一种改进的和声搜索算法求解线性两点边值问题
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摘要
研究了线性两点边值问题的数值解.首先采用有限差分法将线性两点边值问题离散化,进而得到一个无约束优化问题,采用全局和声搜索算法求解.全局和声搜索算法嵌入了位置更新和小概率变异策略,通过反复调整乐队中各乐器的音调,最终达到一个美妙的和声状态的过程.通过求解3个线性两点边值问题,结果表明该方法是有效的.
Numerical solutions of linear two-point boundary value problems are studied.By using the finite difference method, the discretization of linear two-point boundary value problem is reformed an unconstrained optimization, and solved by heuristic method named novel global harmony search algorithm(NGHS). The NGHS algorithm utilizes position updating and mutation strategy with low probability. By repeatedly adjusting the pitch of the instruments in the band; eventually NGHS reaches a wonderful state of the process of sound.Numerical results show that this method is more effective by solving 3 linear two-point boundary value problems.
Numerical solutions of linear two-point boundary value problems are studied.By using the finite difference method, the discretization of linear two-point boundary value problem is reformed an unconstrained optimization, and solved by heuristic method named novel global harmony search algorithm(NGHS). The NGHS algorithm utilizes position updating and mutation strategy with low probability. By repeatedly adjusting the pitch of the instruments in the band; eventually NGHS reaches a wonderful state of the process of sound.Numerical results show that this method is more effective by solving 3 linear two-point boundary value problems.
引文
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[18] Zou D, Gao L, Li S, et al. Solving 0-1 knapsack problem by a novel global harmony search algorithm[J]. Applied Soft Computing Journal, 2011, 11(3):1556-1564.
[19]雍龙泉.一种全局和声搜索算法求解绝对值方程[J].计算机应用研究,2013, 30(11):3276-3279.
[20] Longquan Yong. Novel global harmony search algorithm for monotone linear complementarity problem[J]. ICIC Express Letters, Part B:Applications, 2014, 5(6):1513-1521.
[21] Longquan Yong, Sanyang Liu, Shouheng Tuo, Kai Gao. Improved harmony search algorithm with chaos for absolute value equation[J]. Telkomnika, 2013, 11(4):835-844.
[22]雍龙泉,刘三阳,拓守恒,等.改进的和声搜索算法求绝对值方程[J].黑龙江大学自然科学学报,2013,30(3):321-327.
[23] Zhao J. Highly accurate compact mixed methods for two point boundary value problems[J]. Applied Mathematics and Computation, 2007, 188(3):1402-1418.
[24]赵志红,徐敏强,林迎珍.基于再生核三次样条基底的构造及其应用[J].数学的实践与认识,2017, 47(6):274-278.
[2]爱德华兹.微分方程及边值问题:计算与模型[M].北京:清华大学出版社,2007.
[3]段俊娜,郭子滔,冯仁忠.基于径向基有限差分法求解带小粘性系数非齐次两点边值问题[J].应用数学进展,2018, 7(1):20-29
[4]朱忠才.带p-Laplacan算子两点边值问题对称正解的存在性[J].佛山科学技术学院学报(自然科学版),2018, 36(3):20-26.
[5]路慧芹.一类非线性两点边值问题的正解[J].数学物理学报,2007, 27(5):845-854.
[6]于淑妹,杨俊仙.一类二阶边值问题解的存在性[J].北京联合大学学报,2013, 27(1):90-92.
[7]梁昌弘,马廷福,葛永斌.两点边值问题的混合型高精度紧致差分格式[J].宁夏大学学报(自然科学版),2017, 38(1):1-4.
[8] Longquan Yong. Richardson iteration for linear equations and application in two-point boundary value problem[J].Journal of Interdisciplinary Mathematics, 2018, 21(1):231-242.
[9]雍龙泉,刘三阳,熊文涛,等.一类二阶线性常微分方程两点边值问题的数值解[J].吉林大学学报(理学版), 2015, 53(1):15-20.
[10]耿发展.求解一些奇异微分方程的再生核方法[D].哈尔滨:哈尔滨工业大学,2009.
[11]雍龙泉.和声搜索算法研究进展[J].计算机系统应用,2011, 20(7):244-248.
[12] Zhao X, Liu Z, Hao J, et al. Semi-self-adaptive harmony search algorithm[J]. Natural Computing,2017, 16(4):1-18.
[13] Wang L, Hu H, Liu R, et al. An improved differential harmony search algorithm for function optimization problems[J]. Soft Computing, 2018(4):1-26.
[14]翟军昌,秦玉平.随机交叉全局和声搜索算法[J].计算机工程与应用,2018, 54(12):21-26.
[15]雍龙泉,拓守恒,史加荣.约束处理技术及应用[J].计算机科学与探索,2018,12(6):1013-1020.
[16] D.X.Zou,L.Q.Gao,J.H.Wu,S.Li,Y.Li.A novel global harmony search algorithm for reliability problems[J]. Computers&Industrial Engineering, 2010, 58(3):307-316.
[17]邹德旋,高立群,吴沛锋,等.一种全局和声搜索算法及在PID控制中的应用[J].东北大学学报(自然科学版),2010,31(11):1534-1537.
[18] Zou D, Gao L, Li S, et al. Solving 0-1 knapsack problem by a novel global harmony search algorithm[J]. Applied Soft Computing Journal, 2011, 11(3):1556-1564.
[19]雍龙泉.一种全局和声搜索算法求解绝对值方程[J].计算机应用研究,2013, 30(11):3276-3279.
[20] Longquan Yong. Novel global harmony search algorithm for monotone linear complementarity problem[J]. ICIC Express Letters, Part B:Applications, 2014, 5(6):1513-1521.
[21] Longquan Yong, Sanyang Liu, Shouheng Tuo, Kai Gao. Improved harmony search algorithm with chaos for absolute value equation[J]. Telkomnika, 2013, 11(4):835-844.
[22]雍龙泉,刘三阳,拓守恒,等.改进的和声搜索算法求绝对值方程[J].黑龙江大学自然科学学报,2013,30(3):321-327.
[23] Zhao J. Highly accurate compact mixed methods for two point boundary value problems[J]. Applied Mathematics and Computation, 2007, 188(3):1402-1418.
[24]赵志红,徐敏强,林迎珍.基于再生核三次样条基底的构造及其应用[J].数学的实践与认识,2017, 47(6):274-278.