Interactive multiple objective optimization: Survey I—continuous case

The interactive methods developed for solving continuous multiple objective optimization problems and their applications are surveyed, based on the nature of preference assessments, functional assumptions and relationships between the methods.

Abstract

This paper surveys the interactive methods developed for solving continuous multiple objective optimization problems and their applications. Most of the methods fall into the following categories: feasible region reduction methods; feasible direction methods; criterion weight space methods; tradeoff cutting plane methods; Lagrange multiplier methods; visual interactive methods; branch-and-bound methods; relaxation methods; sequential methods; and scalarizing function methods. The methods of each category are reviewed based on the nature of preference assessments, functional assumptions and relationships between the methods. Other aspects such as multiple decision makers (DMs), DM's inconsistency, priorities of objectives and computational studies are also discussed, along with potential areas for future research.