.. _differential_evolution: Global minimization of a non-expensive scalar function ========================================================================================== :Driver: :ref:`DifferentialEvolution` :Download script: :download:`differential_evolution.py` The target of the study is to minimize a scalar function. The scalar function is assumed to be inexpensive to evaluate (i.e. evaluation time shorter than a second) and to have *no* known derivatives. In this case a heuristic global optimization is advisable. Differential evolution (DE) is an evolutionary optimization algorithm inspired by the mutation, crossover and selection processes occurring in nature. As an example, the 2D `Rastrigin function `_ on a circular domain is minimized, .. math:: &\text{min.}\,& f(x_1,x_2) = 2\cdot10 + \sum_{i=1,2} \left(x_i^2 - 10\cos(2\pi x_i)\right) &\text{s.t.}\,& \sqrt{x_1^2 + x_2^2} \leq 1.5. .. literalinclude:: ./differential_evolution.py :language: python :linenos: