Corana et al.’ Simulated Annealing (CSA)

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

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:

 1>>> import numpy  # engine for numerical computing
 2>>> from pypop7.benchmarks.base_functions import rosenbrock  # function to be minimized
 3>>> from pypop7.optimizers.sa.csa import CSA
 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...            'x': 3*numpy.ones((2,)),
11...            'sigma': 1.0,
12...            'temperature': 100}
13>>> csa = CSA(problem, options)  # initialize the optimizer class
14>>> results = csa.optimize()  # run the optimization process
15>>> # return the number of function evaluations and best-so-far fitness
16>>> print(f"CSA: {results['n_function_evaluations']}, {results['best_so_far_y']}")
17CSA: 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