Diagonal Decoding Covariance Matrix Adaptation (DDCMA)

class pypop7.optimizers.es.ddcma.DDCMA(problem, options)

Diagonal Decoding Covariance Matrix Adaptation (DDCMA).


DDCMA is a state-of-the-art improvement version of the well-designed CMA-ES algorithm, which enjoys both two worlds of SEP-CMA-ES (faster adaptation on nearly separable problems) and CMA-ES (more robust adaptation on ill-conditioned non-separable problems) via adaptive diagonal decoding. It is highly recommended to first attempt other ES variants (e.g., LMCMA, LMMAES) for large-scale black-box optimization, since DDCMA has a quadratic time complexity (w.r.t. each sampling).

  • problem (dict) –

    problem arguments with the following common settings (keys):
    • ’fitness_function’ - objective function to be minimized (func),

    • ’ndim_problem’ - number of dimensionality (int),

    • ’upper_boundary’ - upper boundary of search range (array_like),

    • ’lower_boundary’ - lower boundary of search range (array_like).

  • options (dict) –

    optimizer options with the following common settings (keys):
    • ’max_function_evaluations’ - maximum of function evaluations (int, default: np.Inf),

    • ’max_runtime’ - maximal runtime to be allowed (float, default: np.Inf),

    • ’seed_rng’ - seed for random number generation needed to be explicitly set (int);

    and with the following particular settings (keys):
    • ’sigma’ - initial global step-size, aka mutation strength (float),

    • ’mean’ - initial (starting) point, aka mean of Gaussian search distribution (array_like),

      • if not given, it will draw a random sample from the uniform distribution whose search range is bounded by problem[‘lower_boundary’] and problem[‘upper_boundary’].

    • ’n_individuals’ - number of offspring, aka offspring population size (int, default: 4 + int(3*np.log(problem[‘ndim_problem’]))).


Use the optimizer DDCMA to minimize the well-known test function Rosenbrock:

 1>>> import numpy
 2>>> from pypop7.benchmarks.base_functions import rosenbrock  # function to be minimized
 3>>> from pypop7.optimizers.es.ddcma import DDCMA
 4>>> problem = {'fitness_function': rosenbrock,  # define problem arguments
 5...            'ndim_problem': 2,
 6...            'lower_boundary': -5*numpy.ones((2,)),
 7...            'upper_boundary': 5*numpy.ones((2,))}
 8>>> options = {'max_function_evaluations': 5000,  # set optimizer options
 9...            'seed_rng': 2022,
10...            'is_restart': False,
11...            'mean': 3*numpy.ones((2,)),
12...            'sigma': 0.1}  # the global step-size may need to be tuned for better performance
13>>> ddcma = DDCMA(problem, options)  # initialize the optimizer class
14>>> results = ddcma.optimize()  # run the optimization process
15>>> # return the number of function evaluations and best-so-far fitness
16>>> print(f"DDCMA: {results['n_function_evaluations']}, {results['best_so_far_y']}")
17DDCMA: 5000, 0.0

For its correctness checking of coding, refer to this code-based repeatability report for more details.


initial (starting) point, aka mean of Gaussian search distribution.




number of offspring, aka offspring population size.




final global step-size, aka mutation strength.




Akimoto, Y. and Hansen, N., 2020. Diagonal acceleration for covariance matrix adaptation evolution strategies. Evolutionary Computation, 28(3), pp.405-435. https://direct.mit.edu/evco/article/28/3/405/94999/Diagonal-Acceleration-for-Covariance-Matrix

See its official Python implementation from Prof. Akimoto: https://gist.github.com/youheiakimoto/1180b67b5a0b1265c204cba991fa8518