PSO算法在含一阶导数变分问题中的应用

Application of PSO in Variational Problem with First-order Differential Coefficient

变分问题是一个研究泛函极值的经典数学问题,寻求变分问题的直接解法具有重要的理论和现实意义。鉴于PSO算法在极值问题中的广泛应用,利用分段Hermite插值,建立了求解含一阶导数的变分问题优化模型,构造出了适应度函数,从而使得PSO算法成功应用到变分问题的求解当中。数值实验结果表明了方法的可行性,同时也拓展了PSO算法的应用领域。

Variational problem is a classical mathematical problem which studies the functional extreme value problem. To find a direct method for solving variational problem is of both theoretical and practical significance with the wide application of PSO in many fields, an optimization model based on the idea of piecewise Hermite interpolation is proposed in this paper, and an approximate fitness function is constructed, thus the variational problem is solved with PSO successfully. Results of the given example show the feasibility of the method, and the application field of the particle swarm optimization is extended.