An Evolutionary Strategy for the Multidimensional 0-1 Knapsack Problem Based on Genetic Computation of Surrogate Multipliers

  • César L. Alonso
  • Fernando Caro
  • José Luis Montaña
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3562)


In this paper we present an evolutionary algorithm for the multidimensional 0–1 knapsack problem. Our algorithm incorporates a heuristic operator which computes problem-specific knowledge. The design of this operator is based on the general technique used to design greedy-like heuristics for this problem, that is, the surrogate multipliers approach of Pirkul (see [7]). The main difference with work previously done is that our heuristic operator is computed following a genetic strategy -suggested by the greedy solution of the one dimensional knapsack problem- instead of the commonly used simplex method. Experimental results show that our evolutionary algorithm is capable of obtaining high quality solutions for large size problems requiring less amount of computational effort than other evolutionary strategies supported by heuristics founded on linear programming calculation of surrogate multipliers.


Evolutionary computation genetic algorithms knapsack problem 0–1 integer programming combinatorial optimization 


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  1. 1.
    Balas, E., Martin, C.H.: Pivot and Complement–A Heuristic for 0–1 Programming. Management Science 26(1), 86–96 (1980)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Balas, E., Zemel, E.: An Algorithm for Large zero–one Knapsack Problems. Operations Research 28, 1130–1145 (1980)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Beasley, J.E.: Obtaining Test Problems via Internet. Journal of Global Optimization 8, 429–433 (1996)zbMATHCrossRefGoogle Scholar
  4. 4.
    Chu, P.C., Beasley, J.E.: A Genetic Algorithm for the Multidimensional Knapsack Problem. Journal of Heuristics 4, 63–86 (1998)zbMATHCrossRefGoogle Scholar
  5. 5.
    Freville, A., Plateau, G.: Heuristics and Reduction Methods for Multiple Constraints 0–1 Linear Programming Problems. Europena Journal of Operationa Research 24, 206–215 (1986)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Gavish, B., Pirkul, H.: Allocation of Databases and Processors in a Distributed Computing System. In: Akoka, J. (ed.) Management od Distributed Data Processing, pp. 215–231. North-Holland, Amsterdam (1982)Google Scholar
  7. 7.
    Gavish, B., Pirkul, H.: Efficient Algorithms for Solving Multiconstraint Zero–One Knapsack Problems to Optimality. Mathematical Programming 31, 78–105 (1985)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Goldberg, D.E.: Genetic Algorithms in Search, Optimization and Machine Learning. Addison-Wesley, Reading (1989)zbMATHGoogle Scholar
  9. 9.
    Khuri, S., Bäck, T., Heitkötter, J.: The Zero/One Multiple Knapsack Problem and Genetic Algorithms. In: Proceedings of the 1994 ACM Symposium on Applied Computing (SAC 1994), pp. 188–193. ACM Press, New York (1994)CrossRefGoogle Scholar
  10. 10.
    Martello, S., Toth, P.: Knapsack Problems: Algorithms and Computer Implementations. John Wiley & Sons, Chichester (1990)zbMATHGoogle Scholar
  11. 11.
    Pirkul, H.: A Heuristic Solution Procedure for the Multiconstraint Zero–One Knapsack Problem. Naval Research Logistics 34, 161–172 (1987)zbMATHCrossRefGoogle Scholar
  12. 12.
    Raidl, G.R.: An Improved Genetic Algorithm for the Multiconstraint Knapsack Problem. In: Proceedings of the 5th IEEE International Conference on Evolutionary Computation, pp. 207–211 (1998)Google Scholar
  13. 13.
    Rinnooy Kan, A.H.G., Stougie, L., Vercellis, C.: A Class of Generalized Greedy Algorithms for the Multi-knapsack Problem. Discrete Applied Mathematics 42, 279–290 (1993)zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Thiel, J., Voss, S.: Some Experiences on Solving Multiconstraint Zero–One Knapsack Problems with Genetic Algorithms. INFOR 32, 226–242 (1994)zbMATHGoogle Scholar
  15. 15.
    Vasquez, M., Hao, J.K.: A Logic-constrained Knapsack Formulation and a Tabu Algorithm for the Daily Photograph Scheduling of an Earth Observation Satellite. Computational Optimization and Applications 20, 137–157 (2001)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • César L. Alonso
    • 1
  • Fernando Caro
    • 2
  • José Luis Montaña
    • 3
  1. 1.Centro de Inteligencia ArtificialUniversidad de OviedoGijónSpain
  2. 2.Departamento de InformáticaUniversidad de Oviedo 
  3. 3.Departamento de Matemáticas, Estadística y ComputaciónUniversidad de Cantabria 

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