具有脉冲毒素输入的生态毒理动力学的函数优化方法
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摘要
为了解决某些函数优化问题,基于具有脉冲毒素输入的生态毒理动力学模型提出了可全局收敛的函数优化算法。在该算法中,令环境系统与优化问题的搜索空间相对应,该环境系统存在污染现象,污染源定期地向环境系统注入有毒污染物。有多种不同类型的种群生活在该环境系统中,不同类型的种群之间存在竞争关系和捕食-被捕食关系,每个种群对应着优化问题的一个试探解。将生态毒理动力学模型映射成对种群的特征的变化规律的描述,利用环境和种群以及种群与种群之间的相互作用构造种群的进化算子,这些算子从多种角度实现了种群与环境以及种群与种群之间的信息交换。结果表明:因环境污染影响的是种群的很少部分特征,当种群演化时,只涉及到很少一部分特征参与运算,故收敛速度可得到提升;环境系统脉冲式注入毒素,可以导致种群的特征状态值发生突然改变,这种特点有利于使搜索跳出局部最优解陷阱;使能够抵抗污染的强壮种群获得生长,而无法抵抗污染的虚弱种群则停止生长,此特点确保了该算法具有全局收敛性。测试结果表明:对某些函数优化问题的求解,本算法与已有的群智能优化算法相比,均具有较高的精度和性能。
To solve some function optimization problems,the optimization algorithm based on the impulsive toxicant input model of ecotoxicology dynamics was constructed.In the algorithm,an environment system corresponds to the search space of an optimization problem,and there is pollution in the environment system,and some pollution sources pour toxicant pollutants into the environment system impulsively and periodically.Many different classes of population live in the system,and there are competition and predatory-prey relation among different classes of population,and each population in a class of population is just an alternative solution of an optimization problem.The ecotoxicology dynamics model is mapped into describing the change of some features of a population.The interaction between environment and populations as well as among populations is used to construct evolution operators of populations,and these operators realize sufficient information exchange between environment and populations as well as among populations.The research results show that environment pollution gives influence on a very small part of features of a population,which means that only a very small part of features take part in computation.Then convergence speed of the algorithm can be substantially improved,and impulsively discharged toxicant pollutants result in fierce change of state value of a feature of the population,which enables a search to jump out from local optima easily.Strong populations who can endure pollution keep growing,while week populations who can not endure pollution will stop growing,which ensures the algorithm to converge.The case study shows that for some function optimization problems the algorithm has higher speed of convergence and higher accuracy of global optima than the existed population-based intelligent optimization algorithms.
To solve some function optimization problems,the optimization algorithm based on the impulsive toxicant input model of ecotoxicology dynamics was constructed.In the algorithm,an environment system corresponds to the search space of an optimization problem,and there is pollution in the environment system,and some pollution sources pour toxicant pollutants into the environment system impulsively and periodically.Many different classes of population live in the system,and there are competition and predatory-prey relation among different classes of population,and each population in a class of population is just an alternative solution of an optimization problem.The ecotoxicology dynamics model is mapped into describing the change of some features of a population.The interaction between environment and populations as well as among populations is used to construct evolution operators of populations,and these operators realize sufficient information exchange between environment and populations as well as among populations.The research results show that environment pollution gives influence on a very small part of features of a population,which means that only a very small part of features take part in computation.Then convergence speed of the algorithm can be substantially improved,and impulsively discharged toxicant pollutants result in fierce change of state value of a feature of the population,which enables a search to jump out from local optima easily.Strong populations who can endure pollution keep growing,while week populations who can not endure pollution will stop growing,which ensures the algorithm to converge.The case study shows that for some function optimization problems the algorithm has higher speed of convergence and higher accuracy of global optima than the existed population-based intelligent optimization algorithms.
引文
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[2]Colorni A,Dorigo M.Distributed optimization by ant colonies[C]∥Proceedings of the 1st Europe Conference on Artificial Life.1991:134-142
[3]Eberhart R,Kennedy J.New optimizer using particle swarm theory[C]∥MHS’95Proceedings of the Sixth International Symposium on Micro Machine and Human Science.IEEE,Piscataway,NJ,USA,1995:38-43
[4]崔志华,曾建潮.微粒群优化算法[M].北京:科学出版社,2011
[5]李晓磊,邵之江,钱积.一种基于动物自治体的寻优模式:鱼群算法[J].系统工程理论与实践,2002,22(11):32-38
[6]Simon D.Biogeography-based Optimization[J].IEEE Transactions on Evolutionary Computation,2008,12(6):702-713
[7]Price K,Storn R.Differential evolution[J].Dr.Dobb’s Journal,1997,22(4):18-24,78
[8]王磊,潘进,焦李成.免疫算法[J].电子学报,2000,28(7):74-78
[9]李茂军,罗安,童调生.人工免疫算法及其应用研究[J].控制理论与应用,2004,21(2):153-158
[10]Beyer H.The Theory of Evolution Strategies[M].New York:Springer,2001
[11]Mezura-Montes E,Coello C.A simple multimembered evolution strategy to solve constrained optimization problems[J].IEEE Transactions on Evolutionary Computation,2005,9(2):1-17
[12]陈兰荪,孟新柱,焦建军.生物动力学[M].北京:科学出版社,2009
[13]王克.随机生物数学模型进展[M].北京:科学出版社,2010
[14]Hallam T G,Clark C E,Lassider R R.Effects of toxicant on population:A qualitative approach I:Equilibrium environmental exposure[J].Ecology Modelling,1983,8:291-304
[15]Hallam T G,Clark C E,Jordan G S.Effects of toxicant on population:A qualitative approach II:First Order Kinetics[J].Journal of Mathematical Biology,1983,18:25-37
[16]Hallam T G,Deluua J T.Effects of toxicant on population:A qualitative approach III:Environmental and food chain patways[J].Journal of Theoretical Biology,1984,109:411-429
[17]Liu Yi-liang,Liu Qun,Liu Zhen-hai.Dynamical behaviors of a stochastic delay logistic system with impulsive toxicant input in apolluted environment[J].Journal of Theoretical Biology,2013,329:1-5
[18]Iisufescu M.Finite Markov Processes and Their Applications[M].Wiley:Chichester,1980