MVRC Heuristic for Solving the Multi-Choice Multi-Constraint Knapsack Problem

  • Maria Chantzara
  • Miltiades Anagnostou
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3991)


This paper presents the heuristic algorithm Maximizing Value per Resources Consumption (MVRC) that solves the Multi-Choice Multi-Constraint Knapsack Problem, a variant of the known NP-hard optimization problem called Knapsack problem. Starting with an initial solution, the MVRC performs iterative improvements through exchanging the already picked items in order to conclude to the optimal solution. Following a three step procedure, it tries to pick the items with the maximum Value per Aggregate Resources Consumption. The proposed algorithm has been evaluated in terms of the quality of the final solution and its run-time performance.


Feasible Solution Resource Constraint Resource Consumption Knapsack Problem Iterative Improvement 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Khan, S., Kin, F.L., Manning, E., Akbar, M.: Solving the Knapsack Problem for Adaptive Multimedia Systems. Studia Informatica 2(1), 154–174 (2002); Special Issue on Combinatorial ProblemsGoogle Scholar
  2. 2.
    Chantzara, M., Anagnostou, M.: Evaluation and Selection of Context Information. In: Proceedings of the 2nd International Workshop on Modelling and Retrieval of Context (MRC 2005), Edinburgh, Scotland, July 31- August 1. CEUR Workshop Proceedings (2005) ISSN 1613-0073Google Scholar
  3. 3.
    Martello, S., Toth, P.: Knapsack Problems: Algorithms and Computer Implementations. Wiley-Inrescience Series in Discrete Mathematics and Optimization. John Wiley & Sons, Chichester (1990)MATHGoogle Scholar
  4. 4.
    Kellerer, H., Pferschy, U., Pisinger, D.: Knapsack Problems, p. 546. Springer, Heidelberg (2004) ISBN: 3-540-40286-1MATHGoogle Scholar
  5. 5.
    Khan, S.: Quality Adaptation in a Multi-Session Adaptive Multimedia System: Model, Algorithms and Architecture. PhD Thesis, Department of Electronical and Computer Engineering, University of Victoria, Canada (1998)Google Scholar
  6. 6.
    Moser, M., Jokanovic, D., Shiratori, N.: An Algorithm for the Multidimensional Multiple-Choice Knapsack Problem. IECE Trans Fundamentals Electron 80, 582–589 (1997)Google Scholar
  7. 7.
    Toyoda, Y.: A Simplified Algorithm for Obtaining Approximate Solutions to Zero-one Programming Problems. Management Science 21(12), 1417–1427 (1975)MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Akbar, M., Rahman, M., Kaykobad, M., Manning, E., Shoja, G.: Solving the Multidimensional Multiple-choice Knapsack Problem by Constructing Convex Hulls. Computers & Operations Research 33(5), 1259–1273 (2006)MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Hifi, M., Micrafy, M., Sbihi, A.: Heuristic Algorithms for the Multiple-choice Multidimensional Knapsack Problem. Journal of the Operational Research Society 55, 1323–1332 (2004)MATHCrossRefGoogle Scholar
  10. 10.
    Pisinger, D.: Where are the hard knapsack problems? Computers and Operations Research 32(9), 2271–2284 (2005)MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Cormen, T., Leiserson, C., Rivest, R., Stein, C.: Introduction to Algorithms. MIT Press and McGraw-HillGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Maria Chantzara
    • 1
  • Miltiades Anagnostou
    • 1
  1. 1.School of Electrical & Computer EngineeringNational Technical University of AthensZografou, AthensGreece

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