cma.evolution_strategy.CMAEvolutionStrategyResult2

A results class.

This class is of rather declarative nature allowing to access the result in its attributes after running an optimization. Additionally, the class provides a names and an asdict property.

>>> import cma
>>> es = cma.CMA(2 * [1], .1, {'verbose': -9}).optimize(cma.ff.sphere, 4, iterations=5)
>>> isinstance(es.result, cma.evolution_strategy.CMAEvolutionStrategyResult2)
True

The easiest ways to examine the results visually is by list(es.result) or like

>>> es.result.asdict  # doctest: +ELLIPSIS
{'xbest':...

We can also check the available attribute names like

>>> es.result.names  # doctest: +ELLIPSIS
['xbest', 'fbest',...

and then check a value like

>>> float(es.result.xbest[0]) < 10
True

Otherwise, the result class acts largely like a dataclass and like the original namedtuple CMAEvolutionStrategyResult, however with _additional_ attributes: as of 2025 the .best_feasible attribute has been added. For backward compatibility, index access of the original entries is possible but discouraged, like

>>> es.result[1] == es.result[-7] == es.result.fbest  # deprecated
True

The nine result attributes are:

xbest best solution evaluated, this may not reflect a good solution under noise or with a changing fitness function like in the constrained case.

fbest objective function value of the best solution

evals_best evaluation count when xbest was evaluated

best_feasible is a dictionary with the keys 'x', 'f', 'evals' (and possibly others), the feasible counterparts to xbest, fbest, evals_best. This is particularly useful with constraints. best_feasible is not accessible by index.

evaluations overall done, including preceeding runs

iterations done, not including preceeding runs

xfavorite final distribution mean in "phenotype" space, considered to be the current best estimate of the optimum.

stds effective final standard deviations, can be used to compute a lower bound on the expected coordinate-wise distance to the true optimum, which is (very!) approximately stds[i] * dim**0.5 * 3 / np.minimum(popsize, 3 * dim + 15) (was: stds[i] * dimension**0.5 / min(mueff, dimension) / 1.5 / 5 ~ stds[i] * dimension**0.5 / min(popsize / 2, dimension) / 5, where dimension = CMAEvolutionStrategy.N and mueff = CMAEvolutionStrategy.sp.weights.mueff ~ 0.3 * popsize).

stop termination conditions in a dictionary. The module attribute cma.evolution_strategy.all_stoppings and the attribute .all_stoppings[1:] of CMAEvolutionStrategy contain the termination conditions for all runs from a single call of fmin2, the latter only when more than one run was conducted.

runs number of runs when restarted. Usually these are restarts with increasing population size, IPOP, via fmin2. evaluations and ..best.. entries are carried over, iterations are only those from the last run.

CAVEAT: in contrast to a named tuple, this class iterates over items, not values, hence dict(es.result) works as expected. list(es.result) is not backward compatible (providing a list of values without keys seems rather pointless given the values are not homogenuous). The previous value of list(es.result) can be obtained by [r[1] for r in es.result].

While not provided in this class, the (penalized-)best solution of the last completed iteration can be accessed via the attribute .pop_sorted[0] of CMAEvolutionStrategy and the respective objective function value via .fit.fit[0].

Details:

• in addition to ._asdict() and dir(.) (which works rather poorly) for the old CMAEvolutionStrategyResult, viewing with dict(.) and .asdict works for this class too.
• list(CMA.fit.idx).index(i) is the index of the i-ths sampled solution of the last completed iteration in pop_sorted. In other words, it is the (original) index of the i+1-th best solution.

Technical details:

• The class allows to have new attributes while keeping backward compatible index access of the original eight attributes of the namedtuple CMAEvolutionStrategyResult. es.result[-8] still equals es.result[0]. Newly introduced attributes are ignored in this count and cannot be accessed by position index. Index access is discouraged.
• inheriting from a list would work too, but we would have the list methods as additional attributes.