采用复合规则约束的多种群自适应进化算法
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摘要
针对种群固定的进化算法容易使个体集中分布在局部区域,不利于处理大尺度空间和多峰类型的优化问题,提出了一种多种群分布并且动态变化的种群自适应进化算法.采用Logistic模型模拟多个种群在有限资源下的竞争关系,设计了稳定性规则、熵规则和精英规则以确定不同种群的Logistic模型参数,从而控制种群数量的变化.同时,算法引入了算术内插和外插两种交叉算子,使得各个种群依据自身类型来缩小或扩展搜索空间.此外,算法还通过周期性的调整规则重新构建种群和分配资源.通过5组大尺度和多峰优化问题的测试结果表明,所提的种群自适应方法能够有效改善算法的寻优性能,在达到同等优化水平时所提算法消耗的函数调用次数为对比算法的61.08%～91.55%.
Evolutionary algorithm with fixed population size is easy to fall into local optimum. Thus it is unsuitable to solve large scale or multi-modal problems. In this paper,an evolutionary algorithm with multiple populations and self-adaptive population size is proposed. This algorithm uses Logistic model to describe the competitive relationship among populations in limited resources, and designs several rules including Stability, Entropy and Elitist,to identify the parameters of each population's Logistic model to control the variety of population size. The algorithm also adopts two crossover operators named arithmetic interpolation and arithmetic extrapolation such that each population can expand or shrink its searching space based on its characteristics. Besides, a periodic adjusting rule is designed to reconstruct populations and reassign resources. Experimental results on five large scale or multi-modal problems show that the proposed self-adaptive method on populations can remarkably improve the performance of our algorithm, wherein to reach the same optimal accuracy, the function calling times of our algorithm only occupy 61.08% 91.55% of those in other algorithms.
Evolutionary algorithm with fixed population size is easy to fall into local optimum. Thus it is unsuitable to solve large scale or multi-modal problems. In this paper,an evolutionary algorithm with multiple populations and self-adaptive population size is proposed. This algorithm uses Logistic model to describe the competitive relationship among populations in limited resources, and designs several rules including Stability, Entropy and Elitist,to identify the parameters of each population's Logistic model to control the variety of population size. The algorithm also adopts two crossover operators named arithmetic interpolation and arithmetic extrapolation such that each population can expand or shrink its searching space based on its characteristics. Besides, a periodic adjusting rule is designed to reconstruct populations and reassign resources. Experimental results on five large scale or multi-modal problems show that the proposed self-adaptive method on populations can remarkably improve the performance of our algorithm, wherein to reach the same optimal accuracy, the function calling times of our algorithm only occupy 61.08% 91.55% of those in other algorithms.
引文
[1]宁桂英,曹敦虔,周永权.一种融合Powell搜索法的差分进化算法[J].高等学校计算数学学报,2017,39(3):267-280.
[2]王丽萍,章鸣雷,邱飞岳,等.基于角度惩罚距离精英选择策略的偏好高维目标优化算法[J].计算机学报,2018, 41(1):236-253.
[3]何剑,李强,张启敏.带Markov跳时变随机种群收获系统数值解的收敛性[J].数学的实践与认识,2017,47(15):218-226.
[4]余味,乔韵璇.随机环境下种群增长模型的冰数值模拟与最优解[J].系统科学与数学,2016, 36(11):2087-2098.
[5]吴鹏,何泽荣.基于弹性增长的尺度结构种群的最优平衡收获[J].应用数学,2017, 30(1):162-167.
[6]何廷年,李晓红,蒋芸.改进多种群差分进化算法的混沌系统参数估计[J].计算机工程,2015, 41(2):178-183.
[7]冯变英,李秋英.一类基于个体尺度的种群模型的适定性及最优不育控制策略[J].系统科学与数学,2016,36(2):278-288.
[8]呼忠权,王洪斌,李硕.自适应双模式差分进化算法[J].计算机工程与设计,2015,36(8):2250-2254.
[9] Brest J, Maucec M S. Self-adaptive differential evolution algorithm using population size reduction and three strategies[J]. Soft Computing-A fusion of foundations, Methodologies and Applications,2011, 15(11):2157-2174.
[10]郑金华,申瑞艰,李密青,等.多目标优化的进化环境模型及实现[J].计算机学报,2014, 37(12):2530-2547.
[11] Zamuda A, Brest J. Population reduction differential evolution with multiple mutation strategies in real world industry challenges[C]//In Proc. Swarm and Evolutionary Computation. International Symposia, SIDE 2012 and EC 2012, Zakopane, 2012:154-161.
[12]侯爱华,高伟,汪霖.基于逻辑回归模型的流量异常检测方法研究[J].工程数学学报,2017, 34(5):479-489.
[13]向万里,马寿峰,安美清.具有Pbest引导机制的适应性多策略差分进化算法[J].模式识别与人工智能,2013, 26(8):711-721.
[14]何泽荣,吴鹏.模拟弹性增长的非线性尺度结构种群模型分析[J].系统科学与数学,2017, 37(1):289-303.
[15]韩雪,程维虎.基于矩和L矩的三参数Ⅰ型广义Logistic分布的参数估计[J].应用数学学报,2017,40(3):331-344.
[16]李响,华敏.速度多样性自适应选择模型的改进粒子群算法[J].计算机工程与设计,2014,35(8):2907-2911.
[17] Hsieh S T, Sun T Y, Liu C C, et al. Solving large scale global optimization using improved particle swarm optimizer[C]//Proceedings of IEEE World Congress on Computational Intelligence, CEC2008, Hongkong, 2008:1777-1784.
[18]郑金华,刘磊,李密青,等.差分选择策略在复杂多目标优化问题中的研究[J].计算机研究与发展,2015,52(9):2123-2134.
[19]徐东方,郭战伟,侯春娟.约束尺度和算子自适应变化的差分进化算法[J].数学的实践与认识,2017,47(16):149-156.
[2]王丽萍,章鸣雷,邱飞岳,等.基于角度惩罚距离精英选择策略的偏好高维目标优化算法[J].计算机学报,2018, 41(1):236-253.
[3]何剑,李强,张启敏.带Markov跳时变随机种群收获系统数值解的收敛性[J].数学的实践与认识,2017,47(15):218-226.
[4]余味,乔韵璇.随机环境下种群增长模型的冰数值模拟与最优解[J].系统科学与数学,2016, 36(11):2087-2098.
[5]吴鹏,何泽荣.基于弹性增长的尺度结构种群的最优平衡收获[J].应用数学,2017, 30(1):162-167.
[6]何廷年,李晓红,蒋芸.改进多种群差分进化算法的混沌系统参数估计[J].计算机工程,2015, 41(2):178-183.
[7]冯变英,李秋英.一类基于个体尺度的种群模型的适定性及最优不育控制策略[J].系统科学与数学,2016,36(2):278-288.
[8]呼忠权,王洪斌,李硕.自适应双模式差分进化算法[J].计算机工程与设计,2015,36(8):2250-2254.
[9] Brest J, Maucec M S. Self-adaptive differential evolution algorithm using population size reduction and three strategies[J]. Soft Computing-A fusion of foundations, Methodologies and Applications,2011, 15(11):2157-2174.
[10]郑金华,申瑞艰,李密青,等.多目标优化的进化环境模型及实现[J].计算机学报,2014, 37(12):2530-2547.
[11] Zamuda A, Brest J. Population reduction differential evolution with multiple mutation strategies in real world industry challenges[C]//In Proc. Swarm and Evolutionary Computation. International Symposia, SIDE 2012 and EC 2012, Zakopane, 2012:154-161.
[12]侯爱华,高伟,汪霖.基于逻辑回归模型的流量异常检测方法研究[J].工程数学学报,2017, 34(5):479-489.
[13]向万里,马寿峰,安美清.具有Pbest引导机制的适应性多策略差分进化算法[J].模式识别与人工智能,2013, 26(8):711-721.
[14]何泽荣,吴鹏.模拟弹性增长的非线性尺度结构种群模型分析[J].系统科学与数学,2017, 37(1):289-303.
[15]韩雪,程维虎.基于矩和L矩的三参数Ⅰ型广义Logistic分布的参数估计[J].应用数学学报,2017,40(3):331-344.
[16]李响,华敏.速度多样性自适应选择模型的改进粒子群算法[J].计算机工程与设计,2014,35(8):2907-2911.
[17] Hsieh S T, Sun T Y, Liu C C, et al. Solving large scale global optimization using improved particle swarm optimizer[C]//Proceedings of IEEE World Congress on Computational Intelligence, CEC2008, Hongkong, 2008:1777-1784.
[18]郑金华,刘磊,李密青,等.差分选择策略在复杂多目标优化问题中的研究[J].计算机研究与发展,2015,52(9):2123-2134.
[19]徐东方,郭战伟,侯春娟.约束尺度和算子自适应变化的差分进化算法[J].数学的实践与认识,2017,47(16):149-156.