一种新颖的花朵授粉优化算法及收敛性分析

A Novel Flower Pollination Optimization Algorithm and Its Convergent Analysis

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.