Pymoo学习 (6)：终止条件

1 默认设置

  对于多目标优化，默认设置包括：

from pymoo.util.termination.default import MultiObjectiveDefaultTermination

termination = MultiObjectiveDefaultTermination(
    x_tol=1e-8,         # 设计空间中的运动
    cv_tol=1e-6,        # 收敛性
    f_tol=0.0025,       # 目标空间值
    nth_gen=5,          # 每多少代检查一次终止条件
    n_last=30,          # 计算过程中应当被考虑的最后几代数量
    n_max_gen=1000,     # 最大后代数量
    n_max_evals=100000  # 最大评估次数
)

  对于单目标优化，默认设置包括：

from pymoo.util.termination.default import SingleObjectiveDefaultTermination

termination = SingleObjectiveDefaultTermination(
    x_tol=1e-8,
    cv_tol=1e-6,
    f_tol=1e-6,
    nth_gen=5,
    n_last=20,
    n_max_gen=1000,
    n_max_evals=100000
)

2 评估数量 (n_eval)

from pymoo.algorithms.moo.nsga2 import NSGA2`在这里插入代码片`
from pymoo.factory import get_problem, get_termination
from pymoo.optimize import minimize

problem = get_problem("zdt3")
algorithm = NSGA2(pop_size=100)
termination = get_termination("n_eval", 300)

res = minimize(problem,
               algorithm,
               termination,
               pf=problem.pareto_front(),
               seed=1,
               verbose=True)

  输出如下：

============================================================
n_gen |  n_eval |     igd      |      gd      |      hv     
============================================================
    1 |     100 |  1.304648356 |  1.530191068 |  0.00000E+00
    2 |     200 |  1.304200356 |  1.517648901 |  0.00000E+00
    3 |     300 |  0.988539101 |  1.378914374 |  0.00000E+00

3 迭代次数 (n_gen)

from pymoo.algorithms.moo.nsga2 import NSGA2
from pymoo.factory import get_problem, get_termination
from pymoo.optimize import minimize

problem = get_problem("zdt3")
algorithm = NSGA2(pop_size=100)
termination = get_termination("n_gen", 10)

res = minimize(problem,
               algorithm,
               termination,
               pf=problem.pareto_front(),
               seed=1,
               verbose=True)

  输出如下：

============================================================
n_gen |  n_eval |     igd      |      gd      |      hv     
============================================================
    1 |     100 |  1.304648356 |  1.530191068 |  0.00000E+00
    2 |     200 |  1.304200356 |  1.517648901 |  0.00000E+00
    3 |     300 |  0.988539101 |  1.378914374 |  0.00000E+00
    4 |     400 |  0.920567183 |  1.351594290 |  0.00000E+00
    5 |     500 |  0.920567183 |  1.282794381 |  0.00000E+00
    6 |     600 |  0.894035691 |  1.360904372 |  0.00000E+00
    7 |     700 |  0.817395517 |  1.280727114 |  0.00000E+00
    8 |     800 |  0.802167697 |  1.189542707 |  0.00000E+00
    9 |     900 |  0.730335663 |  0.993344639 |  0.002211246
   10 |    1000 |  0.699750404 |  0.851632873 |  0.002211246

4 时间 (time)

  基于时间的终止标准的格式应当设置为类似于get_termination(“time”, “01:30:00”)，表示运行1个小时30分钟：

from pymoo.algorithms.moo.nsga2 import NSGA2
from pymoo.factory import get_problem, get_termination
from pymoo.optimize import minimize

problem = get_problem("zdt3")
algorithm = NSGA2(pop_size=100)
termination = get_termination("time", "00:00:03")

res = minimize(problem,
               algorithm,
               termination,
               pf=problem.pareto_front(),
               seed=1,
               verbose=False)

print(res.algorithm.n_gen)

5 设计空间容忍度 (x_tol)

from pymoo.algorithms.moo.nsga2 import NSGA2
from pymoo.factory import get_problem
from pymoo.optimize import minimize
from pymoo.util.termination.x_tol import DesignSpaceToleranceTermination

problem = get_problem("zdt3")
algorithm = NSGA2(pop_size=100)
termination = DesignSpaceToleranceTermination(tol=0.0025, n_last=20)

res = minimize(problem,
               algorithm,
               termination,
               pf=problem.pareto_front(),
               seed=1,
               verbose=False)

print(res.algorithm.n_gen)

6 目标空间容忍度 (f_tol)

  这是一个用的很多的标准：

from pymoo.algorithms.moo.nsga2 import NSGA2
from pymoo.factory import get_problem
from pymoo.optimize import minimize
from pymoo.util.termination.f_tol import MultiObjectiveSpaceToleranceTermination
from pymoo.visualization.scatter import Scatter

problem = get_problem("zdt3")
algorithm = NSGA2(pop_size=100)
termination = MultiObjectiveSpaceToleranceTermination(tol=0.0025,
                                                      n_last=30,
                                                      nth_gen=5)

res = minimize(problem,
               algorithm,
               termination,
               pf=True,
               seed=1,
               verbose=False)

print("Generations", res.algorithm.n_gen)
plot = Scatter(title="ZDT3")
plot.add(problem.pareto_front(use_cache=False, flatten=False), plot_type="line", color="black")
plot.add(res.F, facecolor="none", edgecolor="red", alpha=0.8, s=20)
plot.show()

  输出如下：

参考文献

【1】https://pymoo.org/interface/termination.html