非线性二层混合整数规划问题的区间算法

doi:10.6040/j.issn.1671-9352.0.2017.135

山东大学学报（理学版） ›› 2018, Vol. 53 ›› Issue (2): 9-17.doi: 10.6040/j.issn.1671-9352.0.2017.135

非线性二层混合整数规划问题的区间算法

刘园园¹,曹德欣^1*,秦军²

1.中国矿业大学数学学院, 江苏徐州 221000;2.新华三技术有限公司, 北京 100085

收稿日期:2017-03-31 出版日期:2018-02-20 发布日期:2018-01-31
通讯作者: 曹德欣(1962— ),男,教授,博士生导师,研究方向为数值优化. E-mail:caodx@cumt.edu.com E-mail:1446706637@qq.com
作者简介:刘园园(1990— ),女,硕士研究生,研究方向为区间算法及应用. E-mail:1446706637@qq.com

Interval algorithm for mixed integer nonlinear two-level programming problems

1. College of Mathematics, China University of Mining and Technology, Xuzhou 221000, Jiangsu, China;
2. New H3C Technologies Co. Ltd., Beijing 100085, China

Received:2017-03-31 Online:2018-02-20 Published:2018-01-31

摘要/Abstract

摘要： 讨论了目标函数和约束条件均为一阶连续可微函数的带约束非线性二层混合整数规划问题的区间算法。利用罚函数法和构造目标函数的区间扩张、无解区域的删除检验原则,建立了求解非线性二层混合整数规划问题的区间算法,并进行了数值实验。结论证明和数值实验均表明该算法是可行且有效的。

关键词: 非线性二层规划, 整数规划, 区间算法, 罚函数

Abstract: The interval algorithm for a class of constrained mixed integer nonlinear two-level programming problems is discussed, in which the objective functions and constrained functions are in C¹. Based on the penalty function method and constructing the interval extensions of two-level objective functions and introducing the test rules of region deletion, an interval algorithm for solving mixed integer nonlinear two-level programming problems is established. Experimentation upon numerical examples is performed. Both theoretical proof and numerical experiments show that the algorithm is reliable and effective.

Key words: nonlinear two-level programming, interval algorithm, penalty function, integer programming

中图分类号:

O242.29

刘园园,曹德欣,秦军. 非线性二层混合整数规划问题的区间算法[J]. 山东大学学报（理学版）, 2018, 53(2): 9-17.

参考文献

[1] MOOER J T, BARD J F.The mixed integer linear bilevel programming problem[J]. Operations Research, 1990,(38):911-921.
[2] BARD J, MOOER J T. An algorithm for the discrete bilevel programming problem[J]. Naval Research Logistics, 1992,(39):419-435.
[3] EDMUNDS T, BARD J. An algorithm for the mixed-integer nonlinear bilevel programming problem[J]. Annals of Operations Research, 1992, 34: 149-162.
[4] 秦军,曹德欣.一类二层规划问题的区间算法[J].计算机工程与应用,2012,48(7):51-54. QIN Jun, CAO Dexin. Interval algorithm for a class of two-level programming problems[J]. Computer Engineering and Applications, 2012, 48(7):51-54.
[5] 秦军,曹德欣.一类无约束二层规划问题的区间算法[J].山东大学学报(理学版), 2012,47(3):120-126. QIN Jun, CAO Dexin. An interval algorithm for a class of unconstrained two-level programming problems[J]. Journal of Shangdong University(Natural Science), 2012, 47(3):120-126.
[6] MOORE R E. Methods and applications of interval analysis[M]. Philadelphia: SIAM, 1979.
[7] RATSCHEK H, ROKNE J. New computer methods for global optimization[M]. Chichester: Ellis Horwood Limited, 1988.
[8] RATSCHEK H, ROKNE J. Computer methods for range of functions[M]. Chichester: Ellis Horwood Limited, 1984.
[9] BAUMANN E. Optimal centered forms[J]. BIT, 1988, 28:80-87.
[10] HANSEN E. Sharpening interval computions[J]. Reliable Computing, 2006, 12(1):21-34.
[11] 叶帅民. 两层规划问题的区间算法研究[D]. 徐州:中国矿业大学,2000. YE Shuaimin. Study on the interval algorithms for solving bilevel programming problem[D]. Xuzhou: China University of Mining and Technology, 2000.
[12] 韩进,仲伟俊. 含整变量两层决策问题的禁忌搜索解法[J]. 系统工程理论方法应用,1999,8(3):27-33. HAN jin, ZHONG Weijun. Solving the integer bilevel decision making problem by Tabu search[J]. Systems Engineering Theory Methodology Applications, 1999, 8(3):27-33.
[13] 宿伟玲,郑丕谔,李彤. 非线性两级整数规划问题的最优化方法[J].天津大学学报,2003,36(4):512-517. SU Weiling, ZHENG Pie, LI Dong. A global optimization method for nonlinear bilevel integer programming[J]. Journal of Tianjin University, 2003, 36(4):512-517.
[14] 张建雄,唐万生.基于混沌遗传算法的一类非线性两层混合整数规划问题求解[J].系统工程理论方法应用,2005,14(5):429-433. ZHANG Jianxiong, TANG Wansheng. Chaos cenetic algorithm method for a class of nonlinear bilevel mixed integer programming problem[J]. Systems Engineering Theory Methodology Applications, 2005, 14(5):429-433.

多维度评价

Viewed

Full text

Abstract

Cited

Shared

Discussed

非线性二层混合整数规划问题的区间算法

Interval algorithm for mixed integer nonlinear two-level programming problems

PDF (PC)

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 5

多维度评价

本文评价

推荐阅读 0

[1]	郑英杰,周岩. 考虑零售商横向公平的二层供应链网络均衡决策[J]. 山东大学学报（理学版）, 2018, 53(9): 69-82.
[2]	李双安,陈凤华,赵艳伟. 超记忆梯度法在大规模信号重构问题中的应用[J]. 山东大学学报（理学版）, 2017, 52(1): 65-73.
[3]	崔安刚,李海洋. 仿射约束矩阵秩最小问题与无约束矩阵秩最小问题的等价性[J]. 山东大学学报（理学版）, 2016, 51(4): 86-89.
[4]	秦军,曹德欣. 一类无约束二层规划问题的区间算法[J]. J4, 2012, 47(3): 120-126.
[5]	丁卫平1,2,3,王建东2,段卫华2,施佺1. 一种求解属性约简优化的协同粒子群算法[J]. J4, 2011, 46(5): 97-102.