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import numpy as np
import pulp
def cargo_load_planning_mip1(weights, cargo_names, cargo_types_dict, positions, cg_impact, cg_impact_2u, cg_impact_4u,
max_positions):
"""
使用混合整数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 (pulp.LpStatus): 求解状态。
cg_change (float): 最优解的重心变化量。
solution_matrix (np.ndarray): 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
# 创建优化问题实例
prob = pulp.LpProblem("Cargo_Load_Planning", pulp.LpMinimize)
# 创建决策变量 x_ij (是否将货物i放置在位置j)
# 使用字典键 (i,j) 来标识变量
x = pulp.LpVariable.dicts("x",
((i, j) for i in range(num_cargos) for j in range(num_positions)),
cat='Binary')
# 定义目标函数：最小化重心的变化量
objective_terms = []
for i in range(num_cargos):
for j in range(num_positions):
if cargo_types[i] == 1:
impact = abs(weights[i] * cg_impact[j])
elif cargo_types[i] == 2 and j % 2 == 0 and j < len(cg_impact_2u) * 2:
impact = abs(weights[i] * cg_impact_2u[j // 2])
elif cargo_types[i] == 4 and j % 4 == 0 and j < len(cg_impact_4u) * 4:
impact = abs(weights[i] * cg_impact_4u[j // 4])
else:
impact = 0
objective_terms.append(impact * x[i, j])
prob += pulp.lpSum(objective_terms), "Total_CG_Change"
# 约束1：每个货物只能装载到一个位置
for i in range(num_cargos):
prob += pulp.lpSum([x[i, j] for j in range(num_positions)]) == 1, f"Cargo_{i}_Single_Position"
# 约束2：每个位置只能装载一个货物
for j in range(num_positions):
prob += pulp.lpSum([x[i, j] for i in range(num_cargos)]) <= 1, f"Position_{j}_Single_Cargo"
# 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):
prob += x[i, j] + x[i, j + 1] <= 1, f"Cargo_{i}_Type2_Position_{j}_{j+1}"
elif cargo_type == 4: # 四个连续位置组合
for j in range(0, num_positions - 3, 4):
prob += x[i, j] + x[i, j + 1] + x[i, j + 2] + x[i, j + 3] <= 1, f"Cargo_{i}_Type4_Position_{j}_{j+3}"
# 求解问题
solver = pulp.GLPK_CMD(msg=False) # 使用默认的CBC求解器，不显示求解过程
prob.solve(solver)
# 检查求解状态
if pulp.LpStatus[prob.status] == 'Optimal':
# 构建装载方案矩阵
solution = np.zeros((num_cargos, num_positions))
for i in range(num_cargos):
for j in range(num_positions):
var_value = pulp.value(x[i, j])
if var_value is not None and var_value > 0.5:
solution[i, j] = 1
# 计算最终重心变化
cg_change = 0.0
for i in range(num_cargos):
for j in range(num_positions):
if solution[i, j] == 1:
if cargo_types[i] == 1:
cg_change += weights[i] * cg_impact[j]
elif cargo_types[i] == 2 and j % 2 == 0 and j < len(cg_impact_2u) * 2:
cg_change += 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 += weights[i] * cg_impact_4u[j // 4]
return pulp.LpStatus[prob.status], cg_change, solution
else:
# 若求解失败，则返回空结果和错误标志
return pulp.LpStatus[prob.status], -1000000, None
# 示例输入和调用
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
status, cg_change, solution = cargo_load_planning_mip(
weights, cargo_names, cargo_types_dict, positions, cg_impact, cg_impact_2u, cg_impact_4u, max_positions
)
if status == 'Optimal':
print("成功找到最优装载方案！")
print("装载方案矩阵:")
print(solution)
print(f"重心的变化量: {cg_change:.2f}")
# 输出实际分布
for i in range(len(weights)):
assigned_positions = []
for j in range(len(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_dict[cargo_names[i]]} 单位): 放置位置 -> {assigned_positions}")
else:
print("未能找到可行解。")
print(f"求解状态: {status}")
if __name__ == "__main__":
main()
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