Journal of Combinatorial Optimization

, Volume 31, Issue 1, pp 95–117 | Cite as

Algorithms for randomized time-varying knapsack problems

  • Yichao He
  • Xinlu Zhang
  • Wenbin Li
  • Xiang Li
  • Weili Wu
  • Suogang Gao
Article
First Online:

Abstract

In this paper, we first give the definition of randomized time-varying knapsack problems (\(\textit{RTVKP}\)) and its mathematic model, and analyze the character about the various forms of \(\textit{RTVKP}\). Next, we propose three algorithms for \(\textit{RTVKP}\): (1) an exact algorithm with pseudo-polynomial time based on dynamic programming; (2) a 2-approximation algorithm for \(\textit{RTVKP}\) based on greedy algorithm; (3) a heuristic algorithm by using elitists model based on genetic algorithms. Finally, we advance an evaluation criterion for the algorithm which is used for solving dynamic combinational optimization problems, and analyze the virtue and shortage of three algorithms above by using the criterion. For the given three instances of \(\textit{RTVKP}\), the simulation computation results coincide with the theory analysis.

Keywords

Knapsack problem Exact algorithm Approximations Heuristics 
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Notes

Acknowledgments

Support in part by NSF of China (No. 11271257), the Specialized Research Fund for the Doctoral Program of Higher Education of China (No. 20121303110005), the NSF of Hebei Province (No. A2013205021).

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Yichao He
    • 1
  • Xinlu Zhang
    • 2
  • Wenbin Li
    • 3
  • Xiang Li
    • 4
  • Weili Wu
    • 5
  • Suogang Gao
    • 2
  1. 1.College of Information EngineeringShijiazhuang University of EconomicsShijiazhuang China
  2. 2.College of Mathematics and Information ScienceHebei Normal UniversityShijiazhuang China
  3. 3.Laboratory of Network and Information SecurityShijiazhuang University of EconomicsShijiazhuang China
  4. 4.Department of Industrial and System EngineeringUniversity of FloridaGainesvilleUSA
  5. 5.Department of Computer ScienceUniversity of Texas at DallasRichardsonUSA

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