Derandomized Self-Adaptation Evolution Strategy (DSAES)

class, options)

Derandomized Self-Adaptation Evolution Strategy (DSAES).


DSAES adapts all the individual step-sizes on-the-fly with a relatively small population. The default setting (i.e., using a small population) may result in relatively fast (local) convergence, but with the risk of getting trapped in suboptima on multi-modal fitness landscape.

  • 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: 10),

    • ’lr_sigma’ - learning rate of global step-size self-adaptation (float, default: 1.0/3.0).


Use the optimizer DSAES 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 import DSAES
 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...            'mean': 3*numpy.ones((2,)),
11...            'sigma': 0.1}  # the global step-size may need to be tuned for better performance
12>>> dsaes = DSAES(problem, options)  # initialize the optimizer class
13>>> results = dsaes.optimize()  # run the optimization process
14>>> # return the number of function evaluations and best-so-far fitness
15>>> print(f"DSAES: {results['n_function_evaluations']}, {results['best_so_far_y']}")
16DSAES: 5000, 0.04805047881994932

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


learning rate of global step-size self-adaptation.




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




number of offspring, aka offspring population size.




initial global step-size, aka mutation strength.




final individuals step-sizes from the elitist.




Hansen, N., Arnold, D.V. and Auger, A., 2015. Evolution strategies. In Springer Handbook of Computational Intelligence (pp. 871-898). Springer, Berlin, Heidelberg.

Ostermeier, A., Gawelczyk, A. and Hansen, N., 1994. A derandomized approach to self-adaptation of evolution strategies. Evolutionary Computation, 2(4), pp.369-380.