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

  • Davoud MougoueiEmail author
  • David M. W. Powers
  • Asghar Moeini
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10400)


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.


Binary knapsack problem Integer linear programming Dependency Value Fuzzy graph 


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Davoud Mougouei
    • 1
    Email author
  • David M. W. Powers
    • 1
  • Asghar Moeini
    • 1
  1. 1.School of Computer Science, Engineering, and MathematicsFlinders UniversityAdelaideAustralia

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