基于遗传模拟退火算法的绝对值方程求解

封京梅; 卢楠

doi:10.3969/j.issn.2095-476X.2015.3/4.034

CN 41-1437/TS ISSN 2096-1553

基于遗传模拟退火算法的绝对值方程求解

封京梅 , 卢楠

封京梅, 卢楠. 基于遗传模拟退火算法的绝对值方程求解[J]. 轻工学报, 2015, 30(3-4): 161-164. doi: 10.3969/j.issn.2095-476X.2015.3/4.034

引用本文: 封京梅, 卢楠. 基于遗传模拟退火算法的绝对值方程求解[J]. 轻工学报, 2015, 30(3-4): 161-164. doi: 10.3969/j.issn.2095-476X.2015.3/4.034

FENG Jing-mei and LU Nan. Solving absolute value equations based on genetic simulated annealing algorithm[J]. Journal of Light Industry, 2015, 30(3-4): 161-164. doi: 10.3969/j.issn.2095-476X.2015.3/4.034

Citation: FENG Jing-mei and LU Nan. Solving absolute value equations based on genetic simulated annealing algorithm[J]. Journal of Light Industry, 2015, 30(3-4): 161-164. doi: 10.3969/j.issn.2095-476X.2015.3/4.034

基于遗传模拟退火算法的绝对值方程求解

封京梅 ¹ ,
卢楠 ^{2

,}

陕西广播电视大学工程管理系, 陕西西安 710119;
西安电子科技大学数学与统计学院, 陕西西安 710126

通讯作者: 卢楠

基金项目: 国家自然科学基金项目(11301409)
陕西广播电视大学校级项目(14D-07-B11)
中图分类号: O221;TP301

Solving absolute value equations based on genetic simulated annealing algorithm

FENG Jing-mei ¹ ,
LU Nan ^{2

,}

Department of Project Management, Shanxi Radio TV University, Xi'an 710119, China;
School of Mathematics and Statistics, Xi'an Electronics Science and Technology University, Xi'an 710126, China

Corresponding author: LU Nan,

Received Date: 2014-12-18
Available Online: 2015-09-15
CLC number: O221;TP301

摘要: 将遗传算法的全局搜索能力和模拟退火算法的局部细化能力结合起来,设计了一种新的遗传模拟退火算法(GSAA),将该算法用于求解一类不可微的NP-hard问题:绝对值方程Ax-|x|=b.数值仿真表明,该算法有效地克服了遗传算法易早熟、模拟退火算法运算效率低的缺点.
- 绝对值方程 /
- 遗传算法 /
- 模拟退火算法
Abstract: Combining the global search ability of genetic algorithm and the local refinement ability of simulated annealing algorithm,a new kind of genetic simulated annealing algorithm was designed.The algorithm was used for solving a class of no differentiable NP-hard problem:Absolute value equations Ax-|x|=b.Numerical experiments showed that the algorithm could effectively overcome the shortcomings that the genetic algorithm was easy to premature and simulated annealing algorithm had low efficiency of operation.
- absolute value equation /
- genetic algorithm /
- simulated annealing algorithm
1. [1]
  Mangasarian O L,Meyer R R.Absolute value equations[J].Linear Algebra and Its Application,2006,419(5):359.
2. [2]
  Rohn J.An algorithm for computing all solutions of an absolute value equation[J].Optimization Letters,2012,6(5):851.
3. [3]
  Hu S L,Huang Z H.A note onabsolute value equations[J].Optimization Letters,2009,4(3):417.
4. [4]
  Hu S L,Huang Z H,Zhang Q.A generalized Newton method for absolute value equation associated with second order cones[J].Computational Optimaization and Applications,2011,235:1490.
5. [5]
  Yong L Q,Liu S Y,Feng Q X,et al.Hybrid differential evolution with biogeography-based optimization for absolute value equation[J].Journal of Information & Computational Science,2013,10(8):2417.
6. [6]
  李国成,肖庆宪.绝对值方程的交叉熵蝙蝠算法求解[J].计算机应用研究,2014,28(10):2966.
7. [7]
  刘佳,梁秋丽,王书青,等.基于模拟退火算法的萤火虫群优化算法研究[J].计算机仿真,2014,31(5):284.
8. [8]
  刘波,孟培生.采用基于模拟退火的蚁群算法求解旅行商问题[J].华中科技大学学报:自然科学版,2009,37(11):26.
9. [9]
  卢莉蓉,行小帅,霍冰鹏.基于免疫规划的模拟退火算法[J].计算机工程,2007,33(10):196.
10. [10]
  梁衡,刘新新,郑远攀,等.基于退火遗传算法的无线传感器网络路由优化研究[J].郑州轻工业学院学报:自然科学版,2012,27(6):93.
11. [11]
  梁艳春,吴春国,时小虎,等.群智能优化算法理论与应用[M].北京:北京科学技术出版社,2009:1-33.
12. [12]
  陈宝林.最优化理论与算法[M].2版.北京:清华大学出版社,2005:349-359.
13. [13]
  史峰, 王辉, 胡斐, 等.MATLAB智能算法30个案例分析[M].北京:北京航空航天大学出版社,2011.