粒子群优化算法及其在非线性回归模型中的应用研究
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摘要
粒子群优化算法采用实数编码、设置参数少、收敛速度快、算法高度并行,已成为计算智能领域的新研究热点,目前在函数优化、过程控制等复杂领域中得到了广泛的应用。但是粒子群优化算法同其它演化算法一样,存在易于陷入局部最优、收敛精度低等缺点。
本文针对标准粒子群优化算法易陷入局部最优、收敛精度低的缺点,结合极值优化算法具有波动性的典型特征,提出了嵌入极值优化的混合粒子群优化算法(EPSO算法)。运用Matlab7.0对15个无约束标准测试问题进行数值实验仿真。结果表明,本文提出的混合算法能有效实现全局寻优,尤其是对于求解高维多峰连续优化问题,它的优势更突出。
接着遵循约束优化算法=约束处理技术+进化算法的思想框架,采用增广Lagrange乘子法作为约束处理技术,将约束优化问题转化为无约束优化问题,从而将本文提出的混合算法扩展应用于处理约束优化问题。运用Matlab7.0对13个约束标准测试问题进行数值实验仿真。结果表明,本文的新方法能以较小的种群规模和较少的迭代次数实现全局寻优,取得了满意的优化结果。
最后利用非线性回归模型的参数估计实质上是求解残差平方和为最小的无约束优化问题的特点,将EPSO算法用于求解非线性回归模型的参数估计问题。通过对两个典型算例的仿真实验结果进行分析,可知EPSO算法实现方便、操作简单,它为求解非线性回归问题模型的参数估计问题提供了一种有效的途径。
Particle Swarm Optimization (PSO) is characterized by real number coding, fewer parameters, fast convergence and highly parallell. This algorithm has become a new hotspot in computation intelligence field and has been widely used in comples domains, such as function optimizaiton problems, process control. However, PSO algoritnm has the problems which exist in other evolutionary algorithms, for instance, relapsing into local optimization easily and low accuracy computationin.
To overcome the limitation of falling into local optimum easily and low accuracy computationin in PSO algorithm, this paper makes full use of the fluctuations ensue of extreme optimization and proposes a novel hybrid algorithm (EPSO algorithm), through introducing extremal optimization into PSO algorithm. For unconstrained problems, numerical simulation experiments on the fifteen benchmark functions are made by Matlab7.0. Simulation results show that the hybrid method is an effective way to locate global optima, and the hybrid algorithm shows more prominent for solving high-dimensional peak continuous optimization problems than unimodal benchmark functions.
Secondly, the conceptual framework of constrained optimization algorithm equals to constraint processing technology and evolutionary algorithm is followed, we adopt augmented Lagrange multiplier method as a constraint handling technique, and the proposed hybrid algorithm is extended to handle constrained optimization problems. We testify the performance of the proposed algorithm on thirteen benchmark functions based on Matlab7.0. The results show that the novel method has achieved satisfactory results by smaller polulation size and less iteration.
Finally, EPSO algorithm is used to solve the parameter estimation problem of nonlinear regression model through taking advantage of its essence is minimum squares critertion. Experimental results on two typical examples are truned out to be EPSO algorithm is convenient and easy to implement. EPSO algorithm is an efficient way to solve parameter estimation problem of nonlinear regression model.
本文针对标准粒子群优化算法易陷入局部最优、收敛精度低的缺点,结合极值优化算法具有波动性的典型特征,提出了嵌入极值优化的混合粒子群优化算法(EPSO算法)。运用Matlab7.0对15个无约束标准测试问题进行数值实验仿真。结果表明,本文提出的混合算法能有效实现全局寻优,尤其是对于求解高维多峰连续优化问题,它的优势更突出。
接着遵循约束优化算法=约束处理技术+进化算法的思想框架,采用增广Lagrange乘子法作为约束处理技术,将约束优化问题转化为无约束优化问题,从而将本文提出的混合算法扩展应用于处理约束优化问题。运用Matlab7.0对13个约束标准测试问题进行数值实验仿真。结果表明,本文的新方法能以较小的种群规模和较少的迭代次数实现全局寻优,取得了满意的优化结果。
最后利用非线性回归模型的参数估计实质上是求解残差平方和为最小的无约束优化问题的特点,将EPSO算法用于求解非线性回归模型的参数估计问题。通过对两个典型算例的仿真实验结果进行分析,可知EPSO算法实现方便、操作简单,它为求解非线性回归问题模型的参数估计问题提供了一种有效的途径。
Particle Swarm Optimization (PSO) is characterized by real number coding, fewer parameters, fast convergence and highly parallell. This algorithm has become a new hotspot in computation intelligence field and has been widely used in comples domains, such as function optimizaiton problems, process control. However, PSO algoritnm has the problems which exist in other evolutionary algorithms, for instance, relapsing into local optimization easily and low accuracy computationin.
To overcome the limitation of falling into local optimum easily and low accuracy computationin in PSO algorithm, this paper makes full use of the fluctuations ensue of extreme optimization and proposes a novel hybrid algorithm (EPSO algorithm), through introducing extremal optimization into PSO algorithm. For unconstrained problems, numerical simulation experiments on the fifteen benchmark functions are made by Matlab7.0. Simulation results show that the hybrid method is an effective way to locate global optima, and the hybrid algorithm shows more prominent for solving high-dimensional peak continuous optimization problems than unimodal benchmark functions.
Secondly, the conceptual framework of constrained optimization algorithm equals to constraint processing technology and evolutionary algorithm is followed, we adopt augmented Lagrange multiplier method as a constraint handling technique, and the proposed hybrid algorithm is extended to handle constrained optimization problems. We testify the performance of the proposed algorithm on thirteen benchmark functions based on Matlab7.0. The results show that the novel method has achieved satisfactory results by smaller polulation size and less iteration.
Finally, EPSO algorithm is used to solve the parameter estimation problem of nonlinear regression model through taking advantage of its essence is minimum squares critertion. Experimental results on two typical examples are truned out to be EPSO algorithm is convenient and easy to implement. EPSO algorithm is an efficient way to solve parameter estimation problem of nonlinear regression model.
引文
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[3]Colomi A, Dorigo M, Maniezzo V. Distributied Optimization by Ant Colonies. Proceedings of the First European Conference on Artificial Life. Paris, France, 1991
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[5]Heppner F, Grenander U. A Stochastic Nonlinear Model for Coordinated Bird Flocks. Washington, USA:American Association for the Advancement of Science, 1990:233-238
[6]Kennedy J, Eberhart R C, Shi Yuhui. Swarm Intelligence. San Francisco, USA: Morgan Kaufmann Publishers,2001
[7]Riccardo P. Analysis of the Publications on the Applications of Particle Swarm Optimization. Colchester:Hindawi Publishing Corperation,2008
[8]Clerc M. and Kennedy J. The Particle Swarm:Explosion, Stability and Convege-nce in a Multi-dimensional Complex Space. IEEE Transaction on Evolutionary Computation,2002,6(1):58-73
[9]Trelea I C. The Particle Swarm Optimization Algorithm:Convergence Analysis and Parameter Selection. Information Processing Letters,2003,85(6):317-325
[10]Ozcan E, Mohan C. Particle Swarm Optimization:Surfing the Waves. Proceeding of the Congress on Evolutionary Computation, Washington DC,1999:1939-1944
[11]Jie CHEN, Feng PAN, Tao CAI, Xuyan Tu. Stability Analysis of Particle Swarm Optimization without Lipschitz Condition Constrain. Journal of Control Theory and Applications,2003,1(1):86-90
[12]Kadirkamanathan V, Selvarajah K, Fleming P J. Stability Analysis of the Particle Dynamics in Particle Swarm Optimization. IEEE Transactions on Evolutionary Computation,2006,10(3):245-255
[13]金欣磊,马龙华,吴铁军,钱积新.基于随机过程的PSO收敛性分析.自动化学报,2007,33(12)：1263-1268
[14]P N Suganthan. Particle Swarm Optimization with Neighbourhood Operator. Proceedings of the 1999 Congress on Evolutionary Computation. Piscataway, NJ, IEEE Service Center,1999:158-1962
[15]Lovberg M, Krink T. Extending Particle Swarms with Self-organized Critiality. Proceedings of the Fourth Congress on Evolutionary Computation, Honolulu, HI USA,2002:1588-1593
[16]Xie X F, Zhang W J, Yang Z L. A Dissipative Particle Swarm Optimization. Proceedings of the IEEE Congress on Evolutionary Computation, Honolulu, HIUSA,2002:1456-1461
[17]李士勇,陈永强,李研.蚁群算法及其应用.哈尔滨：哈尔滨工业大学出版社,2004
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[19]Lope H S. Coello L S. Particle Swarm Optimization with Fast Local Search for the Blind Traveling Salesman Problem. Fifth International Conference on Hybrid Intelligent Systems,2005:245-250
[20]Jin-Gao J. Bo-Shian L. Kuo-Chih C. Automatic Landing Control using Particle Swarm Optimization. IEEE International Conference on Mechatrinics,2005: 721-726
[21]Coello C. A, Pulido G. T and Lechuga M. S. Handling Multiple Objectives with Particle Swarm Optimization. IEEE Transcations on Evolutionary Computation, 2004,8(3):256-279
[22]Kassabalidis I. N, El-Sharkawi M. A and Marks R. J. Dynamic Security Border Identification Using Enhanced Particle Swarm Optimization. IEEE Transcations on Power Systems,2002,17(3):723-729
[23]Boettcher S, Percus A G. Extremal Optimization:Methods Devised from Coevolution. Proceedings of the Genetic and Evolutionary Computation Conference San Francisco:Morgan Kaufmann,1999:825-832
[24]Boettcher S A, Percus A G. Extremal Optimization at the Phase Transition of the 3-coloring Problem. Physical Review,2004,69(62):1-8
[25]Sousa F L, Vlassov V, Ramos F M. Generalized Extremal Optimization for Solving Complex Optimal Design Problems. Lecture Notes in Computer Science, 2003,27 (6):375-376
[26]Meshoul S, Batouche M. Combining Extremal Optimization with Singular Value Decomposition for Effective Point Matching. Pattern Recongnition and Artificial Intelligence,2003,17(7):1111-1116
[27]Sousa F L, Ramos F M, Paglione P. Mew Stochastic Algorithm for Design Optimization. Artificial Intelligence,2003,41(9):1808-1818
[28]Courant R. Variational Methods for the Solution of Problems of Equilibrium and Vibrations, Bull. America Math,1943,49:1-23
[29]FiaccoA. V. and McCormick G. P. Computational Algorithm for the Sequential Unconstrained Minimization Technique for Nonlinear Programming, Management Science,1964,10:601-617
[30]FiaccoA. V. and McCormick G. P. The Sequential Unconstrained Minimization Technique (SUMT) without Parameters, Operations Research,1967,15:820-827
[31]Camp G. D. Inequality-constrained Stationary Value Problems,1995,3:548-550
[32]Pietrzykowski T. An Exact Potential Method for Constrained Maxima, SIAM J, 1969,6:269-304
[33]Zangwill W. L. Nonlinear Programming via Penealty Functions, Management Science,1967,13:344-358
[34]Hestenes M R. Multiplier and Gradient Methods. Journal of Optimization Theory and Application,1969,4(5):303-320
[35]Powell M J D. Optimization. London:Academic Press,1969
[36]Shi Y, Eberhart R. A Modified Particle Swarm Optimizer. IEEE International Conference on on Evolutionary Computation. Piscataway, NJ, IEEE Service Center,1998:69-73
[37]Shi Y, Eberhart R. Empirical Study of Particle Swarm Optimization. Proceedings of the 1999 Congress on Evolutionary Computation,1999:1945-1950
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