基于多代种群进化信息改进的差分进化算法研究
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摘要
差分进化算法是进化算法中一种性能较为优良的全局数值优化算法,已在人工智能、信号处理等方面取得广泛应用,但当前研究往往仅考虑进化过程中某一代种群的分布信息,而忽略进化过程中多代种群累积的分布信息,造成信息利用不充分。借助自适应协方差矩阵进化策略的思想,充分利用进化过程中累积的种群分布信息,同时,由于自适应协方差矩阵存在收敛早熟、易陷入局部最优的缺点,先后对变异和交叉操作进行相应改进,以平衡算法的全局搜索能力和局部搜索能力。首先,根据种群中个体适应度值进行排序,由余弦函数改进的概率模型计算个体参与变异操作的概率,基向量和差分向量中末端向量根据概率值降序选择,差分向量中起始向量升序选择,从而提高种群的搜索范围;然后,对协方差矩阵进行特征分解,并在由特征向量构建的坐标系中执行交叉操作,该种方式生成的实验向量更接近全局最优解。针对上述改进操作,采用IEEE CEC2014作为评估函数,实验结果表明,相比现有的差分进化改进算法,本改进算法的实验性能提升更为明显。
The differential evolution algorithm is one of the global numerical optimized algorithms with excellent performance,and it has been widely applied in artificial intelligence,signal processing and so on.However,the current research takes into account the population distribution information of generation and neglects the distribution information accumulated by the multi-generation cumulative population in the evolution process,thus the distribution information is not fully utilized.Inspired by covariance matrix adaption evolutionary strategy(CMA-ES),we propose a new method that can make full use of the accumulated population distribution information in the evolution process.As the CMA tends to premature converge and falls into local optimum,the proposed method improve the mutation operation and cross operation to balance global and local search capability.Firstly,we sort the vectors according to their fitness value,and calculate the probability of individual vector participating in mutation operation based on the probability model improved by cosine function.To improve the global search ability,the proposed method selects the base vectors and the end vectors of difference vectors by their probability value in descending order,and the initial vectors of difference vector are selected in ascending order.Then,we establish the new coordinate system by eigenvectors which are generated from the decomposition of the covariance matrix.Executing crossover operation in the new coordinate system makes the trial vector closer to the global optimum than the traditional way.Experimental results show that,the proposed algorithm outperforms the existing improved algorithms on test function IEEE CEC2014.
The differential evolution algorithm is one of the global numerical optimized algorithms with excellent performance,and it has been widely applied in artificial intelligence,signal processing and so on.However,the current research takes into account the population distribution information of generation and neglects the distribution information accumulated by the multi-generation cumulative population in the evolution process,thus the distribution information is not fully utilized.Inspired by covariance matrix adaption evolutionary strategy(CMA-ES),we propose a new method that can make full use of the accumulated population distribution information in the evolution process.As the CMA tends to premature converge and falls into local optimum,the proposed method improve the mutation operation and cross operation to balance global and local search capability.Firstly,we sort the vectors according to their fitness value,and calculate the probability of individual vector participating in mutation operation based on the probability model improved by cosine function.To improve the global search ability,the proposed method selects the base vectors and the end vectors of difference vectors by their probability value in descending order,and the initial vectors of difference vector are selected in ascending order.Then,we establish the new coordinate system by eigenvectors which are generated from the decomposition of the covariance matrix.Executing crossover operation in the new coordinate system makes the trial vector closer to the global optimum than the traditional way.Experimental results show that,the proposed algorithm outperforms the existing improved algorithms on test function IEEE CEC2014.
引文
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[10]Wang Y,Li H X,Huang T W,et al.Differential evolution based on covariance matrix learning and bimodal distribution parameter setting[J].Applied Soft Computing,2014,18(1):232-247.
[11]Yu Sheng-wei.Analysis and application of Matlab optimization algorithm[M].Beijing:Tsinghua University Press,2015.(in Chinese)
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[14]Epitropakis M G,Tasoulis D K,Pavlidis N G,et al.Enhancing differential evolution utilizing proximity-based mutation operators[J].IEEE Transactions on Evolutionary Computation,2011,15(1):99-119.
[15]Hu Zhong-bo,Xiong Sheng-wu,Wang Xiu-hua,et al.Subspace clustering mutation operator for developing convergent differential evolution algorithm[J].Mathematical Problems in Engineering,2014:Article ID 154626.
[16]Izzo D,Rucinski M,Ampatzis C.Parallel global optimisation meta-heuristics using an asynchronous island-model[C]∥Proc of the 11th Conference on Congress on Evolutionary Computation,2009:2301-2308.
[17]Gong W,Cai Z,Wang Y.Repairing the crossover rate in adaptive differential evolution[J].Applied Soft Computing,2014,15(2):149-168.
[18]Hansen N,Ostermeier A.Completely derandomized selfadaptation in evolution strategies[J].Evolutionary Computation,2001,9(2):159-195.
[19]Li Y L,Zhan Z H,Gong Y J,et al.Differential evolution with an evolution path:A deep evolutionary algorithm[J].IEEE Transactions on Cybernetics,2015,45(9):1798-1810.
[20]Liang J J,Qu B Y,Suganthan P N.Problem definitions and evaluation criteria for the CEC 2014special session and competition on single objective real-parameter numerical optimization:technical report 201311[R].Zhengzhou:Zhengzhou University,2013.
[2]刘波,王凌,金以慧.差分进化算法研究进展[J].控制与决策,2007,22(7):721-729.
[11]余胜威.MATLAB优化算法案例分析与应用[M].北京:清华大学出版社,2015.
[2]Liu Bo,Wang Ling,Jin Yi-hui.Advances in differential evolution[J].Control and Decision,2007,22(7):721-729.(in Chinese)
[3]Zhang J,Sanderson A C.JADE:Adaptive differential evolution with optional external archive[J].IEEE Transactions on Evolutionary Computation,2009,13(5):945-958.
[4]Brest J,Greiner S,Boskovic B,et al.Self-adapting control parameters in differential evolution:A comparative study on numerical benchmark problems[J].IEEE Transactions on Evolutionary Computation,2006,10(6):646-657.
[5]Qin A K,Huang V L,Suganthan P N.Differential evolution algorithm with strategy adaptation for global numerical optimization[J].IEEE Transactions on Evolutionary Computation,2009,13(2):398-417.
[6]Gong W,Cai Z.Differential evolution with ranking-based mutation operators[J].IEEE Transactions on Systems,Man,and Cybernetics,2013,43(6):2066-2081.
[7]Dorronsoro B,Bouvry P.Improving classical and decentralized differential evolution with new mutation operator and population topologies[J].IEEE Transactions on Evolutionary Computation,2011,15(1):67-98.
[8]Wang Y,Liu Z Z,Li J B,et al.Utilizing cumulative population distribution information in differential evolution[J].Applied Soft Computing,2016,48(C):329-346.
[9]Guo S M,Yang C C.Enhancing differential evolution utilizing eigen vector-based crossover operator[J].IEEE Transactions on Evolutionary Computation,2015,19(1):31-49.
[10]Wang Y,Li H X,Huang T W,et al.Differential evolution based on covariance matrix learning and bimodal distribution parameter setting[J].Applied Soft Computing,2014,18(1):232-247.
[11]Yu Sheng-wei.Analysis and application of Matlab optimization algorithm[M].Beijing:Tsinghua University Press,2015.(in Chinese)
[12]Zhou Y,Li X,Gao L.A differential evolution algorithm with intersect mutation operator[J].Applied Soft Computing,2013,13(1):390-401.
[13]Sarker R A,Elsayed S M,Ray T.Differential evolution with dynamic parameters selection for optimization problems[J].IEEE Transactions on Evolutionary Computation,2014,18(5):689-707.
[14]Epitropakis M G,Tasoulis D K,Pavlidis N G,et al.Enhancing differential evolution utilizing proximity-based mutation operators[J].IEEE Transactions on Evolutionary Computation,2011,15(1):99-119.
[15]Hu Zhong-bo,Xiong Sheng-wu,Wang Xiu-hua,et al.Subspace clustering mutation operator for developing convergent differential evolution algorithm[J].Mathematical Problems in Engineering,2014:Article ID 154626.
[16]Izzo D,Rucinski M,Ampatzis C.Parallel global optimisation meta-heuristics using an asynchronous island-model[C]∥Proc of the 11th Conference on Congress on Evolutionary Computation,2009:2301-2308.
[17]Gong W,Cai Z,Wang Y.Repairing the crossover rate in adaptive differential evolution[J].Applied Soft Computing,2014,15(2):149-168.
[18]Hansen N,Ostermeier A.Completely derandomized selfadaptation in evolution strategies[J].Evolutionary Computation,2001,9(2):159-195.
[19]Li Y L,Zhan Z H,Gong Y J,et al.Differential evolution with an evolution path:A deep evolutionary algorithm[J].IEEE Transactions on Cybernetics,2015,45(9):1798-1810.
[20]Liang J J,Qu B Y,Suganthan P N.Problem definitions and evaluation criteria for the CEC 2014special session and competition on single objective real-parameter numerical optimization:technical report 201311[R].Zhengzhou:Zhengzhou University,2013.
[2]刘波,王凌,金以慧.差分进化算法研究进展[J].控制与决策,2007,22(7):721-729.
[11]余胜威.MATLAB优化算法案例分析与应用[M].北京:清华大学出版社,2015.