数值积分的回溯搜索优化算法

Backtracking Search Optimization Algorithm for Numerical Integration

针对数值积分问题,提出了基于回溯搜索优化算法(Backtracking Search Optimization Algorithm,BSA)不等距节点分割的数值积分方法。该方法将不等距节点的定位看作是一个优化问题,用回溯搜索优化算法寻找最优分割节点,然后在分割而成的每个小区间上应用辛普森公式计算函数的数值积分。与同类算法的对比实验表明,该方法在收敛速度和积分精度上都表现出较强的竞争力。

To solve numerical integration problems, this paper proposes the non-isometric point segmentation numerical integration method based on backtracking search optimization algorithm （BSA）, in which the determination of the non-isometric nodes is considered as an optimization problem. In this method, BSA is used to find the optimal segmentation nodes on the integral interval of a function. In each sub-interval of the integral interval, Simpson formula is then employed to calculate numerical integral of the function. The comparative experiments with similar algorithms indicated that the proposed method shows strong competitiveness in terms of convergence speed and integral precision, in both convergence speed and integral precision show strong competitiveness.