Journal of Heuristics

, Volume 8, Issue 2, pp 215–239

Cooperative Strategies for Solving the Bicriteria Sparse Multiple Knapsack Problem

  • F. Sibel Salman
  • Jayant R. Kalagnanam
  • Sesh Murthy
  • Andrew Davenport


For hard optimization problems, it is difficult to design heuristic algorithms which exhibit uniformly superior performance for all problem instances. As a result it becomes necessary to tailor the algorithms based on the problem instance. In this paper, we introduce the use of a cooperative problem solving team of heuristics that evolves algorithms for a given problem instance. The efficacy of this method is examined by solving six difficult instances of a bicriteria sparse multiple knapsack problem. Results indicate that such tailored algorithms uniformly improve solutions as compared to using predesigned heuristic algorithms.

multiple knapsack bicriteria multiple heuristics cooperation asynchronous teams 


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  1. Battiti, R. and G. Tecchiolli. (1994). “The Reactive Tabu Search.” ORSA Journal on Computing 6(2), 120–140.Google Scholar
  2. Coffman, E., M. Garey, and D. Johnson. (1984). “Approximation Algorithms for Binpacking: An Updated Survey.” In G. Ausiello, M. Lucertini, and P. Serafini (eds.), Algorithm Design for Computer System Design. Wien: Springer-Verlag, pp. 49–106.Google Scholar
  3. Coffman, E., M. Garey, and D. Johnson. (1997). “Approximation Algorithms for Binpacking: A Survey.” In D. Hochbaum (ed.), Approximation Algorithms for NP-hard Problems. Boston: PWS Publishing Company, pp. 46–93.Google Scholar
  4. CPLEX (1994). “Using the CPLEX Linear Optimizer.” CPLEX Optimization Inc.Google Scholar
  5. Dawande, M., J. Kalagnanam, P. Keskinocek, R. Ravi, and F.S. Salman. (1998). “Approximation Algorithms for the Multiple Knapsack Problem with Assignment Restrictions.” Technical Report, IBM T. J. Watson Research Center, P.O. Box 18, Yorktown Heights, New York 10598, USA.Google Scholar
  6. Erman, L.D., F.A. Hayes-Roth, V.R. Lesser, and D.R. Reddy. (1980). “The Hearsay-II Speech-Understanding System: Integrating Knowledge to Resolve Uncertainty.” Computing Surveys 12, 213–253.Google Scholar
  7. Ferreira, C., A. Martin, and R. Weismantel. (1996). “Solving Multiple Knapsack Problems by Cutting Planes.” SIAM J. Optimization 6(3), 858–877.Google Scholar
  8. Friesen, D. and M. Langston. (1986). “Variable Sized Bin Packing.” SIAM J. Computing 15, 222–230.Google Scholar
  9. Garey, M. and D. Johnson. (1979). Computers and Intractibility: A Guide to the Theory of NP-Completeness. San Francisco: W.H. Freeman and Co.Google Scholar
  10. Glover, F. (1989). “Tabu Search Part I.” Operations Research Society of America (ORSA) Journal on Computing 1(3), 109–206.Google Scholar
  11. Glover, F. (1990). “Tabu Search Part II.” Operations Research Society of America (ORSA) Journal on Computing 2(1), 4–32.Google Scholar
  12. Gomes, C.P. and B. Selman. (1997). “Algorithm Portfolio Design: Theory vs. Practice.” In Proc. Uncertainty in Artificial Intelligence.Google Scholar
  13. Holland, J.H. (1975). Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence. Ann Arbor, MI: University of Michigan Press.Google Scholar
  14. Huberman, B.A., R.M. Lukose, and T. Hogg. (1997). “An Economics Approach to Hard Computational Problems.” Science 265, 51–54.Google Scholar
  15. Hung, M. and J. Fisk. (1978). “An Algorithm for 0-1 Multiple Knapsack Problems.” Naval Res. Logist. Quarterly 24, 571–579.Google Scholar
  16. Kalagnanam, J., M. Dawande, M. Trumbo, and H.S. Lee. (1998). “The Surplus Inventory Matching Problem in the Process Industry.” Technical Report RC21071, IBM T. J. Watson Research Center.Google Scholar
  17. Karp, R. (1972). “Reducibility among Combinatorial Problems.” In R. Miller and J. Thatcher (eds.), Complexity of Computer Computations. New York: Plenum Press, pp. 85–103.Google Scholar
  18. Keskinocak, P., F. Wu, R. Goodwin, S. Murthy, R. Akkiraju, S. Kumaran, and A. Derebail. (1998). “Scheduling Solutions for the Paper Industry.” Technical Report, IBM T. J.Watson Research Center, P.O. Box 18, Yorktown Heights, New York 10598.Google Scholar
  19. Lee, H., S. Murthy, S. Haider, and D. Morse. (1996). “Primary Production Scheduling at Steel-Making Industries.” IBM Journal of Research and Development.Google Scholar
  20. Martello, S. and P. Toth. (1980). “Solution of the Zero-One Multiple Knapsack Problem.” Euro. J. Oper. Res. 4, 322–329.Google Scholar
  21. Martello, S. and P. Toth. (1981a). “A Bound and Bound Algorithm for the Zero-One Multiple Knapsack Problem.” Discrete Applied Math. 3, 275–288.Google Scholar
  22. Martello, S. and P. Toth. (1981b). “Heuristic Algorithms for the Multiple Knapsack Problem.” Computing 27, 93–112.Google Scholar
  23. Martello, S. and P. Toth. (1989). Knapsack Problems. New York: John Wiley and Sons.Google Scholar
  24. Martello, S. and P. Toth. (1990). Lower Bounds and Reduction Procedures for the Bin Packing Problem. Discrete Applied Math. 28, 59–70.Google Scholar
  25. Mockus, J. (1989). Bayesian Approach to Global Optimization. Dordrecht: Kluwer Academic Publishers.Google Scholar
  26. Murthy, S. (1992). “Synergy in Cooperating Agents: Designing Manipulators from Task Specifications.” Ph.D. Thesis, Dept. of Electrical and Computer Engineering, Carnegie Mellon University.Google Scholar
  27. Murthy, S., R. Akkiraju, J. Rachlin, and F. Wu. (1997). “Agent-Based Cooperative Scheduling.” In E.C. Charniak (ed.), Constraints and Agents, AAAI-97 Workshop, pp. 112–117.Google Scholar
  28. Näher, S. and C. Uhrig. (1995). Leda User Manual. Saarbrücken, Germany: Max-Planck-Institute für Informatik.Google Scholar
  29. Rodosek, R., M.G. Wallace, and M.T. Hajian. (1999). “ANewApproach to Integrating Mixed Integer Programming with Constraint Logic Programming.” In Annals of Operational Research: Recent Advances in Combinatorial Optimization: Theory and Applications.Google Scholar
  30. Smith, S.F., P.S. Ow, J. Potwin, N. Muscettola, and D.C. Matthys. (1990). “An Integrated Framework for Generating and Revising Factory Schedules.” Journal of the Operational Research Society 41, 539–552.Google Scholar
  31. Talukdar, S. and P. de Souza. (1993). “Asynchronous Organizations for Multi-Algorithm Problems.” In E. Deaton, H. George, K.M. Bergel, and G. Hedrick (eds.), Proceeding of 8th SIGAPP Symposium on Applied Computing, pp. 286–293.Google Scholar
  32. Talukdar, S., P. de Souza, and S. Murthy. (1993). “Organizations for Computer-Based Agents.” Engineering Intelligent Systems 1(2).Google Scholar

Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • F. Sibel Salman
    • 1
  • Jayant R. Kalagnanam
    • 2
  • Sesh Murthy
    • 2
  • Andrew Davenport
    • 2
  1. 1.GSIA, Carnegie Mellon UniversityPittsburghUSA
  2. 2.IBM T. J. Watson Research CenterYorktown HeightsUSA

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