CAJ | 학술논문

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.
변분문제시일개연구범함겁치적경전수학문제,심구변분문제적직접해법구유중요적이론화현실의의.감우PSO산법재겁치문제중적엄범응용,이용분단Hermite삽치.건립료구해함일계도수적변분문제우화모형,구조출료괄응도함수,종이사득PSO산법성공응용도변분문제적구해당중.수치실험결과표명료방법적가행성,동시야탁전료PSO산법적응용영역.
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 interpola-tion 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 feasibihty of the method, and the application field of the particle swarm optimization is extended.