改进的蝙蝠算法在数值积分中的应用研究

Application of the improved bat algorithm in numerical integration

蝙蝠算法具有收敛速度快、潜在分布式和并行性等特点,但也存在着寻优精度不高、后期收敛速度慢、易陷入局部最优等问题。针对蝙蝠算法和目前数值积分方法的不足,把具有很强的全局寻优能力和局部搜索能力的差分进化算法融合到蝙蝠算法中,提出了一种基于差分进化算法的改进蝙蝠算法求任意函数数值积分的新方法,该算法不仅能求解通常意义下任意函数的定积分,而且能计算振荡积分和奇异积分。通过6个不同算例与当前数值积分方法比较,实验仿真结果表明,该算法是有效的和可行的,能够快速有效地获取任意函数的数值积分值。同时,扩展了蝙蝠算法的应用领域。

The bat optimization algorithm is a new swarm intelligence algorithm that has appeared in recent years. It is a kind of intelligent optimization tool with very good and strong optimization ability. This algorithm has characteristics including fast convergence,potential distribution and parallelism. However,it also has shortcomings including low precision in optimizing,low convergence speed in later periods,ease of falling into local optimization,etc. To overcome the shortcomings of current numerical integration methods and the bat algorithm,by fusing the differential evolution algorithm that has excellent abilities of local searching and global optimizing into the bat algorithm,this paper presents an improved bat algorithm based on the differential evolution algorithm that is applied to solving the numerical integration of any function. This algorithm not only can solve the definite integral for any function of common sense,but it can also calculate the oscillatory integrals and singular integrals. By comparing six different examples with current numerical integration methods,the simulations show that the improved algorithm is efficient and feasible. It is able to compute the numerical integration of any function. Meanwhile,it extends the application field of the bat algorithm.