Tradeoff directions in multiobjective optimization problems

Mordechai I. Henig, John T. Buchanan*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Multiobjective optimization problems (MOP) typically have conflicting objectives wherein a gain in one objective is at the expense of another. Tradeoff directions, which measure the change in some objectives relative to changes in others, provide important information as to the best direction of improvement from the current solution. In this paper we present a general definition of tradeoffs as a cone of directions and provide a general method of calculating tradeoffs at every Pareto optimal point of a convex MOP. This extends current definitions of tradeoffs which assume certain conditions on the feasible set and the objective functions. Two comprehensive numerical examples are provided to illustrate the tradeoff directions and the methods used to calculate them.

Original languageEnglish
Pages (from-to)357-374
Number of pages18
JournalMathematical Programming
Issue number3
StatePublished - 1 Sep 1997


  • Multiple objective programming
  • Pareto optimal
  • Tradeoff directions


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