Partial convexification cuts for 0-1 mixed-integer programs

Hanif D. Sherali, Youngho Lee, Youngjin Kim

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

In this research, we propose a new cut generation scheme based on constructing a partial convex hull representation for a given 0-1 mixed-integer programming problem by using the reformulation-linearization technique (RLT). We derive a separation problem that projects the extended space of the RLT formulation into the original space, in order to generate a cut that deletes a current fractional solution. Naturally, the success of such a partial convexification based cutting plane scheme depends on the process used to tradeoff the strength of the cut derived and the effort expended. Accordingly, we investigate several variable selection rules for performing this convexification, along with restricted versions of the accompanying separation problems, so as to be able to derive strong cuts within a reasonable effort. We also develop a strengthening procedure that enhances the generated cut by considering the binariness of the remaining unselected 0-1 variables. Finally, we present some promising computational results that provide insights into implementing the proposed cutting plane methodology.

Original languageEnglish
Pages (from-to)625-648
Number of pages24
JournalEuropean Journal of Operational Research
Volume165
Issue number3
DOIs
Publication statusPublished - 2005 Sep 16

Fingerprint

Convexification
Mixed Integer Program
Linearization
Partial
Reformulation-linearization Technique (RLT)
Integer programming
Cutting Planes
0-1 Integer Programming
programming
Selection Rules
Mixed Integer Programming
Several Variables
Variable Selection
Strengthening
Convex Hull
methodology
Computational Results
Fractional
Trade-offs
Mixed integer program

Keywords

  • Branch-and-cut
  • Convexification cut
  • Cutting plane
  • Integer programming
  • Reformulation-linearization technique (RLT)

ASJC Scopus subject areas

  • Information Systems and Management
  • Management Science and Operations Research
  • Statistics, Probability and Uncertainty
  • Applied Mathematics
  • Modelling and Simulation
  • Transportation

Cite this

Partial convexification cuts for 0-1 mixed-integer programs. / Sherali, Hanif D.; Lee, Youngho; Kim, Youngjin.

In: European Journal of Operational Research, Vol. 165, No. 3, 16.09.2005, p. 625-648.

Research output: Contribution to journalArticle

Sherali, Hanif D. ; Lee, Youngho ; Kim, Youngjin. / Partial convexification cuts for 0-1 mixed-integer programs. In: European Journal of Operational Research. 2005 ; Vol. 165, No. 3. pp. 625-648.
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