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An accelerated covering relaxation algorithm for solving 0–1 positive polynomial programs

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Abstract

The purpose of this note is to present an accelerated algorithm for solving 0–1 positive polynomial (PP) problems. Like our covering relaxation algorithm (Management Science 1979), the accelerated algorithm is a cutting plane method, which uses the linear set covering problem as a relaxation for PP. However, a unique and novel feature of the accelerated algorithm is that it attempts to generate cutting planes from heuristic solutions to the set covering problem whenever possible. Computational results reveal that this strategy of generating cutting planes has led to a significant reduction in the computational time required to solve a PP problem.

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References

  1. E. Balas, “An additive algorithm for solving linear programs with zero–one variables”,Operations Research 13 (1965) 517–546.

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  2. J. Etcheberry, “The set covering problem: A new implicit enumeration algorithm”,Operations Research 25 (1977) 760–772.

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  3. D. Granot, F. Granot and J. Kallberg, “Covering relaxation for positive 0–1 polynomial programs”,Management Science 25 (1979) 264–273.

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  4. D. Granot, F. Granot and W. Vaessen, “An accelerated covering relaxation algorithm for solving 0–1 positive polynomial programs”, Working Paper 718, Faculty of Commerce and Business Administration, U.B.C., Vancouver, B.C. (March 1980).

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  5. F. Granot, “Efficient heuristic algorithms for positive 0–1 polynomial programming problems”, Working Paper 595, Faculty of Commerce and Business Administration, U.B.C., Vancouver, B.C. (August 1978). (To appear inManagement Science.)

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  6. W. Vaessen, “Covering relaxation methods for solving the zero–one positive polynomial programming problems”, M.Sc. Thesis, Computer Science Department, U.B.C., Vancouver, B.C. (May 1980).

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Authors and Affiliations

  1. Faculty of Commerce, University of British Columbia, Vancouver, B.C., Canada

    Daniel Granot & Frieda Granot

  2. Computer Science Department, University of British Columbia, Vancouver, B.C., Canada

    Willem Vaessen

Authors
  1. Daniel Granot
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  2. Frieda Granot
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  3. Willem Vaessen
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Additional information

This research was partially supported by National Sciences and Engineering Research Council Canada Grants 67-4181 and 67-3998, Office of Naval Research Contract N00014-76-C-0418, and National Science Foundation Grant ECS80-22027.

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Granot, D., Granot, F. & Vaessen, W. An accelerated covering relaxation algorithm for solving 0–1 positive polynomial programs. Mathematical Programming 22, 350–357 (1982). https://doi.org/10.1007/BF01581048

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  • DOI: https://doi.org/10.1007/BF01581048

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