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Algorithms for randomized time-varying knapsack problems

Algorithms for randomized time-varying knapsack problems 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Combinatorial Optimization Springer Journals

Algorithms for randomized time-varying knapsack problems

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References (41)

Publisher
Springer Journals
Copyright
Copyright © 2014 by Springer Science+Business Media New York
Subject
Mathematics; Combinatorics; Convex and Discrete Geometry; Mathematical Modeling and Industrial Mathematics; Theory of Computation; Optimization; Operation Research/Decision Theory
ISSN
1382-6905
eISSN
1573-2886
DOI
10.1007/s10878-014-9717-1
Publisher site
See Article on Publisher Site

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.

Journal

Journal of Combinatorial OptimizationSpringer Journals

Published: Feb 23, 2014

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