object --+
         |
        CMAES

Examples

The Jupyter notebook or IPython are the favorite environments to execute these examples, both in %pylab mode. All examples minimize the function elli, output is not shown.

First we need to import the module we want to use. We import purecma from cma as (aliased to) pcma:

from cma import purecma as pcma

The shortest example uses the inherited method OOOptimizer.optimize:

es = pcma.CMAES(8 * [0.1], 0.5).optimize(pcma.ff.elli)

See method CMAES.__init__ for a documentation of the input parameters to CMAES. We might have a look at the result:

print(es.result[0])  # best solution and
print(es.result[1])  # its function value

result is a property of CMAES. In order to display more exciting output, we may use the CMAESDataLogger instance in the logger attribute of CMAES:

es.logger.plot()  # if matplotlib is available

Virtually the same example can be written with an explicit loop instead of using optimize, see also fmin. This gives insight into the CMAES class interface and entire control over the iteration loop:

pcma.fmin??  # print source, works in jupyter/ipython only
es = pcma.CMAES(9 * [0.5], 0.3)  # calls CMAES.__init__()

# this loop resembles the method optimize
while not es.stop():  # iterate
    X = es.ask()      # get candidate solutions
    f = [pcma.ff.elli(x) for x in X]  # evaluate solutions
    es.tell(X, f)     # do all the real work
    es.disp(20)       # display info every 20th iteration
    es.logger.add(es) # log another "data line"

# final output
print('termination by', es.stop())
print('best f-value =', es.result[1])
print('best solution =', es.result[0])

print('potentially better solution xmean =', es.result[5])
print("let's check f(xmean) = ", pcma.ff.elli(es.result[5]))
es.logger.plot()  # if matplotlib is available

A very similar example which may also save the logged data within the loop is the implementation of function fmin.

Details

Most of the work is done in the method tell. The property result contains more useful output.

m + sigma * Normal(0,C) = m + sigma * B * D * Normal(0,I)
                        = m + B * D * sigma * Normal(0,I)