An interior multiple objective primal-dual linear programming algorithm using efficient anchoring points

Ami Arbel*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We present an interior Multiple Objective Linear Programming (MOLP) algorithm based on the path-following primal-dual algorithm. In contrast to the simplex algorithm, which generates a solution path on the exterior of the constraints polytope by following its vertices, the path-following primal-dual algorithm moves through the interior of the polytope. Interior algorithms lend themselves to modifications capable of addressing MOLP problems in a way that is quite different from current solution approaches. In addition, moving through the interior of the polytope results in a solution approach that is less sensitive to problem size than simplex-based MOLP algorithms. The modification of the interior single-objective algorithm to MOLP problems, as presented here, is accomplished by combining the step direction vectors generated by applying the single-objective algorithm to each of the cost vectors into a combined direction vector along which we step from the current iterate to the next iterate.

Original languageEnglish
Pages (from-to)1121-1132
Number of pages12
JournalJournal of the Operational Research Society
Volume46
Issue number9
DOIs
StatePublished - Sep 1995

Keywords

  • Interior-point linear programming
  • Karmarkar’s algorithm
  • Multicriteria decision making
  • Multiple objective linear programming

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