Valid inequalities for a single constrained 0-1 MIP set intersected with a conflict graph

Agostinho Agra*, Mahdi Doostmohammadi, Cid C. De Souza

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract / Description of output

In this paper a mixed integer set resulting from the intersection of a single constrained mixed 0-1 set with the vertex packing set is investigated. This set arises as a subproblem of more general mixed integer problems such as inventory routing and facility location problems. Families of strong valid inequalities that take into account the structure of the simple mixed integer set and that of the vertex packing set simultaneously are introduced. In particular, the well-known mixed integer rounding inequality is generalized to the case where incompatibilities between binary variables are present. Exact and heuristic algorithms are designed to solve the separation problems associated to the proposed valid inequalities. Preliminary computational experiments show that these inequalities can be useful to reduce the integrality gaps and to solve integer programming problems.

Original languageEnglish
Pages (from-to)42-70
Number of pages29
JournalDiscrete Optimization
Early online date21 Jun 2016
Publication statusPublished - 1 Aug 2016

Keywords / Materials (for Non-textual outputs)

  • Conflict graph
  • Independent set
  • Mixed integer programming
  • Separation
  • Valid inequality
  • Vertex packing set


Dive into the research topics of 'Valid inequalities for a single constrained 0-1 MIP set intersected with a conflict graph'. Together they form a unique fingerprint.

Cite this