Algorithms for randomized time-varying knapsack problems

Yichao He (), Xinlu Zhang (), Wenbin Li, Xiang Li (), Weili Wu () and Suogang Gao ()
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Yichao He: Shijiazhuang University of Economics
Xinlu Zhang: Hebei Normal University
Wenbin Li: Shijiazhuang University of Economics
Xiang Li: University of Florida
Weili Wu: University of Texas at Dallas
Suogang Gao: Hebei Normal University

Journal of Combinatorial Optimization, 2016, vol. 31, issue 1, No 9, 95-117

Abstract: Abstract In this paper, we first give the definition of randomized time-varying knapsack problems ( $$\textit{RTVKP}$$ RTVKP ) and its mathematic model, and analyze the character about the various forms of $$\textit{RTVKP}$$ RTVKP . Next, we propose three algorithms for $$\textit{RTVKP}$$ RTVKP : (1) an exact algorithm with pseudo-polynomial time based on dynamic programming; (2) a 2-approximation algorithm for $$\textit{RTVKP}$$ 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 $$\textit{RTVKP}$$ RTVKP , the simulation computation results coincide with the theory analysis.

Keywords: Knapsack problem; Exact algorithm; Approximations; Heuristics (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10878-014-9717-1

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