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

doi:10.1007/978-3-319-54157-0_34

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

Escuela Superior de Cómputo (ESCOM)

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

32 Scopus citations

Abstract

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 language	English
Title of host publication	Evolutionary Multi-Criterion Optimization - 9th International Conference, EMO 2017, Proceedings
Editors	Oliver Schütze, Gunter Rudolph, Kathrin Klamroth, Yaochu Jin, Heike Trautmann, Christian Grimme, Margaret Wiecek
Publisher	Springer Verlag
Pages	499-513
Number of pages	15
ISBN (Print)	9783319541563
DOIs	https://doi.org/10.1007/978-3-319-54157-0_34
State	Published - 2017
Event	9th International Conference on Evolutionary Multi-Criterion Optimization, EMO 2017 - Munster, Germany Duration: 19 Mar 2017 → 22 Mar 2017

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	10173 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	9th International Conference on Evolutionary Multi-Criterion Optimization, EMO 2017
Country/Territory	Germany
City	Munster
Period	19/03/17 → 22/03/17

Keywords

Evolutionary algorithms
Many-objective optimization
Scalarizing function
Tuning process

Access to Document

10.1007/978-3-319-54157-0_34

Cite this

Pescador-Rojas, M., Gómez, R. H., Montero, E., Rojas-Morales, N., Riff, M. C., & Coello Coello, C. A. (2017). An overview of weighted and unconstrained scalarizing functions. In O. Schütze, G. Rudolph, K. Klamroth, Y. Jin, H. Trautmann, C. Grimme, & M. Wiecek (Eds.), Evolutionary Multi-Criterion Optimization - 9th International Conference, EMO 2017, Proceedings (pp. 499-513). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10173 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-319-54157-0_34

Pescador-Rojas, Miriam ; Gómez, Raquel Hernández ; Montero, Elizabeth et al. / An overview of weighted and unconstrained scalarizing functions. Evolutionary Multi-Criterion Optimization - 9th International Conference, EMO 2017, Proceedings. editor / Oliver Schütze ; Gunter Rudolph ; Kathrin Klamroth ; Yaochu Jin ; Heike Trautmann ; Christian Grimme ; Margaret Wiecek. Springer Verlag, 2017. pp. 499-513 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "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 Lam{\'e} 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.",

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Pescador-Rojas, M, Gómez, RH, Montero, E, Rojas-Morales, N, Riff, MC & Coello Coello, CA 2017, An overview of weighted and unconstrained scalarizing functions. in O Schütze, G Rudolph, K Klamroth, Y Jin, H Trautmann, C Grimme & M Wiecek (eds), Evolutionary Multi-Criterion Optimization - 9th International Conference, EMO 2017, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 10173 LNCS, Springer Verlag, pp. 499-513, 9th International Conference on Evolutionary Multi-Criterion Optimization, EMO 2017, Munster, Germany, 19/03/17. https://doi.org/10.1007/978-3-319-54157-0_34

An overview of weighted and unconstrained scalarizing functions. / Pescador-Rojas, Miriam; Gómez, Raquel Hernández; Montero, Elizabeth et al.
Evolutionary Multi-Criterion Optimization - 9th International Conference, EMO 2017, Proceedings. ed. / Oliver Schütze; Gunter Rudolph; Kathrin Klamroth; Yaochu Jin; Heike Trautmann; Christian Grimme; Margaret Wiecek. Springer Verlag, 2017. p. 499-513 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10173 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AU - Pescador-Rojas, Miriam

AU - Gómez, Raquel Hernández

AU - Montero, Elizabeth

AU - Rojas-Morales, Nicolás

AU - Riff, María Cristina

AU - Coello Coello, Carlos A.

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N2 - 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.

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Pescador-Rojas M, Gómez RH, Montero E, Rojas-Morales N, Riff MC, Coello Coello CA. An overview of weighted and unconstrained scalarizing functions. In Schütze O, Rudolph G, Klamroth K, Jin Y, Trautmann H, Grimme C, Wiecek M, editors, Evolutionary Multi-Criterion Optimization - 9th International Conference, EMO 2017, Proceedings. Springer Verlag. 2017. p. 499-513. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-319-54157-0_34

An overview of weighted and unconstrained scalarizing functions

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