Enhanced Simulated Annealing (ESA)

class pypop7.optimizers.sa.esa.ESA(problem, options)

Enhanced Simulated Annealing (ESA).

Note

ESA adopts a random decomposition strategy to alleviate the curse of dimensionality for large-scale black-box optimization. Note that it shares some similaries (i.e., axis-parallel decomposition) to the Cooperative Coevolution framework, which uses population-based sampling (rather than individual-based sampling of ESA) for each subproblem (corresponding to a search subspace).

Parameters:

• 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):

  • ’p’ - subspace dimension (int, default: int(np.ceil(problem[‘ndim_problem’]/3))),

  • ’n1’ - factor to control temperature stage w.r.t. accepted moves (int, default: 12),

  • ’n2’ - factor to control temperature stage w.r.t. attempted moves (int, default: 100).

Examples

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

>>> import numpy
>>> from pypop7.benchmarks.base_functions import rosenbrock  # function to be minimized
>>> from pypop7.optimizers.sa.esa import ESA
>>> problem = {'fitness_function': rosenbrock,  # define problem arguments
...            'ndim_problem': 2,
...            'lower_boundary': -5*numpy.ones((2,)),
...            'upper_boundary': 5*numpy.ones((2,))}
>>> options = {'max_function_evaluations': 5000,  # set optimizer options
...            'seed_rng': 2022,
...            'x': 3*numpy.ones((2,))}
>>> esa = ESA(problem, options)  # initialize the optimizer class
>>> results = esa.optimize()  # run the optimization process
>>> # return the number of function evaluations and best-so-far fitness
>>> print(f"ESA: {results['n_function_evaluations']}, {results['best_so_far_y']}")
ESA: 5000, 6.481109148014023

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

n1

factor to control temperature stage w.r.t. accepted moves.

Type:

int

n2

factor to control temperature stage w.r.t. attempted moves.

Type:

int

p

subspace dimension.

Type:

int

References

Siarry, P., Berthiau, G., Durdin, F. and Haussy, J., 1997. Enhanced simulated annealing for globally minimizing functions of many-continuous variables. ACM Transactions on Mathematical Software, 23(2), pp.209-228. https://dl.acm.org/doi/abs/10.1145/264029.264043