An overview of weighted and unconstrained scalarizing functions

Miriam Pescador-Rojas, Raquel Hernández Gómez, Elizabeth Montero, Nicolás Rojas-Morales, María Cristina Riff, Carlos A. Coello Coello

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

23 Citations (Scopus)


Scalarizing functions play a crucial role in multi-objective evolutionary algorithms (MOEAs) based on decomposition and the R2 indicator, since they guide the population towards nearly optimal solutions, assigning a fitness value to an individual according to a predefined target direction in objective space. This paper presents a general review of weighted scalarizing functions without constraints, which have been proposed not only within evolutionary multi-objective optimization but also in the mathematical programming literature. We also investigate their scalability up to 10 objectives, using the test problems of Lamé Superspheres on the MOEA/D and MOMBI-II frameworks. For this purpose, the best suited scalarizing functions and their model parameters are determined through the evolutionary calibrator EVOCA. Our experimental results reveal that some of these scalarizing functions are quite robust and suitable for handling many-objective optimization problems.

Original languageEnglish
Title of host publicationEvolutionary Multi-Criterion Optimization - 9th International Conference, EMO 2017, Proceedings
EditorsOliver Schütze, Gunter Rudolph, Kathrin Klamroth, Yaochu Jin, Heike Trautmann, Christian Grimme, Margaret Wiecek
PublisherSpringer Verlag
Number of pages15
ISBN (Print)9783319541563
Publication statusPublished - 1 Jan 2017
Event9th International Conference on Evolutionary Multi-Criterion Optimization, EMO 2017 - Munster, Germany
Duration: 19 Mar 201722 Mar 2017

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10173 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference9th International Conference on Evolutionary Multi-Criterion Optimization, EMO 2017


  • Evolutionary algorithms
  • Many-objective optimization
  • Scalarizing function
  • Tuning process

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)


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