一种新颖的花朵授粉优化算法及收敛性分析
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摘要
针对现有花朵授粉算法存在易早熟、寻优精度不高、搜索效率低下等问题,研究设计了一种改进的花朵授粉算法。该算法利用逻辑自映射函数对花粉粒进行混沌扰动,使缺乏变异机制的花粉粒集具有较强的自适应能力,有效地防止了算法后期最优解趋同的现象。利用变换算子对搜索空间进行动态收缩,使算法在寻优过程中保持较高的种群多样性,降低算法陷入局部极值的概率,从而提高算法的搜索效率和寻优精度。同时,结合花朵授粉的生物学特征,从机理上描述了改进后算法的具体实现步骤,对算法的收敛性和寻优性能进行了详细的剖析,并采用实数编码的方法分析了算法的收敛性,给出了算法的生物学模型和理论基础。实验结果表明,改进后的算法具有较好的性能。
In order to deal with the deficiencies of the existing flower pollination algorithm such as the prematurity problem, low optimization accuracy, inefficient searching capacity, etc., this paper proposes a newly-revised flower pollination algorithm. The self-logical mapping function is used to carry on the chaotic disturbance to the pollen grains in the proposed algorithm, which can make the defective variation mechanism have strong adaptive capacities, and avoid the later potential homogeneity phenomenon of the optimal solutions. The use of the transformation operator to dynamically shrink the search space can keep the diversity of the population and reduce the probability of getting into the local extremum in the process of optimization, thus improving the searching efficiency and degree of accuracy of the algorithm. Meanwhile, in combination with the biological characteristics of flower pollination, a mechanistic description of the specific implementation steps of the improved flower pollination algorithm is given, and the convergence property and optimization performance of the algorithm are analyzed. The method of real number encoding is used to further analyze the convergence of the algorithm, thus the biological model and theoretical basis of the algorithm are supplied. The experimental results show that the algorithm proposed in this paper has a better performance.
In order to deal with the deficiencies of the existing flower pollination algorithm such as the prematurity problem, low optimization accuracy, inefficient searching capacity, etc., this paper proposes a newly-revised flower pollination algorithm. The self-logical mapping function is used to carry on the chaotic disturbance to the pollen grains in the proposed algorithm, which can make the defective variation mechanism have strong adaptive capacities, and avoid the later potential homogeneity phenomenon of the optimal solutions. The use of the transformation operator to dynamically shrink the search space can keep the diversity of the population and reduce the probability of getting into the local extremum in the process of optimization, thus improving the searching efficiency and degree of accuracy of the algorithm. Meanwhile, in combination with the biological characteristics of flower pollination, a mechanistic description of the specific implementation steps of the improved flower pollination algorithm is given, and the convergence property and optimization performance of the algorithm are analyzed. The method of real number encoding is used to further analyze the convergence of the algorithm, thus the biological model and theoretical basis of the algorithm are supplied. The experimental results show that the algorithm proposed in this paper has a better performance.
引文
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[20] 冯艳红,刘建芹,贺毅朝.基于混沌理论的动态种群萤火虫算法[J]. 计算机应用, 2013,33(3):796-799.
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[27] Yang X S. Nature inspired meta-heuristic algorithms (2nd Edition)[M]. UK: Luniver Press, 2010.
[28] Yang X S, Karamanoglu M, He X. Flower pollination algorithm: A novel approach for multiobjective optimization [J]. Engineering Optimization, 2014, 46(9): 1222-1237.
[2] Ponsich A, Jaimes A L, Coello C. A survey on multiobjective evolutionary algorithms for the solution of the portfolio optimization problem and other finance and economics applications[J]. Evolutionary Computation, IEEE Transactions on, 2013, 17(3): 321-344.
[3] Sidky E Y, J?rgensen J H, Pan X. Convex optimization problem prototyping for image reconstruction in computed tomography with the Chambolle-Pock algorithm[J]. Physics in Medicine and Biology, 2012, 57(10): 3065-3091.
[4] Colorni A, Dorigo M, Maniezzo V. Distributed optimization by ant colonies[C]//Proceedings of ECAL91, European Conference on Artificial Life. Paris, France:[s.n.], 1991: 134-142.
[5] Yang X S. Flower pollination algorithm for global optimization[M]//Springer Berlin Heidelberg: Unconventional Computation and Natural Computation, 2012: 240-249.
[6] Edwards A M. Overturning conclusions of Lévy flight movement patterns by fishing boats and foraging animals[J]. Ecology, 2011, 92(6): 1247-1257.
[7] Wang R, Zhou Y, Qiao S, et al. Flower pollination algorithm with bee pollinator for cluster analysis[J]. Information Processing Letters, 2016, 116(1): 1-14.
[8] Wang R, Zhou Y, Zhao C, et al. A hybrid flower pollination algorithm based modified randomized location for multi-threshold medical image segmentation[J]. Bio-Medical Materials and Engineering, 2015, 26(s1): 1345-1351.
[9] Abdel-Raouf O, El-Henawy I, Abdel-Baset M. A novel hybrid flower pollination algorithm with chaotic harmony search for solving sudoku puzzles[J]. International Journal of Modern Education and Computer Science (IJMECS), 2014, 6(3): 38-44.
[10] Huang S J, Gu P H, Su W F, et al. Application of flower pollination algorithm for placement of distribution transformers in a low-voltage grid[C]//IEEE:Industrial Technology (ICIT), 2015 IEEE International Conference on. [s.l.]: IEEE, 2015: 1280-1285.
[11] Dubey H M, Pandit M, Panigrahi B K. Hybrid flower pollination algorithm with time-varying fuzzy selection mechanism for wind integrated multi-objective dynamic economic dispatch[J]. Renewable Energy, 2015, 83(11): 188-202.
[12] Alam D F, Yousri D A, Eteiba M B. Flower pollination algorithm based solar PV parameter estimation[J]. Energy Conversion and Management, 2015, 101(9): 410-422.
[13] Dubey H M, Panigrahi B K, Pandit M. Improved flower pollination algorithm for short term hydrothermal scheduling[M]//Swarm, Evolutionary, and Memetic Computing. Switzerland: Springer International Publishing, 2015: 721-737.
[14] Askarzadeh A. A discrete chaotic harmony search-based simulated annealing algorithm for optimum design of PV/wind hybrid system[J]. Solar Energy, 2013, 97(11): 93-101.
[15] Cheng M Y, Huang K Y, Chen H M. Dynamic guiding particle swarm optimization with embedded chaotic search for solving multidimensional problems[J]. Optimization Letters, 2012, 6(4): 719-729.
[16] Tan Y, Tan G, Deng S. Hybrid particle swarm optimization with chaotic search for solving integer and mixed integer programming problems[J]. Journal of Central South University, 2014, 21(7): 2731-2742.
[17] Yang Xin-She. Nature-inspired metaheuristic algorithms[M]. 2nd Eds. Frome: Luniver Press, 2010.
[18] Yang X S, Karamanoglu M, He X. Flower pollination algorithm: A novel approach for multiobjective optimization[J]. Engineering Optimization, 2014, 46(9): 1222-1237.
[19] 刘长平,叶春明.基于逻辑自映射的变尺度混沌粒子群优化算法[J].计算机应用研究, 2011, 28(8): 2825-2827.
[20] 冯艳红,刘建芹,贺毅朝.基于混沌理论的动态种群萤火虫算法[J]. 计算机应用, 2013,33(3):796-799.
[21] Ferone V. Isoperimetric inequalities and applications[J]. Bollettion della Unione Matematica, 2008,1(3):539-557.
[22] 肖辉辉,万常选,段艳明.一种改进的新型元启发式花朵授粉算法[J].计算机应用研究, 2016(1):126-131.
[23] 甘特马赫尔.矩阵论(下)[M].哈尔滨:哈尔滨工业大学出版社, 2013.
[24] Whittle P. Finite Markov processes and their applications[M]. Nature:Dover Publications, 2007.
[25] 刘静.协同进化算法及其应用研究[D].西安:西安电子科技大学, 2004.
[26] Kennedy J, Eberhart R. Particle swarm optimization[C]//Proceedings of IEEE International Conference on Neural Networks. Perth:[s.n.], 1995: 1942-1948.
[27] Yang X S. Nature inspired meta-heuristic algorithms (2nd Edition)[M]. UK: Luniver Press, 2010.
[28] Yang X S, Karamanoglu M, He X. Flower pollination algorithm: A novel approach for multiobjective optimization [J]. Engineering Optimization, 2014, 46(9): 1222-1237.