中文

Operations Research Transactions >

2020 , Vol. 24 >Issue 4: 63 - 73

DOI: https://doi.org/10.15960/j.cnki.issn.1007-6093.2020.04.005

Non-parameter filled function method for nonlinear integer programming

Expand
  • 1. School of Mathematics and Information Science, North Minzu University, Yinchuan 750021, China;
    2. Ningxia Collaborative Innovation Center of Scientific Computing and Intelligent Information Processing, Yinchuan 750021, China;
    3. Ningxia Province Key Laboratory of Intelligent Information and Data Processing, Yinchuan 750021, China

Received date: 2019-01-11

  Online published: 2020-11-18

Fold

Abstract

In this paper, we proposed a new non-parameter filled function method to solve unconstrained nonlinear integer programming. The filled function we constructed has the same local minimizer with the original objective function, so the computation cost is greatly reduced and the efficiency is improved. In this paper, the numerical experiments of six test functions are carried out, and the results show that the algorithm is effective and feasible.

Key words： global optimization; filled function method; nonlinear integer programming

Cite this article

ZHAO Dan, GAO Yuelin . Non-parameter filled function method for nonlinear integer programming[J]. Operations Research Transactions, 2020 , 24(4) : 63 -73 . DOI: 10.15960/j.cnki.issn.1007-6093.2020.04.005

References

[1] Ge R P. A filled function method for finding a global minimizer of a function of several variables[J]. Mathematical Programming, 1990, 50(1-3):191-204.
[2] Ge R P, Qin Y F. A class of filled functions for finding global minimizers of a function of several variables[J]. Journal of Optimization Theory & Applications, 1987, 54(2):241-252.
[3] Levy A V, Montalvo A. The tunneling algorithm for the global minimization of functions[J]. SIAM Journal on Scientific and Statistical Computing, 1985, 6(1):15-29.
[4] 申培萍. 全局优化方法[M]. 北京:科学出版社, 2006.
[5] 邬冬华, 田蔚文, 张连生, 等. 一种修正的求总极值的积分-水平集方法的实现算法收敛性[J]. 应用数学学报, 2001, 24(1):100-110.
[6] 陈华根, 吴健生, 王家林, 等. 模拟退火算法机理研究[J]. 同济大学学报(自然科学版), 2004, 32(6):802-805.
[7] 邢文训, 谢金星. 现代优化计算方法[M]. 北京:清华大学出版社, 2006.
[8] Leung Y W, Wang Y. Multiobjective programming using uniform design and genetic algorithm[J]. IEEE-transactions on Systems, Man, and Cybernetics, 2000, 30(3):293-304.
[9] Michel L, Hentenryck P V. A simple tabu search for warehouse location[J].European Journal of Operational Research, 2004, 157(3):576-591.
[10] Zhu W X. An approximate algorithm for nonlinear integer programming[J]. European Journal of Operational Research, 1997, 74(1):170-178.
[11] Shang Y L, Zhang L S. A filled function method for finding a global minimizer on global integer optimization[J]. Journal of Computational & Applied Mathematics, 2005, 181(1):200-210.
[12] Ng C K, Zhang L S, Li D, et al. Discrete filled function method for discrete global optimization[J]. Computational Optimization & Applications, 2005, 31(1):87-115.
[13] Ng C K, Li D, Zhang L S. Discrete global descent method for discrete global optimization and nonlinear integer programming[J]. Journal of Global Optimization, 2007, 37(1):357-379.
[14] Yang Y, Liang Y. A new discrete filled function algorithm for discrete global optimization[J]. Journal of Computational & Applied Mathematics, 2007, 202(2):280-291.
[15] Yang Y J, Wu Z Y, Bai F S. A filled function method for constrained nonlinear integer programming[J]. Journal of Industrial & Management Optimization, 2017, 4(2):353-362.
[16] Woon S F, Rehbock V. A critical review of discrete filed function methods solving nonlinear discrete optimization problems[J]. Application Mathematics and Computer Science, 2010, 271(1):25-41.
[17] Yang Y J, He M L, Gao Y L. Discrete global optimization problems with a modified discrete filled function[J]. Journal of the Operations Research Society of China, 2015, 3(3):297-315.
[18] Wei F, Wang Y, Lin H. A new filled function method with two parameters for global optimization[J]. Journal of Optimization Theory & Applications, 2014, 163(2):510-527.
[19] 高岳林, 吴佩佩. 非线性整数规划的一个新的无参数填充函数算法[J]. 计算数学, 2017, 39(3):321-327.
Options
Outlines

/

〈 〉