cma.integer_centering.IntegerCentering

round values of int-variables that are different from the int-mean.

This callable class changes a population of solutions in place, in particular rounding some of the integer variables. The call does not guaranty to round any or all integer variables. The class assumes that the fitness function only interprets the rounded values of integer variables, that is, it assumes that int-variables change the fitness only if their rounded (genotype) value change. (This may easily become a wrong assumption if a geno-pheno transformation is applied). The class tries to correct for the bias introduced by rounding values.

This class should generally be used in combination with a lower bound on the integer variables along the lines of min((0.2, mueff/dimension)), as it is induced by passing a nonempty 'integer_variables' option to CMAEvolutionStrategy. Applying lower bounds alone is generally more effective than applying integer centering alone.

Class instances have no dynamically changing state variables!

When integer variable indices are passed to CMAEvolutionStrategy via the 'integer_variables' CMAOptions, an IntegerCentering class instance is created, and it is called in CMAEvolutionStrategy.tell before the update of the state variables of CMA, passing mu (genotypic) solutions, like int_centering(self.pop_sorted[:self.sp.weights.mu], self.mean) . The call changes the numpy arrays of self.pop_sorted in place. The call tries to access the (phenotypic) bounds as defined in es.boundary_handler from the constructor argument. Hence it is expected to fail with a combination of bounds and fixed_variables set in CMAOptions.

By default, integer centering is applied, e.g. with fmin2 or CMAEvolutionStrategy, when the integer variable indices are given via the 'integer_variables' option. Since v4.3.0, candidate solutions delivered by CMAEvolutionStrategy.ask have rounded values in all integer variable positions which can be switched off by setting cma.evolution_strategy.round_integer_variables to False.

A simple example code:

>>> import cma
>>>
>>> def int1_sphere(x):
...     return int(x[0] + 0.5 - (x[0] < 0))**2 + 1000 * (sum(xi**2 for xi in x[1:]))

>>> es = cma.CMAEvolutionStrategy(2 * [2], 0.5,
...             {'integer_variables': [0], 'ftarget': 1e-9, 'verbose': -9})
>>> es = es.optimize(int1_sphere)
>>> # assert 'ftarget' in es.stop(), es.stop()  # fails sometimes (like 1%-ish)
>>> # failure is less likely with options ``'tolfun': 0, 'tolfunhist': 0, 'tolflatfitness': 60``

The following pseudocode shows a direct use case to explicitly see how/where integer centering is applied, namely before the state variables are updated in tell:

>>> import numpy as np

>>> # set dimension dependent lower bound on sample standard deviations
>>> es = cma.CMAEvolutionStrategy(2 * [2], 0.5,
...             {'minstd': [0.2, 0], 'popsize_factor': 1.5, 'ftarget': 1e-9, 'verbose': -9})
>>> # when integer_variables were passed in the above options,
>>> # we can inactivate the internal integer centering like
>>> es.integer_centering = lambda *args: args[0] if args else None
>>> ic = cma.integer_centering.IntegerCentering([0])
>>> while not es.stop():
...     X = es.ask()
...     F = [int1_sphere(x) for x in X]
...     # change the mu best solutions in place
...     _ = ic([X[i] for i in np.argsort(F)[:es.sp.weights.mu]], es.mean)
...     es.tell(X, F, check_points=False)  # don't check for changes in X
...     # es.logger.add()
...     # es.disp()
>>> # assert 'ftarget' in es.stop(), es.stop()  # fails sometimes (like 1%-ish)

Details: The default method2 was used in the below reference and, as of version 4.0.0, is activated in CMAEvolutionStrategy when integer_variables are given as option.

Reference: Marty et al, LB+IC-CMA-ES: Two simple modifications of CMA-ES to handle mixed-integer problems. PPSN 2024.