求解函数优化问题的改进布谷鸟搜索算法

在工程优化中,大多问题是连续优化问题,即函数优化问题。针对布谷鸟算法求解函数优化问题时存在的收敛速度慢、求解精度不高和易陷入局部最优等问题,文中提出非线性惯性权重对数递减和随机调整发现概率的布谷鸟搜索算法(Cuc-koo Search Algorithm with Logarithmic Decline of Nonlinear Inertial Weights and Random Adjustment Discovery Probability,DWCS)。首先,在布谷鸟寻窝的路径和位置更新公式中,设计一种随进化迭代次数非线性递减的惯性权重来改进鸟巢位置的更新方式,以协调布谷鸟算法的探索和开发能力;其次,引入随机调整发现概率代替固定值发现概率,使较大和较小的发现概率随机出现,从而有利于平衡算法的全局探索和局部开发能力,加快算法收敛速度,增加种群多样性;最后,分析对数递减参数和随机调整发现概率,选取对数递减最佳参数组合和随机调整发现概率的最佳取值范围,此时,函数的优化效果最好。与BA,CS,PSO,ICS算法相比,所提算法极大地提高了寻优精度,显著地减少了迭代次数,有效地提高了收敛速度和鲁棒性。在16个测试函数中,DWCS均能收敛到全局最优解,证明了DWCS在求解连续复杂函数优化问题上具有较强的竞争力。

Improved Cuckoo Search Algorithm for Function Optimization Problems

In engineering optimization,most problems are continuous optimization problems,that is function optimization problems.Aiming at the problems of slow convergence speed,low precision and easy to fall into local optimization in the later stage of Cuckoo algorithm,this paper proposed an improved Cuckoo search algorithm based on the logarithmic decline of nonlinear inertial weights and the random adjustment discovery probability.Firstly,in the update formula of the path and position of the cuckoo homing nest,a update method that inertia weight decreases nonlinearly with the number of evolutionary iterations is designed to improve the nest location and coordinate the abilities of exploration and exploitation.Secondly,the discovery probability with random adjustment is introduced to replace the discovery probability of fixed value to make the larger and smaller discovery probabi-lity appear randomly,which is beneficial to balancing the global exploration and local exploitation of the algorithm,accelerating the convergence speed,and increasing the diversity of the population.Finally,the logarithmic decreasing parameter and stochastic adjustment discovery probability are analyzed and tested,and the optimal parameter combination of logarithmic decrement and the optimal range of stochastic adjustment discovery probability are selected.At this time,the optimization effect of the function is the best.Compared with other evolutionary algorithms(BA,CS,PSO,ICS),DWCS greatly improves the precision of optimization,significantly reduces the number of iterations,and effectively improves the convergence speed and robustness.In 16 test functions,DWCS can converge to the global optimal solution,which proves that DWCS has a strong competitive power in solving the optimization problem of continuous complex functions.