自适应简化粒子群优化算法及其应用
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摘要
针对粒子群优化算法(Particle Swarm Optimization,PSO)寻优速度慢、收敛精度不高且搜索结果波动性较大的缺点,提出了一种自适应简化粒子群优化算法(Self-Adjusted Simplified Particle Swarm Optimization,SASPSO)。在每次迭代过程中,粒子只受全局最优解影响,且加入按一定规律分布的锁定因子,令粒子受影响的程度有规律性。同时,利用锁定因子和当前粒子位置令惯性权重自适应配置,更有效地利用惯性权重对粒子群优化算法的影响。引入4种近期提出的改进粒子群算法同时搜索不同维度时的18个基准函数,与SASPSO的搜索结果对比,并使用T-test进行差异性分析。为了进一步分析算法性能,统计5个改进算法搜索100维函数达到期望值时的成功率与平均迭代次数。实验结果证明,SASPSO在无约束问题寻优中的收敛速度、寻优精度有了明显提升,且搜索结果异常值较少,波动性弱。将SASPSO应用于机床主轴结构参数优化问题,结果显示SASPSO优化性能更好。
In order to overcome the disadvantages of slow search speed, low convergence accuracy and high search volatility of particle swarm optimization, a Self-Adjusted Simplified Particle Swarm Optimization(SASPSO)algorithm has been proposed. During the evolutionary process, the particles are only affected by the global optima, and the locking factor distributed according to a certain rule is added so that the degree of influence of the particles can be traced. At the same time, the inertia weight is adaptively adjusted by using the locking factor and the current particle position, which makes the influence of inertia weight on the particle swarm optimization algorithm more effective. Four improved particle swarm algorithms proposed recently are introduced to simultaneously search for eighteen benchmark functions with different dimensions. The results are compared and T-test is used to analyze their differences. The success rates and the average iteration times are recorded when five improved algorithms search for 100-dimensional functions, which is beneficial for analyzing the performance of the proposed algorithm. Experimental results show that the convergence speed and optimization accuracy of SASPSO have been improved significantly, and the search results have lower objective function values and smaller standard deviations. The SASPSO is applied to the optimum design of machine-tool spindle parameters. The results show that the SASPSO optimization performance is better.
In order to overcome the disadvantages of slow search speed, low convergence accuracy and high search volatility of particle swarm optimization, a Self-Adjusted Simplified Particle Swarm Optimization(SASPSO)algorithm has been proposed. During the evolutionary process, the particles are only affected by the global optima, and the locking factor distributed according to a certain rule is added so that the degree of influence of the particles can be traced. At the same time, the inertia weight is adaptively adjusted by using the locking factor and the current particle position, which makes the influence of inertia weight on the particle swarm optimization algorithm more effective. Four improved particle swarm algorithms proposed recently are introduced to simultaneously search for eighteen benchmark functions with different dimensions. The results are compared and T-test is used to analyze their differences. The success rates and the average iteration times are recorded when five improved algorithms search for 100-dimensional functions, which is beneficial for analyzing the performance of the proposed algorithm. Experimental results show that the convergence speed and optimization accuracy of SASPSO have been improved significantly, and the search results have lower objective function values and smaller standard deviations. The SASPSO is applied to the optimum design of machine-tool spindle parameters. The results show that the SASPSO optimization performance is better.
引文
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[2]Shi Y,Eberhart R C.Empirical study of particle swarm optimization[C]//Proceedings of the 1999 Congress on Evolutionary Computation.Piscataway,NJ:IEEE Service Center,1999:1945-1950.
[3]Storn R.Differential evolution design of an IIR-filter[C]//Proceedings of 1996 IEEE International Conference on Evolutionary Computation.Piscataway,NJ:IEEE Press,1996:268-273.
[4]Colorni A,Dorigo M,Maniezzo V.Distributed optimization by ant colonies[C]//Proceedings of European Conference on Artificial Life.Paris,France:Elsevier Publishing,1991:134-142.
[5]Kirkpatrick S,Jr G C,Vecchi M P.Optimization by simulated annealing[J].Science,1983,220(4598):671.
[6]马钰戈,刘永,郝娟,等.JIT供应链物料采购协同优化及其粒子群算法[J].计算机工程与应用,2018,54(2):259-265.
[7]Gong M,Cai Q,Chen X,et al.Complex network clustering by multiobjective discrete particle swarm optimization based on decomposition[J].IEEE Transactions on Evolutionary Computation,2014,18(1):82-97.
[8]Abd Elazim S M,Ali E S.A hybrid particle swarm optimization and bacterial foraging for power system stability enhancement[J].International Journal of Electrical Power&Energy Systems,2015,21(2):245-255.
[9]Tang Y,Guan X.Parameter estimation for time-delay chaotic system by particle swarm optimization[J].Chaos Solitons&Fractals,2017,40(3):1391-1398.
[10]Delgarm N,Sajadi B,Kowsary F,et al.Multi-objective optimization of the building energy performance:a simulation-based approach by means of Particle Swarm Optimization(PSO)[J].Applied Energy,2016,170:293-303.
[11]Knight J T,Zahradka F T,Singer D J,et al.Multiobjective particle swarm optimization of a planing craft with uncertainty[J].Journal of Ship Production&Design,2018,30(4):273-279.
[12]龚纯,王正林.精通MATLAB最优化计算[M].3版.北京:电子工业出版社,2014.
[13]周林锦.一种改进的粒子群算法的优化[J].科技通报,2016,32(8):154-159.
[14]赵志刚,林玉娇,尹兆远.基于自适应惯性权重的均值粒子群优化算法[J].计算机工程与科学,2016,38(3):501-506.
[15]唐祎玲,江顺亮,叶发茂,等.最优粒子增强探索粒子群算法[J].计算机工程与应用,2017,53(4):25-32.
[16]李飞,刘建昌,石怀涛,等.基于分解和差分进化的多目标粒子群优化算法[J].控制与决策,2017,32(3):403-410.
[17]Zou D,Li S,Li Z,et al.A new global particle swarm optimization for the economic emission dispatch with or without transmission losses[J].Energy Conversion&Management,2017,139:45-70.
[18]尚俊娜,盛林,程涛,等.基于LQI权重和改进粒子群算法的室内定位方法[J].传感技术学报,2017,30(2):284-290.
[19]刘文婧,王建国,吕达.增加算子扰动项的粒子群优化算法研究[J].机械设计与制造,2017(4):226-228.
[20]Zou D,Gao L,Wu J,et al.Novel global harmony search algorithm for unconstrained problems[J].Neurocomputing,2010,73(16):3308-3318.
[21]胡旺,李志蜀.一种更简化而高效的粒子群优化算法[J].软件学报,2007,18(4):861-868.
[22]Ali M M,Khompatraporn C,Zabinsky Z B.A numerical evaluation of several stochastic algorithms on selected continuous global optimization test problems[J].Journal of Global Optimization,2005,31(4):635-672.
[23]Eberhart R C,Shi Y.Guest editorial special issue on particle swarm optimization[J].IEEE Transactions on Evolutionary Computation,2004,8(3):201-203.
[24]孙湘,周大为,张希望.惯性权重粒子群算法模型收敛性分析及参数选择[J].计算机工程与设计,2010,31(18):4068-4071.
[25]周俊,陈璟华,刘国祥,等.粒子群优化算法中惯性权重综述[J].广东电力,2013,26(7):6-12.
[26]Espitia H E,Sofrony J I.Considerations for parameter configuration on vortex particle swarm optimization[J].Theoretical Computer Science,2018:1-47.
[27]曾攀.有限元基础教程[M].北京:高等教育出版社,2009.
[28]赵建峰,魏锋涛,宋俐.基于ANSYS的机床主轴箱结构优化设计[J].机电产品开发与创新,2010,23(5):140-142.
[29]刘鸿文.材料力学[M].5版.北京:高等教育出版社,2011.