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import numpy as np
from scipy.optimize import linprog
def cargo_load_planning_linear3(weights, cargo_names, cargo_types_dict, positions, cg_impact, cg_impact_2u, cg_impact_4u,
max_positions):
"""
使用整数线性规划方法计算货物装载方案，最小化重心的变化量。
参数:
weights (list): 每个货物的质量列表。
cargo_names (list): 每个货物的名称。
cargo_types_dict (dict): 货物名称和占用的货位数量。
positions (list): 可用的货位编号。
cg_impact (list): 每个位置每kg货物对重心index的影响系数。
cg_impact_2u (list): 两个位置组合的重心影响系数。
cg_impact_4u (list): 四个位置组合的重心影响系数。
max_positions (int): 总货位的数量。
返回:
result.x: 最优装载方案矩阵。
"""
# 将货物类型映射为对应的占用单位数
cargo_types = [cargo_types_dict[name] for name in cargo_names]
num_cargos = len(weights) # 货物数量
num_positions = len(positions) # 可用货位数量
# 决策变量：xij (是否将货物i放置在位置j)
c = [] # 目标函数系数列表
for i in range(num_cargos):
for j in range(num_positions):
if cargo_types[i] == 1:
c.append(abs(weights[i] * cg_impact[j]))
elif cargo_types[i] == 2 and j % 2 == 0 and j < len(cg_impact_2u) * 2:
c.append(abs(weights[i] * cg_impact_2u[j // 2]))
elif cargo_types[i] == 4 and j % 4 == 0 and j < len(cg_impact_4u) * 4:
c.append(abs(weights[i] * cg_impact_4u[j // 4]))
else:
c.append(0) # 不适合的索引默认影响为0
# 决策变量约束：xij只能是0或1 (整型约束由 linprog 近似处理)
bounds = [(0, 1) for _ in range(num_cargos * num_positions)]
# 约束1：每个货物只能装载到一个位置
A_eq = []
b_eq = []
for i in range(num_cargos):
constraint = [0] * (num_cargos * num_positions)
for j in range(num_positions):
constraint[i * num_positions + j] = 1
A_eq.append(constraint)
b_eq.append(1)
# 约束2：每个位置只能装载一个货物
A_ub = []
b_ub = []
for j in range(num_positions): # 遍历所有位置
constraint = [0] * (num_cargos * num_positions)
for i in range(num_cargos): # 遍历所有货物
constraint[i * num_positions + j] = 1
A_ub.append(constraint)
b_ub.append(1) # 每个位置最多只能分配一个货物
# 约束3：占用多个位置的货物
for i, cargo_type in enumerate(cargo_types):
if cargo_type == 2: # 两个连续位置组合
for j in range(0, num_positions - 1, 2):
constraint = [0] * (num_cargos * num_positions)
constraint[i * num_positions + j] = 1
constraint[i * num_positions + j + 1] = 1
A_ub.append(constraint)
b_ub.append(1)
elif cargo_type == 4: # 上两个、下两个组合
for j in range(0, num_positions - 3, 4):
constraint = [0] * (num_cargos * num_positions)
constraint[i * num_positions + j] = 1
constraint[i * num_positions + j + 1] = 1
constraint[i * num_positions + j + 2] = 1
constraint[i * num_positions + j + 3] = 1
A_ub.append(constraint)
b_ub.append(1)
# 转换为numpy数组
A_eq = np.array(A_eq)
b_eq = np.array(b_eq)
A_ub = np.array(A_ub)
b_ub = np.array(b_ub)
c = np.array(c)
# 求解线性规划问题
result = linprog(c, A_ub=A_ub, b_ub=b_ub, A_eq=A_eq, b_eq=b_eq, bounds=bounds, method='highs-ipm')
if result.success:
# print("成功找到最优装载方案！")
solution = result.x.reshape((num_cargos, num_positions))
# print("装载方案矩阵:")
# print(solution)
# 计算最终重心变化
cg_change = 0
for i in range(num_cargos):
for j in range(num_positions):
if cargo_types[i] == 1:
cg_change += solution[i, j] * weights[i] * cg_impact[j]
elif cargo_types[i] == 2 and j % 2 == 0 and j < len(cg_impact_2u) * 2:
cg_change += solution[i, j] * weights[i] * cg_impact_2u[j // 2]
elif cargo_types[i] == 4 and j % 4 == 0 and j < len(cg_impact_4u) * 4:
cg_change += solution[i, j] * weights[i] * cg_impact_4u[j // 4]
# print(f"重心的变化量: {cg_change:.2f}")
return result,cg_change
# 输出实际分布
# print("货物实际分布:")
# for i in range(num_cargos):
# assigned_positions = []
# for j in range(num_positions):
# if solution[i, j] > 0.5: # 判断位置是否被分配
# assigned_positions.append(j)
# print(f"货物 {cargo_names[i]} (占 {cargo_types[i]} 单位): 放置位置 -> {assigned_positions}")
else:
result = []
return result,-1000000
# 示例输入
# def main():
# weights = [500, 800, 1200, 300, 700, 1000, 600, 900] # 每个货物的质量
# cargo_names = ['LD3', 'LD3', 'PLA', 'LD3', 'P6P', 'PLA', 'LD3', 'BULK'] # 货物名称
# cargo_types_dict = {"LD3": 1, "PLA": 2, "P6P": 4, "BULK": 1} # 货物占位关系
# positions = list(range(44)) # 44个货位编号
# cg_impact = [i * 0.1 for i in range(44)] # 每kg货物对重心index的影响系数 (单个位置)
# cg_impact_2u = [i * 0.08 for i in range(22)] # 两个位置组合的影响系数
# cg_impact_4u = [i * 0.05 for i in range(11)] # 四个位置组合的影响系数
# max_positions = 44 # 总货位数量
#
# result = cargo_load_planning(weights, cargo_names, cargo_types_dict, positions, cg_impact, cg_impact_2u,
# cg_impact_4u, max_positions)
#
#
# if __name__ == "__main__":
# main()
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