模拟退火 (SA)

class pypop7.optimizers.sa.sa.SA(problem, options)[源代码]

模拟退火 (SA)。

这是所有模拟退火 (SA) 类的抽象类。请使用其任何实例化的子类来优化手头的黑盒问题。

注意

“SA 算法的典型优势是其非常温和的内存需求和每次迭代的计算量很小。”—[Bouttier&Gavra, 2019, JMLR]

“SA 算法也可以被看作是一种局部搜索算法，其中偶尔会有向上的移动，导致成本增加。人们希望这种向上的移动能帮助逃离局部最小值。”—[Bertsimas&Tsitsiklis, 1993, Statistical Science]

关于其基于 pytest 的测试，请参考此 Python 代码。

参数:

  • problem (dict) –

    问题参数，包含以下通用设置 (键)

    • 'fitness_function' - 需要被最小化的目标函数 (func),

    • 'ndim_problem' - 维度数量 (int),

    • 'upper_boundary' - 搜索范围的上边界 (array_like),

    • 'lower_boundary' - 搜索范围的下边界 (array_like).

  • options (dict) –

    优化器选项，包含以下通用设置 (键)

    • 'max_function_evaluations' - 函数评估的最大次数 (int, 默认: np.inf),

    • 'max_runtime' - 允许的最大运行时间 (float, 默认: np.inf),

    • 'seed_rng' - 随机数生成器的种子，需要明确设置 (int);

    以及以下特定设置 (键)

    • ’temperature’ - 退火温度 (float)，

    • ’x’ - 初始（起始）点 (array_like)。

temperature

退火温度。

类型:

float

x

初始（起始）点。

类型:

array_like

参考文献

Bras, P., 2024. Convergence of Langevin-simulated annealing algorithms with multiplicative noise. Mathematics of Computation, 93(348), pp.1761-1803.

Bouttier, C. and Gavra, I., 2019. Convergence rate of a simulated annealing algorithm with noisy observations. Journal of Machine Learning Research, 20(1), pp.127-171.

Lecchini-Visintini, A., Lygeros, J. and Maciejowski, J., 2007. Simulated annealing: Rigorous finite-time guarantees for optimization on continuous domains. Advances in Neural Information Processing Systems, 20.

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.

Granville, V., Krivánek, M. and Rasson, J.P., 1994. Simulated annealing: A proof of convergence. IEEE Transactions on Pattern Analysis and Machine Intelligence, 16(6), pp.652-656.

Bertsimas, D. and Tsitsiklis, J., 1993. Simulated annealing. Statistical Science, 8(1), pp.10-15.

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/10.1145/66888.356281

Szu, H.H. and Hartley, R.L., 1987. Nonconvex optimization by fast simulated annealing. Proceedings of the IEEE, 75(11), pp.1538-1540.

Kirkpatrick, S., Gelatt, C.D. and Vecchi, M.P., 1983. Optimization by simulated annealing. Science, 220(4598), pp.671-680.

Hastings, W.K., 1970. Monte Carlo sampling methods using Markov chains and their applications. Biometrika, 57(1), pp.97-109.

Metropolis, N., Rosenbluth, A.W., Rosenbluth, M.N., Teller, A.H. and Teller, E., 1953. Equation of state calculations by fast computing machines. Journal of Chemical Physics, 21(6), pp.1087-1092.

模拟退火算法 (SAs)