粒子群优化算法及其在股票市场预测优化问题中的应用
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摘要
本文主要介绍了近些年来新提出的优化算法——粒子群优化算法。该算法简洁、易实现、容易理解,不需要优化函数的梯度信息等优点。粒子群优化算法收敛快,特别是在算法的早期,但也存在着精度较低,易发散等缺点。算法受加权系数、加速系数和最大速度等参数影响比较大,若加权系数、加速系数和最大速度等参数太大,粒子群可能错过最优解,算法不收敛;而在收敛的情况下,由于所有的粒子都向最优解的方向飞去,所以粒子趋向同一化(失去了多样性),使得后期收敛速度明显变慢,同时算法收敛到一定精度时,无法继续优化,所能达到的精度也比遗传算法低,因此本文对粒子群优化算法作了改进,提出了分组粒子群优化算法。在分组粒子群优化算法中将粒子群分成几个小群,每个小群有不同的进化参数且每个小群分别进化,在间隔一定时刻进行组间变异和重组操作,并且在重组的同时对各小组参数进行粒子群优化,仿真结果显示相比标准粒子群优化算法无论在收敛速度还是在精度和操作方便性上都有提高。
因粒子群优化算法具有简洁、易实现、容易理解,不需要优化函数的梯度信息等优点,所以算法一经提出就被广泛应用。在2007年,Hassan和Nath提出了隐马尔科夫模型与神经网络、遗传算法的组合模型—AGHWA模型,并用于股票价格预测,预测结果表明这方法是可行的,但由于隐马尔科夫模型的矩阵运算加上遗传算法的编码与解码使得整个过程相当的复杂。鉴于粒子群优化算法的优点,本文提出了用粒子群优化算法来对这组合模型中的隐马尔科夫模型的初始参数进行了优化,并运用模型对股票价格进行了预测,仿真结果显示优化后的模型有比较好的性能。
This article mainly introduced recent year proposed newly the optimized algorithm, Particle Swarm Optimization. This algorithm succinct, easy to realize, the understand easily, does not need majorized function merits and gradient information and so on. PSO restrains quickly, specially in algorithm early time, but also has the precision to be low, easy to disperse and shortcomings and so on . If the celerating factor, maximum speed and so on are too big, particle swarm possibly misses the optimal solution, the algorithm does not restrain; But in restraining situation, because all particles fly to the optimal solution direction, The particles trend identical (has lost multiplicity), causes later period the convergence rate obviously to slow down, when simultaneously the algorithm restrains to certain precision, is unable to continue to optimize, can achieve lowerly precision also compared to Genetic Algorithm. Therefore this article has made the improvement to the particle swarm optimical algorithm, proposed a grouping grain of subgroup optimizes the algorithm. In a grouping grain of subgroup optimize algorithm , a grain of subgroup divide into several small groups, each small group will have the different evolution parameter, and each small group will evolve separately, In gap certain time carries on the group the variation and the reorganization operation, And carries on a grain of subgroup during reorganization to various groups parameter to optimize, The simulation result showed that compares the ordinary grain of subgroup algorithm, regardless of has the enhancement in the convergence rate in the perusal and in the operation conveniences.
Because this algorithm succinct, easy to realize, the understand easily, does not need majorized function merits and gradient information and so on., therefore the algorithm p widely is applied, In 2007, Hassan and Nath proposed Hidden Markovian model and the ANN algorithm, The Genetic Algorithm combination model - AGHWA model, and uses in the stock price forecasting, the discovery forecasting result is optimistic, but because The Hidden Markovian model matrix operation adds on The Genetic Algorithm the code and the decoding causes entire process suitable complex. In view of the fact that the PSO merit, this article proposed optimized the algorithm with a grain of subgroup to come to carry on the optimization to the hidden Markovian model initial parameter, and has carried on the forecast using the model to the stock price, The simulation result showed after optimizing the model has the quite good performance.
因粒子群优化算法具有简洁、易实现、容易理解,不需要优化函数的梯度信息等优点,所以算法一经提出就被广泛应用。在2007年,Hassan和Nath提出了隐马尔科夫模型与神经网络、遗传算法的组合模型—AGHWA模型,并用于股票价格预测,预测结果表明这方法是可行的,但由于隐马尔科夫模型的矩阵运算加上遗传算法的编码与解码使得整个过程相当的复杂。鉴于粒子群优化算法的优点,本文提出了用粒子群优化算法来对这组合模型中的隐马尔科夫模型的初始参数进行了优化,并运用模型对股票价格进行了预测,仿真结果显示优化后的模型有比较好的性能。
This article mainly introduced recent year proposed newly the optimized algorithm, Particle Swarm Optimization. This algorithm succinct, easy to realize, the understand easily, does not need majorized function merits and gradient information and so on. PSO restrains quickly, specially in algorithm early time, but also has the precision to be low, easy to disperse and shortcomings and so on . If the celerating factor, maximum speed and so on are too big, particle swarm possibly misses the optimal solution, the algorithm does not restrain; But in restraining situation, because all particles fly to the optimal solution direction, The particles trend identical (has lost multiplicity), causes later period the convergence rate obviously to slow down, when simultaneously the algorithm restrains to certain precision, is unable to continue to optimize, can achieve lowerly precision also compared to Genetic Algorithm. Therefore this article has made the improvement to the particle swarm optimical algorithm, proposed a grouping grain of subgroup optimizes the algorithm. In a grouping grain of subgroup optimize algorithm , a grain of subgroup divide into several small groups, each small group will have the different evolution parameter, and each small group will evolve separately, In gap certain time carries on the group the variation and the reorganization operation, And carries on a grain of subgroup during reorganization to various groups parameter to optimize, The simulation result showed that compares the ordinary grain of subgroup algorithm, regardless of has the enhancement in the convergence rate in the perusal and in the operation conveniences.
Because this algorithm succinct, easy to realize, the understand easily, does not need majorized function merits and gradient information and so on., therefore the algorithm p widely is applied, In 2007, Hassan and Nath proposed Hidden Markovian model and the ANN algorithm, The Genetic Algorithm combination model - AGHWA model, and uses in the stock price forecasting, the discovery forecasting result is optimistic, but because The Hidden Markovian model matrix operation adds on The Genetic Algorithm the code and the decoding causes entire process suitable complex. In view of the fact that the PSO merit, this article proposed optimized the algorithm with a grain of subgroup to come to carry on the optimization to the hidden Markovian model initial parameter, and has carried on the forecast using the model to the stock price, The simulation result showed after optimizing the model has the quite good performance.
引文
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[3] Yuhui Shi, Eberhart R. A modified particle swarm optimizer[A].Proceedings of IEEE International Conference on Evolutionary Computation [C]. Piscataway,NJ:IEEE Press ,1998. 69-73.
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[7] Cler M.The swarm and the queen:Towards a Deterministic and Adaptive Particle Swarm Optimization[c].In:Proc of the congress of Evolutionary Computation,1999:1951-1957.
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[10] Veeramachaneni K,PeramT,MohanCK,Osadciw LA(2003)Optimization using particle swarms with near neighbor interactions,Proceedings of genetic and evolutionary computation conference(GECCO),LNCS2723,Cyhicago,IL,pp 110-121.
[11]Ratnaweera A,Halgamuge SK,Watson HC(2004)Self-organising hierarchical particle swarm optimizer with time varying acceleration coefficients,IEEE Trans Evol Comput 8(3):240-255.
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[16]Brits R,Engelbrecht AP,van den Bergh F(2002) A niching particle swarm optimizer,In:Proceedings of the fourth Asia-Pacific conference on simulated evolution and learning.
[17]Lovbjerg M,Rasmussen TK,Krink T(2001)Hybrid particle swarm optimizer with breeding and subpopulations,In:Proceedings of the genetic and evolutionary computation conference(GECCO-2001).
[18]Krink T,Lovbjerg M(2002)The lifecycle model:combining particle swarm optimization,genetic algorithms and hillclimbers In:Proceedings of parallel problem solving from nature Ⅶ(PPSN 2002)Lecture notes in computer science (LNCS)no 2439,pp:621-630.
[19]高鹰,谢胜利.基于模拟退火的粒子群优化算法[J].计算机工程与应用,2004,40(1):47-50.
[20]高鹰,许若宁,李朝晖,等.基于聚类的多子群粒子群优化算法[J].计算机应用研 究,2006,23(4):40-41.
[21]高鹰,谢胜利.免疫粒子群优化算法[J].计算机工程与应用,2004,40(6):4-7.
[22]高鹰,谢胜利.混沌粒子群优化算法[J].计算机科学,2004,31(8):12-15.
[23]高鹰,姚振坚,谢胜利.基于种群密度的多粒子群优化算法[J].系统工程与电子技术,2006,28(6):922-924.
[24]高鹰,谢胜利.一种自适应扩展粒子群优化算法[J].计算机工程与应用,2006(15):12-15.
[25]ChatterjeeA,SiarryP.Nonlinear inertiaweightvariation fordynamic adaptation in particle swarm optimization[J].Computers& OperationsResearch,2006(33):859-871.
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[34]李晓磊一种新型的智能优化方法—人工鱼群算法杭州:浙江大学博士学位论文,2003.
[35]任斌,丰镇平改进遗传算法与粒子群优化算法及其对比分析 南京师范大学学报(工程技术版),2002,2(2):14-20.
[36]刘国平,曾强,多目标最优化的粒子群优化算法 杭州师范学院学报自然科学版,2005,4(1):30-33.
[37]李晓磊,邵之江,钱积新一种基于动物自治体的寻优模式:鱼群算法 系统工程理论与实践,2002,(11):32-38.
[38]李晓磊,钱积新基于分解协调的人工鱼群优化算法研究 电路与系统学报,2003,8(1):1-6.
[39]Ozcan,E.and Mohan,C.K.Parricle Swarm Optimization:surfing the waves.Proceedings of theIEEE Congress on Evolutionary Computation,Picataway,NJ,1999,1939-1944.
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