JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2018, Vol. 53 ›› Issue (2): 9-17.doi: 10.6040/j.issn.1671-9352.0.2017.135

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Interval algorithm for mixed integer nonlinear two-level programming problems

  

  1. 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

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

CLC Number: 

  • O242.29
[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.
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