Corana et al.’ Simulated Annealing (CSA)

class pypop7.optimizers.sa.csa.CSA(problem, options)

Corana et al.’ Simulated Annealing (CSA).

Note

“The algorithm is essentially an iterative random search procedure with adaptive moves along the coordinate directions.”—[Corana et al., 1987, ACM-TOMS]

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):

  • ’sigma’ - initial global step-size (float),

  • ’temperature’ - annealing temperature (float),

  • ’n_sv’ - frequency of step variation (int, default: 20),

  • ’c’ - factor of step variation (float, default: 2.0),

  • ’n_tr’ - frequency of temperature reduction (int, default:

    np.maximum(100, 5*problem[‘ndim_problem’])),

  • ’f_tr’ - factor of temperature reduction (int, default: 0.85).

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.csa import CSA
>>> 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,)),
...            'sigma': 1.0,
...            'temperature': 100}
>>> csa = CSA(problem, options)  # initialize the optimizer class
>>> results = csa.optimize()  # run the optimization process
>>> # return the number of function evaluations and best-so-far fitness
>>> print(f"CSA: {results['n_function_evaluations']}, {results['best_so_far_y']}")
CSA: 5000, 0.0023146719686626344

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

c

factor of step variation.

Type:

float

f_tr

factor of temperature reduction.

Type:

int

n_sv

frequency of step variation

Type:

int

n_tr

frequency of temperature reduction

Type:

int

sigma

initial global step-size.

Type:

float

temperature

annealing temperature.

Type:

float

References

Corana, A., Marchesi, M., Martini, C. and Ridella, S., 1987. Minimizing multimodal functions of continuous variables with the “simulated annealing” algorithm. ACM Transactions on Mathematical Software, 13(3), pp.262-280. https://dl.acm.org/doi/abs/10.1145/29380.29864 https://dl.acm.org/doi/10.1145/66888.356281

Kirkpatrick, S., Gelatt, C.D. and Vecchi, M.P., 1983. Optimization by simulated annealing. Science, 220(4598), pp.671-680. https://science.sciencemag.org/content/220/4598/671