使用Python绘制Pareto前沿时遇TypeError错误求助

错误信息 #

TypeError: '>' not supported between instances of 'generator' and 'int'

原代码 #

import numpy as np
from pymoo.core.problem import Problem
from pymoo.visualization.scatter import Scatter
from pymoo.algorithms.moo.nsga2 import RankAndCrowdingSurvival
from pymoo.core.mixed import MixedVariableGA
from pymoo.optimize import minimize

v=[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
w=[22.0, 31.0, 0.0, 0.0, 11416.0, 0.0, 0.0, 0.0, 0.0, 15376.6, 977.97, 4324.97, 3264.79, 32.4, 43.02, 0.029, 0.2,0.00185, 0.00185, 0.0001, 0.03, 0.017, 0.0,0,0,0,0,0,0]
e=[562.51, 562.51, 0.0, 0.0, 223.16, 0.0, 0.0, 0.0, 0.0, 1401.63, 411.42, 1401.63, 0.0,312.53, 17195.71, 0.623, 15.14,0.01, 4.5, 23.42, 0.66,0,0,0,0,0,0,0,0]
g=[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 840.000,469.000,46.000,18.000,4.000,12.000,0,0,0,0]
        
class WEN(Problem):

    def __init__(self):
        super().__init__(n_var=v, n_obj=2, n_ieq_constr=2, xl=np.array(0 for i in range(29)), xu=None)

    def _evaluate(self, x, out, *args, **kwargs):
        f1=[numpy.dot(v,e)]
        f2=[numpy.dot(v,w)]
        g1=[(numpy.dot(v*w)/100)-585]
        g2=[(numpy.dot(v*g)*0.00001)-1610]
        out["F"] = [f1, f2]
        out["G"] = [g1, g2]

problem = WEN()

algorithm = MixedVariableGA(pop_size=20, survival=RankAndCrowdingSurvival())

res = minimize(problem,
               algorithm,
               ('n_gen', 50),
               seed=1,
               verbose=False)

plot = Scatter()
plot.add(problem.pareto_front(), plot_type="line", color="black", alpha=0.7)
plot.add(res.F, facecolor="none", edgecolor="red")
plot.show()        

错误原因与修正步骤 #

1. Problem初始化参数错误 #

• n_var需要传入变量的数量（整数），原代码传入了列表v，导致后续内部逻辑将其当作迭代器处理，引发类型错误。应改为n_var=29。
• xl=np.array(0 for i in range(29))是生成器表达式，改为xl=np.zeros(29)更高效清晰；xu未设置，若为二进制变量可设为xu=np.ones(29)，根据实际变量范围调整。

2. _evaluate方法误用全局变量 #

目标函数和约束不应使用固定全局列表v，而应使用方法参数x（当前种群的变量矩阵，每行对应一个个体），否则优化过程不会更新变量，失去意义。

3. 矩阵运算与输出格式错误 #

• 列表不能直接做*和dot运算，需先转为numpy数组；对于矩阵x（N×29），可直接用矩阵乘法x @ e计算所有个体的目标值。
• out["F"]需要是形状为(N, 2)的二维数组，out["G"]是(N, 2)的二维数组，不能嵌套列表。

修正后的完整代码 #

import numpy as np
from pymoo.core.problem import Problem
from pymoo.visualization.scatter import Scatter
from pymoo.algorithms.moo.nsga2 import RankAndCrowdingSurvival
from pymoo.core.mixed import MixedVariableGA
from pymoo.optimize import minimize

# 转为numpy数组方便运算
w = np.array([22.0, 31.0, 0.0, 0.0, 11416.0, 0.0, 0.0, 0.0, 0.0, 15376.6, 977.97, 4324.97, 3264.79, 32.4, 43.02, 0.029, 0.2,0.00185, 0.00185, 0.0001, 0.03, 0.017, 0.0,0,0,0,0,0,0])
e = np.array([562.51, 562.51, 0.0, 0.0, 223.16, 0.0, 0.0, 0.0, 0.0, 1401.63, 411.42, 1401.63, 0.0,312.53, 17195.71, 0.623, 15.14,0.01, 4.5, 23.42, 0.66,0,0,0,0,0,0,0,0])
g = np.array([0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 840.000,469.000,46.000,18.000,4.000,12.000,0,0,0,0])
        
class WEN(Problem):
    def __init__(self):
        # 假设变量是二进制（0/1），设置上下限
        super().__init__(n_var=29, n_obj=2, n_ieq_constr=2, 
                         xl=np.zeros(29), xu=np.ones(29))

    def _evaluate(self, x, out, *args, **kwargs):
        # 计算所有个体的目标值，x形状为(N,29)
        f1 = x @ e  # 形状(N,)
        f2 = x @ w  # 形状(N,)
        # 计算约束，pymoo要求G <= 0
        g1 = (x @ w)/100 - 585  # 约束：(x·w)/100 ≤ 585
        g2 = (x @ g)*0.00001 - 1610  # 约束：(x·g)*1e-5 ≤ 1610
        
        out["F"] = np.column_stack([f1, f2])  # 转为(N,2)数组
        out["G"] = np.column_stack([g1, g2])  # 转为(N,2)数组

problem = WEN()

# 明确变量类型，如果是二进制变量，指定var_type
algorithm = MixedVariableGA(
    pop_size=50,  # 增大种群数量
    survival=RankAndCrowdingSurvival(),
    var_type=np.int8  # 二进制变量用int8类型
)

res = minimize(problem,
               algorithm,
               ('n_gen', 100),  # 增加迭代次数
               seed=1,
               verbose=True)  # 开启verbose查看优化过程

plot = Scatter()
# 若没有Pareto前沿解析解，注释掉下面一行，或用res.F中的非支配解
# plot.add(problem.pareto_front(), plot_type="line", color="black", alpha=0.7)
plot.add(res.F, facecolor="none", edgecolor="red")
plot.show()        

额外优化建议 #

• 变量类型确认：如果变量是二进制（0/1），必须在MixedVariableGA中指定var_type=np.int8，否则算法会按连续变量处理，导致结果错误。
• 约束方向检查：pymoo默认要求不等式约束G <= 0，如果你的实际约束是(x·w)/100 >= 585，则需要改为g1 = 585 - (x @ w)/100。
• 种群与迭代次数：29个变量的优化问题，pop_size=50、n_gen=100是更合理的初始设置，可根据优化结果进一步调整。
• Pareto前沿绘制：problem.pareto_front()需要问题类实现_calc_pareto_front方法来提供解析解，若无解析解，可直接用res.F中的非支配解绘制，或使用pymoo的NonDominatedSort筛选非支配解。

内容的提问来源于stack exchange，提问作者Fatima Mansour