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gramEvol: Grammatical Evolution for R

This package includes source code and documentation of gramEvol: Grammatical Evolution for R.

gramEvol implements grammatical evolution (GE) in native R syntax. It allows discovering programs that can achieve a desired goal, by performing an evolutionary optimization over a population of R expressions generated via a user-defined grammar. Functions are provided for creating and manipulating context-free grammars (CFGs), random search, exhaustive search, and evolutionary optimization. Users are only required to define their program structure via a grammar, and a cost function to evaluate the fitness of each program.


You can install this package from CRAN:


You can install the latest version from Github:

if (!require("devtools")) install.packages("devtools")


A tutorial on implementing GE programs is included in the package's vignette (PDF version).

More information regarding GE and its application in parameter optimization can be found in this paper in the Journal of Statistical Software.


This example implements the Kepler law rediscovery problem, as discussed in section 3.1 of the vignette.


# grammar definition for generic symbolic regression
grammarDef <- CreateGrammar(list(
  expr  = grule(op(expr, expr), func(expr), var),
  func  = grule(sin, cos, log, sqrt),
  op    = grule(`+`, `-`, `*`), # define unary operators
  var   = grule(distance, distance^n, n),
  n     = gvrule(1:4) # this is shorthand for grule(1,2,3,4)

# cost function and data
planets <- c("Venus", "Earth", "Mars", "Jupiter", "Saturn", "Uranus")
distance <- c(0.72, 1.00, 1.52, 5.20, 9.53, 19.10)
period <- c(0.61, 1.00, 1.84, 11.90, 29.40, 83.50)

SymRegCostFunc <- function(expr) {
     result <- eval(expr)
       if (any(is.nan(result)))
       return (mean(log(1 + abs(period - result))))

# run GE
ge <- GrammaticalEvolution(grammarDef, SymRegCostFunc, iterations = 50)

# use the best expression
best.expression <- ge$best$expression
print(data.frame(distance, period, Kepler = sqrt(distance^3), GE = eval(best.expression)))

Other resources

Modern Optimization with R, 2nd edition by Pauolo Cortez introduces grammatical evolution is Chapter 5 "Population Based Search", more specifically Section 5.11 "Grammatical Evolution". Examples implemented via gramEvol are available for download.

The book itself (available from Springer and Amazon) gathers in a single document the most relevant concepts related to metaheuristics (e.g., simulated annealing; genetic algorithms), showing how such concepts and methods can be addressed using the open source R tool. The new edition integrates the latest R packages through text and code examples. It also discusses new topics, such as: usage of parallel computing and more modern optimization algorithms (e.g., grammatical evolution).

Contact Information

Release and Development

The latest release and developmental versions of this package are available on:


All files in this package, including the documentation and vignettes, are distributed under GNU GPL v2.0 or later license. For full terms of this license visit