A comparison of three differential evolution strategies in terms of early convergence with different population sizes

Anil Yaman, Giovanni Iacca, Fabio Caraffini

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

1 Citation (Scopus)

Abstract

Differential Evolution (DE) is a popular population-based continuous optimization algorithm that generates new can-didate solutions by perturbing the existing ones, using scaled differences of randomly selected solutions in the population. While the number of generation increases, the differences between the solutions in the population decrease and the population tends to converge to a small hyper-volume within the search space. When these differences become too small, the evolutionary process becomes inefficient as no further improvements on the fitness value can be made-unless specific mechanisms for diversity preser-vation or restart are implemented. In this work, we present a set of preliminary results on measuring the population diversity during the DE process, to investigate how different DE strategies and population sizes can lead to early convergence. In particular, we compare two standard DE strategies, namely "DE/rand/1/bin" and "DE/rand/1/exp", and a rotation-invariant strategy, "DE/current-To-random/1", with populations of 10, 30, 50, 100, 200 solutions. Our results show, quite intuitively, that the lower is the population size, the higher is the chance of observing early convergence. Furthermore, the comparison of the different strategies shows that "DE/rand/1/exp" preserves the population diversity the most, whereas "DE/current-To-random/1" preserves diversity the least.

LanguageEnglish
Title of host publicationProceedings LeGO 2018 � 14th International Global Optimization Workshop
EditorsAndre H. Deutz, Sander C. Hille, Yaroslav D. Sergeyev, Michael T. M. Emmerich
PublisherAmerican Institute of Physics
Number of pages3
ISBN (Electronic)9780735417984
DOIs
StatePublished - 12 Feb 2019
Event2018 International Workshop on Global Optimization (LeGO 2018) - Leiden University, Leiden, Netherlands
Duration: 18 Sep 201821 Sep 2018
http://liacs.leidenuniv.nl/~csmoda/LeGO/

Publication series

NameAIP Conference Proceedings
Volume2070

Conference

Conference2018 International Workshop on Global Optimization (LeGO 2018)
Abbreviated titleLeGO 2018
CountryNetherlands
CityLeiden
Period18/09/1821/09/18
Internet address

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fitness
optimization

Cite this

Yaman, A., Iacca, G., & Caraffini, F. (2019). A comparison of three differential evolution strategies in terms of early convergence with different population sizes. In A. H. Deutz, S. C. Hille, Y. D. Sergeyev, & M. T. M. Emmerich (Eds.), Proceedings LeGO 2018 � 14th International Global Optimization Workshop [20002] (AIP Conference Proceedings ; Vol. 2070). American Institute of Physics. DOI: 10.1063/1.5089969
Yaman, Anil ; Iacca, Giovanni ; Caraffini, Fabio. / A comparison of three differential evolution strategies in terms of early convergence with different population sizes. Proceedings LeGO 2018 � 14th International Global Optimization Workshop. editor / Andre H. Deutz ; Sander C. Hille ; Yaroslav D. Sergeyev ; Michael T. M. Emmerich. American Institute of Physics, 2019. (AIP Conference Proceedings ).
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abstract = "Differential Evolution (DE) is a popular population-based continuous optimization algorithm that generates new can-didate solutions by perturbing the existing ones, using scaled differences of randomly selected solutions in the population. While the number of generation increases, the differences between the solutions in the population decrease and the population tends to converge to a small hyper-volume within the search space. When these differences become too small, the evolutionary process becomes inefficient as no further improvements on the fitness value can be made-unless specific mechanisms for diversity preser-vation or restart are implemented. In this work, we present a set of preliminary results on measuring the population diversity during the DE process, to investigate how different DE strategies and population sizes can lead to early convergence. In particular, we compare two standard DE strategies, namely {"}DE/rand/1/bin{"} and {"}DE/rand/1/exp{"}, and a rotation-invariant strategy, {"}DE/current-To-random/1{"}, with populations of 10, 30, 50, 100, 200 solutions. Our results show, quite intuitively, that the lower is the population size, the higher is the chance of observing early convergence. Furthermore, the comparison of the different strategies shows that {"}DE/rand/1/exp{"} preserves the population diversity the most, whereas {"}DE/current-To-random/1{"} preserves diversity the least.",
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Yaman, A, Iacca, G & Caraffini, F 2019, A comparison of three differential evolution strategies in terms of early convergence with different population sizes. in AH Deutz, SC Hille, YD Sergeyev & MTM Emmerich (eds), Proceedings LeGO 2018 � 14th International Global Optimization Workshop., 20002, AIP Conference Proceedings , vol. 2070, American Institute of Physics, 2018 International Workshop on Global Optimization (LeGO 2018), Leiden, Netherlands, 18/09/18. DOI: 10.1063/1.5089969

A comparison of three differential evolution strategies in terms of early convergence with different population sizes. / Yaman, Anil; Iacca, Giovanni; Caraffini, Fabio.

Proceedings LeGO 2018 � 14th International Global Optimization Workshop. ed. / Andre H. Deutz; Sander C. Hille; Yaroslav D. Sergeyev; Michael T. M. Emmerich. American Institute of Physics, 2019. 20002 (AIP Conference Proceedings ; Vol. 2070).

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

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N2 - Differential Evolution (DE) is a popular population-based continuous optimization algorithm that generates new can-didate solutions by perturbing the existing ones, using scaled differences of randomly selected solutions in the population. While the number of generation increases, the differences between the solutions in the population decrease and the population tends to converge to a small hyper-volume within the search space. When these differences become too small, the evolutionary process becomes inefficient as no further improvements on the fitness value can be made-unless specific mechanisms for diversity preser-vation or restart are implemented. In this work, we present a set of preliminary results on measuring the population diversity during the DE process, to investigate how different DE strategies and population sizes can lead to early convergence. In particular, we compare two standard DE strategies, namely "DE/rand/1/bin" and "DE/rand/1/exp", and a rotation-invariant strategy, "DE/current-To-random/1", with populations of 10, 30, 50, 100, 200 solutions. Our results show, quite intuitively, that the lower is the population size, the higher is the chance of observing early convergence. Furthermore, the comparison of the different strategies shows that "DE/rand/1/exp" preserves the population diversity the most, whereas "DE/current-To-random/1" preserves diversity the least.

AB - Differential Evolution (DE) is a popular population-based continuous optimization algorithm that generates new can-didate solutions by perturbing the existing ones, using scaled differences of randomly selected solutions in the population. While the number of generation increases, the differences between the solutions in the population decrease and the population tends to converge to a small hyper-volume within the search space. When these differences become too small, the evolutionary process becomes inefficient as no further improvements on the fitness value can be made-unless specific mechanisms for diversity preser-vation or restart are implemented. In this work, we present a set of preliminary results on measuring the population diversity during the DE process, to investigate how different DE strategies and population sizes can lead to early convergence. In particular, we compare two standard DE strategies, namely "DE/rand/1/bin" and "DE/rand/1/exp", and a rotation-invariant strategy, "DE/current-To-random/1", with populations of 10, 30, 50, 100, 200 solutions. Our results show, quite intuitively, that the lower is the population size, the higher is the chance of observing early convergence. Furthermore, the comparison of the different strategies shows that "DE/rand/1/exp" preserves the population diversity the most, whereas "DE/current-To-random/1" preserves diversity the least.

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PB - American Institute of Physics

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Yaman A, Iacca G, Caraffini F. A comparison of three differential evolution strategies in terms of early convergence with different population sizes. In Deutz AH, Hille SC, Sergeyev YD, Emmerich MTM, editors, Proceedings LeGO 2018 � 14th International Global Optimization Workshop. American Institute of Physics. 2019. 20002. (AIP Conference Proceedings ). Available from, DOI: 10.1063/1.5089969