Indicator based search in variable orderings: Theory and algorithms

Pradyumn Kumar Shukla, Marlon Alexander Braun

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


Various real world problems, especially in financial applications, medical engineering, and game theory, involve solving a multi-objective optimization problem with a variable ordering structure. This means that the ordering relation at a point in the (multi-)objective space depends on the point. This is a striking difference from usual multi-objective optimization problems, where the ordering is induced by the Pareto-cone and remains constant throughout the objective space. In addition to variability, in many applications (like portfolio optimization) the ordering is induced by a non-convex set instead of a cone. The main purpose of this paper is to provide theoretical and algorithmic advances for general set-based variable orderings. A hypervolume based indicator measure is also proposed for the first time for such optimization tasks. Theoretical results are derived and properties of this indicator are studied. Moreover, the theory is also used to develop three indicator based algorithms for approximating the set of optimal solutions. Computational results show the niche of population based algorithms for solving multi-objective problems with variable orderings.

Original languageEnglish
Title of host publicationEvolutionary Multi-Criterion Optimization - 7th International Conference, EMO 2013, Proceedings
Number of pages15
Publication statusPublished - 2013
Event7th International Conference on Evolutionary Multi-Criterion Optimization, EMO 2013 - Sheffield, United Kingdom
Duration: 19 Mar 201322 Mar 2013

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7811 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference7th International Conference on Evolutionary Multi-Criterion Optimization, EMO 2013
Country/TerritoryUnited Kingdom


  • approximation
  • evolutionary algorithms
  • hypervolume indicator
  • variable ordering


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