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Experimental results on Hillier's linear search

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Abstract

This paper reports an empirical discovery in integer programming. A version of the branch-and-bound approach is used as a control and tested against the same algorithm augmented by the use of Hillier's linear search performed at every node of the search tree. It is shown that the imbedded linear search locates solutions within 1%, and solutions within 5% of the theoretical optimum, which in fact can be seen to have this proximity to the theoretical optimum at the time of termination of computation, over ten times faster than the control.

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References

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

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  2. F.S. Hillier, “Efficient heuristic procedures for integer linear programming with an interior”,Operations Research 17 (1969) 600–637.

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  3. T. Ibaraki, T. Ohashi and H. Mine, “A heuristic algorithm for mixed-integer programming problems”,Mathematical Programming Study 2 (1974) 115–136.

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  4. R.G. Jeroslow and T.H.C. Smith, “Experimental results on Hillier's search imbedded in a branch-and-bound algorithm”, Management Sciences Research Rept. No. 326, GSIA, Carnegie-Mellon University, Pittsburgh, Pa. (November 1973).

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

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Authors and Affiliations

  1. Carnegie-Mellon University, Pittsburgh, Pa., USA

    R. G. Jeroslow & T. H. C. Smith

Authors
  1. R. G. Jeroslow
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  2. T. H. C. Smith
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Additional information

The results of this paper were first reported in a talk given by the first author at the Eighth International Symposium on Mathematical Programming, Stanford University, August 29, 1973.

Supported by NSF Grant GP-37510X.

Supported by a grant from the Council for Scientific and Industrial Research, Republic of South Africa, and by ONR Grant N00014-67-A-0314-007.

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Jeroslow, R.G., Smith, T.H.C. Experimental results on Hillier's linear search. Mathematical Programming 9, 371–376 (1975). https://doi.org/10.1007/BF01681357

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  • DOI: https://doi.org/10.1007/BF01681357

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