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An Algorithm for Nonlinear Knapsack Problems

Author

Listed:
  • Thomas L. Morin

    (The Technological Institute, Northwestern University)

  • Roy E. Marsten

    (Sloan School of Management, Massachusetts Institute of Technology)

Abstract

An algorithm which recursively generates the complete family of undominated feasible solutions to separable nonlinear multidimensional knapsack problems is developed by exploiting discontinuity preserving properties of the maximal convolution. The "curse of dimensionality," which is usually associated with dynamic programming algorithms, is successfully mitigated by reducing an M-dimensional dynamic program to a 1-dimensional dynamic program through the use of the imbedded state space approach. Computational experience with the algorithm on problems with as many as 10 state variables is also reported and several interesting extensions are discussed.

Suggested Citation

  • Thomas L. Morin & Roy E. Marsten, 1976. "An Algorithm for Nonlinear Knapsack Problems," Management Science, INFORMS, vol. 22(10), pages 1147-1158, June.
    • Handle: RePEc:inm:ormnsc:v:22:y:1976:i:10:p:1147-1158
    DOI: 10.1287/mnsc.22.10.1147
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    Cited by:

    1. Kurt M. Bretthauer & Bala Shetty & Siddhartha Syam, 2003. "A specially structured nonlinear integer resource allocation problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 50(7), pages 770-792, October.
    2. SYAFITRI, Utami & SARTONO, Bagus & GOOS, Peter, 2015. "D- and I-optimal design of mixture experiments in the presence of ingredient availability constraints," Working Papers 2015003, University of Antwerp, Faculty of Business and Economics.
    3. AgralI, Semra & Geunes, Joseph, 2009. "Solving knapsack problems with S-curve return functions," European Journal of Operational Research, Elsevier, vol. 193(2), pages 605-615, March.
    4. Safer, Hershel M. & Orlin, James B., 1953-, 1995. "Fast approximation schemes for multi-criteria combinatorial optimization," Working papers 3756-95., Massachusetts Institute of Technology (MIT), Sloan School of Management.

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