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为了解决复合Bessel函数零点计算问题,提出了修正粒子群与量子粒子群优化算法。修正后的算法能够找到复合Bessel函数有限区间内绝大部分函数零点。为了进一步提高函数零点的搜索能力,结合前两种算法特点,借鉴交叉算子操作,对带交叉算子量子粒子群算法进行修正,修正后的算法能找到复合Bessel函数有限区间内所有函数零点,修正后带交叉算子量子粒子群算法收敛速度快,零点计算精度高。计算结果表明:同一参数复合Bessel函数除去前三个零点,后续零点与零点次序在双对数坐标系中符合直线关系。对不同参数计算的零点与零点次序进行直线拟合,相关程度达到9999%,零点拟合的相对误差小于05%,能够满足工程计算的需求。
In order to solve the zero point calculation problem of composite Bessel function, a modified particle swarm optimization algorithm and quantum particle swarm optimization algorithm are proposed. The modified algorithm can find most of the zero points in the finite interval of the composite Bessel function. In order to further improve the searching ability of the zero point of the function, the quantum particle swarm optimization with crossover operator is modified by combining the former two algorithms with the operation of the crossover operator. The modified algorithm can find the zero points of all functions in the finite interval of the composite Bessel function, The corrected quantum particle swarm optimization algorithm with crossover operator has the advantages of fast convergence rate and high precision of zero point calculation. The calculation results show that the same parameter compound Bessel function removes the first three zeroes, and the subsequent zero and zero orders are in a straight line relationship in the double logarithmic coordinate system. The zero and zero order of different parameters are linearly fitted, the correlation degree reaches 99.99%, and the relative error of zero point fitting is less than 0.5%, which can meet the needs of engineering calculation.