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An Integer Linear Programming Model for Binary Knapsack Problem with Dependent Item Values

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AI 2017: Advances in Artificial Intelligence (AI 2017)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10400))

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Abstract

Binary Knapsack Problem (BKP) is to select a subset of items with the highest value while keeping the size within the capacity of the knapsack. This paper presents an Integer Linear Programming (ILP) model for a variation of BKP where the value of an item may depend on presence or absence of other items in the knapsack. Strengths of such Value-Related Dependencies are assumed to be imprecise and hard to specify. To capture this imprecision, we have proposed modeling value-related dependencies using fuzzy graphs and their algebraic structure. We have demonstrated through simulations that our proposed ILP model is scalable to large number of items.

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Authors and Affiliations

  1. School of Computer Science, Engineering, and Mathematics, Flinders University, Adelaide, Australia

    Davoud Mougouei, David M. W. Powers & Asghar Moeini

Authors
  1. Davoud Mougouei
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  2. David M. W. Powers
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  3. Asghar Moeini
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Corresponding author

Correspondence to Davoud Mougouei .

Editor information

Editors and Affiliations

  1. La Trobe University, Melbourne, Australia

    Wei Peng

  2. La Trobe Business School, La Trobe University, Bundoora, Victoria, Australia

    Damminda Alahakoon

  3. RMIT University, Melbourne, Australia

    Xiaodong Li

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Mougouei, D., Powers, D.M.W., Moeini, A. (2017). An Integer Linear Programming Model for Binary Knapsack Problem with Dependent Item Values. In: Peng, W., Alahakoon, D., Li, X. (eds) AI 2017: Advances in Artificial Intelligence. AI 2017. Lecture Notes in Computer Science(), vol 10400. Springer, Cham. https://doi.org/10.1007/978-3-319-63004-5_12

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  • DOI: https://doi.org/10.1007/978-3-319-63004-5_12

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-63003-8

  • Online ISBN: 978-3-319-63004-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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