Simplicial homology global optimisation
Finds the global minimum of a function using simplicial homology global optimisation (shgo). Appropriate for solving general purpose NLP and blackbox optimisation problems to global optimality (low dimensional problems). The general form of an optimisation problem is given by:
minimize f(x) subject to g_i(x) >= 0, i = 1,...,m h_j(x) = 0, j = 1,...,p
where x is a vector of one or more variables. f(x) is the objective function R^n -> R, g_i(x) are the inequality constraints. h_j(x) are the equality constrains.
$ pip install shgo
$ git clone https://bitbucket.org/upiamcompthermo/shgo $ cd shgo $ python setup.py install $ python setup.py test
The project website https://stefan-endres.github.io/shgo/ contains more detailed examples, notes and performance profiles.
Consider the problem of minimizing the Rosenbrock function. This function is implemented in rosen in scipy.optimize
>>> from scipy.optimize import rosen >>> from shgo import shgo >>> bounds = [(0,2), (0, 2), (0, 2), (0, 2), (0, 2)] >>> result = shgo(rosen, bounds) >>> result.x, result.fun (array([ 1., 1., 1., 1., 1.]), 2.9203923741900809e-18)
Note that bounds determine the dimensionality of the objective function and is therefore a required input, however you can specify empty bounds using None or objects like numpy.inf which will be converted to large float numbers.