Comparison of mutation strategies in Differential Evolution – A probabilistic perspective

Karol Opara , Jarosław Arabas


Differential Evolution (DE) is a state-of-the art evolutionary algorithm that solves global optimization problems in a real domain. The algorithm adapts the mutation range and direction by basing these on the differences between individuals in the current population. In this paper, we provide formulas for the expectation vectors and covariance matrices of the mutants’ distribution for several operators of differential mutation. The covariance matrices are proportional to each other, which means that the main difference between the analyzed DE operators is the mutation range. This can be conveniently described using a generalized scaling factor g(F), introduced in this paper. Next, we propose transformations of the scaling factors that make the expectation vectors and covariance matrices of the expected mutants’ distributions equal to the respective statistics of DE/best/1 or DE/rand/1. These transformations establish a framework for a synthetic investigation of various differential mutation operators and for generalizing the results of parameter tuning. A simulation study based on the CEC′13 benchmark in 10, 30 and 50 dimensions confirms that the transformations do not influence the performance much, especially in the case of DE operators with two difference vectors.
Author Karol Opara (SRI)
Karol Opara,,
- Systems Research Institute
, Jarosław Arabas (FEIT / IN)
Jarosław Arabas,,
- The Institute of Computer Science
Journal seriesSwarm and Evolutionary Computation, ISSN 2210-6502, (A 50 pkt)
Issue year2018
Publication size in sheets0.8
Keywords in EnglishDE; Normal distribution; Scaling factor; Differential mutation; CMA-ES
ASJC Classification2600 General Mathematics; 1700 General Computer Science
projectDevelopment of new algorithms in the areas of software and computer architecture, artificial intelligence and information systems and computer graphics . Project leader: Arabas Jarosław, , Phone: +48 22 234 7432, start date 01-06-2017, end date 31-10-2018, II/2017/DS/1, Completed
WEiTI Działalność statutowa
Languageen angielski
1-s2.0-S2210650217303310-main.pdf 1.32 MB
Score (nominal)50
ScoreMinisterial score = 50.0, ArticleFromJournal
Ministerial score (2013-2016) = 50.0, ArticleFromJournal
Publication indicators WoS Citations = 2; Scopus SNIP (Source Normalised Impact per Paper): 2016 = 2.756; WoS Impact Factor: 2017 = 3.818 (2) - 2017=4.607 (5)
Citation count*6 (2019-04-14)
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* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perish system.