter method are systematically interpreted.Then the optimization problem of the data envelopment analysis is transformed into the minimum variance estimate problem of particle filter.Therefore,the basic principles of particle filter can be used to solve the optimization problem of data envelopment analysis to obtain a global optimal solution.Finally,several simulation examples are conducted to verify the effectiveness of the proposed method.The simulation results show that the optimization method based on particle filter can accurately and effectively solve the problem of data envelopment analysis.

Key words: Data envelopment analysis, Filtering problem, Linear programming, Optimization algorithm, Optimization problems, Particle filter

中图分类号:

TP391

黄国兴, 杨泽铭, 卢为党, 彭宏, 王静文. 利用粒子滤波方法求解数据包络分析问题[J]. 计算机科学, 2022, 49(6A): 159-164. https://doi.org/10.11896/jsjkx.210600110

HUANG Guo-xing, YANG Ze-ming, LU Wei-dang, PENG Hong, WANG Jing-wen. Solve Data Envelopment Analysis Problems with Particle Filter[J]. Computer Science, 2022, 49(6A): 159-164. https://doi.org/10.11896/jsjkx.210600110

参考文献

[1] YANG G L,LIU W B,ZHENG H J.Overview of Data Envelopment Analysis(DEA)[J].China Journal of Information systems,2013,28(6):840-860.
[2] WANG Y.Study on the impact of stock issuance system to IPO pricing efficiency [D].Shenyang:Northeastern University,2010.
[3] DUAN Y R,JING Y F,LI G P.Chinese Commercial Bank Efficiency Evaluation Based on Two-stage DEA[J].Operations Research and Management Science,2019,28(2):118-125.
[4] XU J J,WANG L N,JIN C L.Research and Review of Analysis on Economic Operation of Hospitals[J].Chinese Health Service Management,2018,35(12):894-896,899.
[5] GENG H,SHI E P,WANG L Z,et al.Evaluation of the Development Efficiency of Small Towns around Metropolis Based on GIS-DEA:Taking Wuhan as an Example[J].Economic Geography,2018,38(10):72-79.
[6] LI M N,WANG W S.Dynamic Evolution Trend of Regional Innovation Efficiency of High-tech Industry in China[J].Science and Technology Management Research,2019,39(1):1-11.
[7] GUO Q E,WANG X Q,WEI Z.Fuzzy comprehensive evaluation based on cross-evaluation and its application[J].Control and Decision,2012,27(4):575-578,583.
[8] GONG B G,ZHANG X Q,GUO D D.Method for hybrid multiple attribute decision-making based on Dempster-Shafer theory and cross efficiency of DEA[J].Control and Decision,2016,31(5):943-948.
[9] LU K,NIE C L.Application of Data Envelopment Analysis in Analysis of Maintenance Support Efficiency[J].Modern Defense Technology,2017,45(1):167-172.
[10] ZHAO Q,LI C.Two-stage Multi-swarm Particle Swarm Optimizer for Unconstrained and Constrained Global Optimization[J].IEEE Access,2020,8:124905-124927.
[11] KHAN S U,YANG S,WANG L,et al.A Modified Particle Swarm Optimization Algorithm for Global Optimizations of Inverse Problems[J].IEEE Transactions on Magnetics,2016,52(3):1-4.
[12] JIE X,WANG W Q,SHAO H Z,et al.Frequency Diverse Array Transmit Beampattern Optimization With Genetic Algorithm[J].IEEE Antennas and Wireless Propagation Letters,2016,16:469-472.
[13] YUAN Y,WANG G.Self-Adaptive Genetic Algorithm forBucket Wheel Reclaimer Real-Parameter Optimization[J].IEEE Access,2019,7:47762-47768.
[14] HAN X,DONG Y,YUE L,et al.State Transition SimulatedAnnealing Algorithm for Discrete-Continuous Optimization Problems[J].IEEE Access,2019,7:44391-44403.
[15] QIN L,WANG J,LI H,et al.An Approach to Improve the Performance of Simulated Annealing Algorithm utilizing the Variable Universe Adaptive Fuzzy Logic System[J].IEEE Access,2017,5:18155-18165.
[16] WANG F,ZHANG J,LIN B,et al.Two Stage Particle Filter for Nonlinear Bayesian Estimation[J].IEEE Access,2018,6:13803-13809.
[17] AMOR N,KAHLAOUI S,CHEBBI S.Unscented particle filter using studentt distribution with non-Gaussian measurement noise[C]//International Conference on Advanced Systems and Electric Technologies(IC_ASET).2018:34-38.
[18] XIE W,WANG L,BAI B,et al.An Improved Algorithm Based on Particle Filter for 3D UAV Target Tracking[C]//2019 IEEE International Conference on Communications(ICC 2019).2019:1-6.
[19] SANTOS N P,LOBO V,BERNARDINO A.Particle filteringbased optimization applied to 3D model-based estimation for UAV pose estimation[C]//OCEANS 2017.Aberdeen,2017:1-10.
[20] TEULIERE C,MARCHAND E,ECK L.3-D model-basedtracking for UAV indoor localization[J].IEEE Transactions on Cybernetics,2015,45(5):869-879.
[21] BO W,LI Y,DENG Z,et al.A Particle Filter-Based Matching Algorithm With Gravity Sample Vector for Underwater Gravity Aided Navigation[J].IEEE/ASME Transactions on Mechatronics,2016,21(3):1399-1408.
[22] ZHANG T,XU C,YANG M.Learning Multi-Task Correlation Particle Filters for Visual Tracking[J].IEEE Transactions on Pattern Analysis and Machine Intelligence,2019,41(2):365-378.
[23] ZHANG T,SI L,XU C,et al.Correlation Particle Filter for Visual Tracking[J].IEEE Trans Image Process,2018,27(99):2676-2687.
[24] LI T,BOLIC M,DJURIC P M.Resampling Methods for Particle Filtering:Classification,implementation,and strategies[J].Signal Processing Magazine IEEE,2015,32(3):70-86.
[25] LAMBERTI R,PETETIN Y,DESBOUVRIES F,et al.Inde-pendent resampling sequential Monte Carlo algorithms[J].IEEE Transactions on Signal Processing,2017,65(20):5318-5333.
[26] ZHU S C.Management Science Research Method[M].Beijing:Tsinghua University Press,2007:196-204.
[27] LIU J J,JIANG C Z.Research of Evaluating Port Competitiveness Model[J].Journal of Transportation Engineering and Information,2012,10(4):99-104.

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