问在 scipy.minimize不满足约束条件，输出结果与原数据相同？

import numpy as np
from scipy.optimize import minimize

# 定义给定的 (fij, sij) 数据
data = [[(0.5, 8), (0.3, 8), (0.4, 6), (0.2, 5)],
        [(0.7, 6), (0.5, 8), (0.7, 8), (0.4, 5)],
        [(0.6, 8), (0.3, 7), (0.5, 8), (0.9, 5)],
        [(0.8, 7), (0.6, 8), (0.1, 8), (0.5, 8)]]

# 提取fij和sij
fij = np.array([[data[i][j][0] for j in range(4)] for i in range(4)])
sij = np.array([[data[i][j][1] for j in range(4)] for i in range(4)])


# 目标函数
def objective(vars):
    xij = vars[:16].reshape(4, 4)
    yij = vars[16:].reshape(4, 4)
    return 0.457 * (1 / 16) * np.sum(np.abs(fij - xij)) + 0.04 * (1 / 16) * np.sum(np.abs(sij - yij))


# 约束条件1: xij + xji = 1
def constraint1(vars):
    xij = vars[:16].reshape(4, 4)
    cons = []
    for i in range(4):
        for j in range(4):
            if i != j:
                cons.append(xij[i][j] + xij[j][i] - 1)
    return cons


# 约束条件2: yij = yji
def constraint2(vars):
    yij = vars[16:].reshape(4, 4)
    cons = []
    for i in range(4):
        for j in range(4):
            if i != j:
                cons.append(yij[i][j] - yij[j][i])
    return cons


# 约束条件3: [1/288 * ((fij-0.5) * sij - (fkj-0.5) * skj - (fik - 0.5)) * sik] <= 0.2
def constraint3(vars):
    xij = vars[:16].reshape(4, 4)
    yij = vars[16:].reshape(4, 4)
    total_sum = 0
    for i in range(4):
        for j in range(4):
            for k in range(4):
                if i != j and j != k and i != k:
                    Aij, Bij = xij[i][j], yij[i][j]
                    Akj, Bkj = xij[k][j], yij[k][j]
                    Aik, Bik = xij[i][k], yij[i][k]

                    term1 = (Aij - 0.5) * Bij
                    term2 = (Akj - 0.5) * Bkj
                    term3 = (Aik - 0.5) * Bik

                    total_sum += abs(term1 - term2 - term3)
    return 1 - (1 / 288) * total_sum - 0.8


# 约束条件4: xij > 0
def constraint4(vars):
    xij = vars[:16].reshape(4, 4)
    return xij.flatten()


# 约束条件5: yij ∈ (0, 8)
def constraint5(vars):
    yij = vars[16:].reshape(4, 4)
    cons = []
    cons.extend(yij.flatten() - 0)  # yij > 0
    cons.extend(8 - yij.flatten())  # yij < 8
    return cons


# 初始猜测值
x0 = np.hstack((fij.flatten(), sij.flatten()))
# 定义约束条件列表
cons = [{'type': 'ineq', 'fun': constraint3},
        {'type': 'eq', 'fun': constraint1},
        {'type': 'eq', 'fun': constraint2},

        {'type': 'ineq', 'fun': constraint4},
        {'type': 'ineq', 'fun': constraint5}]
# 优化求解
solution = minimize(objective, x0,  constraints=cons, method='SLSQP', options={'disp': True}, tol=1e-1)

# 获取最优解
vars_opt = solution.x
xij_opt = vars_opt[:16].reshape(4, 4)
yij_opt = vars_opt[16:].reshape(4, 4)

print("Optimal xij:")
print(xij_opt)
print("Optimal yij:")
print(yij_opt)

# 输出结果的结构与输入的矩阵结构相同
result = [[(xij_opt[i][j], yij_opt[i][j]) for j in range(4)] for i in range(4)]
print("Result:")
print(result)
sum_term = 0
for i in range(4):
    for j in range(4):
        for k in range(4):
            if i != j and j != k and i != k:
                sum_term += abs((xij_opt[i][j] - 0.5) * yij_opt[i][j] - (xij_opt[k][j] - 0.5) * yij_opt[k][j] - (
                        xij_opt[i][k] - 0.5) * yij_opt[i][k])
constraint_val = 1 - (1 / 288) * sum_term
if constraint_val < 0.8:
    print(f"Constraint not satisfied: {constraint_val}")
print(constraint_val)