具有振荡约束的自然选择萤火虫优化算法

Natural selection firefly optimization algorithm with oscillation and constraint

针对基本萤火虫算法高维求解精度低、收敛速度慢、易早熟等缺点,提出一种具有振荡、约束和自然选择机制的萤火虫算法,引入二阶振荡因子,平衡上一代个体对当前代个体的影响,防止萤火虫个体陷入局部极值;加入基于sigmoid函数的约束因子,动态调整个体移动距离,在算法后期避免萤火虫个体在理论最优值附近因过度扰震而导致精度降低的情况;采用基于高斯积分倒数递减趋势的自然选择,在保持个体多样性的同时加快算法的收敛速度.理论分析证明了改进算法的收敛性和时间复杂度.通过对10个不同特征标准测试函数多个维度的函数优化仿真实验,测试结果表明改进算法的寻优精度和收敛速度均有明显提升,尤其是在高维情况下,几乎对于所有函数仍能找到理论最优解,较好地解决了萤火虫算法不适于高维求解的问题.

Aiming at the shortcomings of low precision in high dimension, slow convergence speed and precocity in the basic firefly algorithm, the firefly algorithm with oscillation, constraint and natural selection mechanism is proposed.Firstly, the second-order oscillation factor is introduced to balance the influence of the previous generation of individuals on the current generation of individuals, so as to prevent the individuals of fireflies from falling into local extremum.Then, the constraint factor based on sigmoid function is added to dynamically adjust the moving distance of individual,so as to avoid the situation that the individual of firefly caused by excessive disturbance near the theoretical optimal value leads to the reduction of precision in the later stage of the algorithm. Finally, natural selection based on the decreasing trend of reciprocal Gaussian integral is used to keep individual diversity and accelerate the convergence speed of the algorithm. The convergence and time complexity of the improved algorithm are proved by theoretical analysis. Through the simulation of 10 standard functions with multiple dimensions and different characteristics, the test results show that the optimization accuracy and convergence speed of the OCSFA(natural selection firefly optimization algorithm with oscillation and constraint) are obviously improved. Especially in the case of high dimension, the theoretical optimum can still be found for almost all functions, which better solves the problem of the unsuitability of the firefly algorithm for high dimension solution.