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Multicriteria integer programming: A (hybrid) dynamic programming recursive approach

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Abstract

Dynamic programming recursive equations are used to develop a procedure to obtain the set of efficient solutions to the multicriteria integer linear programming problem. An alternate method is produced by combining this procedure with branch and bound rules. Computational results are reported.

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References

  1. R.L. Banker, M. Guinard and S.K. Gupta, “An algorithm for generating efficient solutions to the multiple objective integer programming problem”, Working Paper, The Wharton School, University of Pennsylvania (1978).

  2. R.E. Bellman,Dynamic programming (Princeton University Press, Princeton, NJ, 1957).

    Google Scholar 

  3. G.R. Bitran, “Linear multiple objective programs with zero—one variables”,Mathematical Programming 13 (1977) 121–139.

    Google Scholar 

  4. G.R. Bitran, “Theory and algorithms for linear multiple objective programs with zero–one variables”, Technical Report No. 150, Operations Research Center, Massachusetts Institute of Technology (1978).

  5. V.J. Bowman, “On the relationship of the Tchebycheff norm and the efficient frontier of multiple criteria objectives”, in H. Thiriez and S. Zionts, eds.,Multiple criteria decision making (Jouy-en-Josas, France, 1975) (Springer-Verlag, Berlin, 1976) pp. 76–85.

    Google Scholar 

  6. A.M. Geoffrion, “Proper efficiency and the theory of vector maximization”,Journal of Mathematical Analysis and Applications 22 (1968) 618–630.

    Google Scholar 

  7. A.M. Geoffrion, “Lagrangian relaxation and its uses in integer programming”,Mathematical Programming Study 2 (1974) 82–114.

    Google Scholar 

  8. F. Glover, “Surrogate constraint duality in mathematical programming”,Operations Research 23 (1975) 434–451.

    Google Scholar 

  9. H.J. Greenberg and W.P. Pierskalla, “Surrogate mathematical programming”,Operations Research 18 (1970) 1138–1162.

    Google Scholar 

  10. M.H. Karwan and R.L. Rardin, “Some relationships between lagrangian and surrogate duality in integer linear programming”,Mathematical Programming 17 (1979) 320–334.

    Google Scholar 

  11. R. Loulou and E. Michaelides, “New greedy—like heuristics for the multidimensional 0–1 knapsack problem”, Worker Paper, McGill University (1977).

  12. R.E. Marsten and T.L. Morin, “A hybrid approach to discrete mathematical programming”,Mathematical programming 14 (1978) 21–40.

    Google Scholar 

  13. T.L. Morin and A.M.O. Esobgue, “The imbedded state space approach to reducing dimensionality in dynamic programs of higher dimensions”,Journal of Mathematical Analysis and Applications 48 (1974) 801–810.

    Google Scholar 

  14. T.L. Morin and R.E. Marsten, “Branch and bound strategies for dynamic programming”,Operations Research 24 (1976) 611–627.

    Google Scholar 

  15. T.L. Morin and R.E. Marsten, “An algorithm for nonlinear knapsack problems”,Management Science 22 (1976) 1147–1158.

    Google Scholar 

  16. G.L. Nemhauser,Introduction to dynamic programming (Wiley, New York, 1966).

    Google Scholar 

  17. G.L. Nemhauser and R.S. Garfinkel,Integer programming (Wiley, New York, 1972).

    Google Scholar 

  18. C.C. Petersen, “Computational experience with variants of the Balas algorithm applied to the selection of R & D projects”,Management Science 13 (1967) 736–750.

    Google Scholar 

  19. A.K. Simopoulos, “Multicriteria integer zero–one programming: A tree-search type algorithm”, Masters Thesis, Naval Postgraduate School (Monterey, CA, 1977).

    Google Scholar 

  20. Y. Toyoda, “A simplified algorithm for obtaining approximate solutions to zero–one programming problems”,Management Science 21 (1975) 1417–1427.

    Google Scholar 

  21. B. Villarreal and M.H. Karwan, “Dynamic programming approaches for multicriterion integer programming”, Working Paper 78-3, State University of New York at Buffalo (1978).

  22. B. Villarreal, Personal notes for PhD dissertation, State University of New York at Buffalo (1978).

  23. P.L. Yu and M. Zeleny, “The set of all nondominated solutions in linear cases and a multicriteria simplex method”,Journal of Mathematical Analysis and Applications 49 (1975) 430–468.

    Google Scholar 

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Villarreal, B., Karwan, M.H. Multicriteria integer programming: A (hybrid) dynamic programming recursive approach. Mathematical Programming 21, 204–223 (1981). https://doi.org/10.1007/BF01584241

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  • DOI: https://doi.org/10.1007/BF01584241

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