In search of equitable solutions using multi-objective evolutionary algorithms

Pradyumn Kumar Shukla, Christian Hirsch, Hartmut Schmeck

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


Over the last two decades, evolutionary algorithms have been applied in solving multi-objective optimization problems. Most of these algorithms use the concept of Pareto-optimality to drive their search. However, many real-world multi-objective applications, in particular from location theory and general resource allocation models, require finding so-called equitably efficient points. These solutions form a subset of the Pareto-optimal set. In equitable efficiency, objective functions are considered impartial which makes the distribution of outcomes more important rather than assignment of several outcomes to an objective. In literature, we found two classical approaches to compute an equitably efficient point. These approaches rely on either solving a problem which is always non-differentiable or on solving a more difficult problem. In this paper, for the first time, a multi-objective evolutionary approach to this problem is proposed. The approach finds a diverse set of equitably optimal solutions and, in addition, tackles the non-differentiability which is inherently present in the classical approach. It is shown that even for simple differentiable problems, which belong to the realm of classical techniques, the evolutionary approach is a better choice than the classical ones. Computational studies on a number of test problems of varying complexity demonstrate the efficiency of the evolutionary approach in solving a large class of both simple and complex equitable multi-objective optimization problems.

Original languageEnglish
Title of host publicationParallel Problem Solving from Nature, PPSN XI - 11th International Conference, Proceedings
Number of pages10
EditionPART 1
Publication statusPublished - 2010
Event11th International Conference on Parallel Problem Solving from Nature, PPSN 2010 - Krakow, Poland
Duration: 11 Sept 201015 Sept 2010

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
NumberPART 1
Volume6238 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference11th International Conference on Parallel Problem Solving from Nature, PPSN 2010


  • Optimal point
  • Inverted generational distance
  • Warm start strategy
  • Attainment surface
  • Normal boundary intersection method


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