Mathematica-GA
A Mathematica implementation of genetic algorithm, which seems to be faster than Mathematica built-in NMaximize or NMinimize with the option "DifferentialEvolution".
Two main functions in this packages are GAMaximize and GAMinimize.
GAMaximize[func, vars]/GAMinimize[func, vars] maximizes/minimizes the given function func numerically with the Genetic Algorithm.
Variables should be written in form of {Element[x, Reals],Element[y, Integers]}.
Example
func[x_, y_] := (x + 0.1)^2 + (y + 0.1)^2
GAMinimize[func, {Element[x, Reals], Element[y, Integers]}, PopulationSize -> 100]
References:
[1] K.Deep,M.Thakur,A new crossover operator for real coded genetic algorithms,Applied Mathematics and Computation.188 (2007) 895[Dash]911. https://doi.org/10.1016/j.amc.2006.10.047.
[2] K.Deep,M.Thakur,A new mutation operator for real coded genetic algorithms,Applied Mathematics and Computation.193 (2007) 211[Dash]230. https://doi.org/10.1016/j.amc.2007.03.046.
[3] K. Deep, K.P. Singh, M.L. Kansal, C. Mohan, A real coded genetic algorithm for solving integer and mixed integer optimization problems, Applied Mathematics and Computation. 212 (2009) 505[Dash]518. https://doi.org/10.1016/j.amc.2009.02.044.
[4] R. Hinterding, Gaussian mutation and self-adaption for numeric genetic algorithms, in: Proceedings of 1995 IEEE International Conference on Evolutionary Computation, IEEE, Perth, WA, Australia, 1995: p. 384. https://doi.org/10.1109/ICEC.1995.489178.
Options
PrecisionGoal: integer, default value 5
AccuracyGoal: integer, default value 5
MaxIterations: integer, default value 10000
PopulationSize: integer, default value 10 * number of variables
Bounds: default value None
ShrinkingFactor: real, default value 1, must be smaller than 1
Scale: real, default value: 1
TournamentSize: integer, default value 3
MutationProbability: real, default value 0.01
CrossoverProbability: real, default value 0.8
MaxUnchangedGeneration: integer, default value MaxIterations/4
bReal: real, default value 0.15
bInt: real, default value 0.35
a: real, default value 0
pReal: real, default value 10
pInt: real, default value 4